ɎȿȾȿɊȺɅɖɇɈȿ ȺȽȿɇɌɋɌȼɈ ɉɈ ɈȻɊȺɁɈȼȺɇɂɘ ȽɈɋɍȾȺɊɋɌȼȿɇɇɈȿ ɈȻɊȺɁɈȼȺɌȿɅɖɇɈȿ ɍɑɊȿɀȾȿɇɂȿ ȼɕɋɒȿȽɈ ɉɊɈɎȿɋɋɂɈɇȺɅɖɇɈȽɈ ɈȻɊȺɁɈȼȺɇɂə «ȼɈɊɈɇȿɀɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɍɇɂȼȿɊɋɂɌȿɌ» ɍɬɜɟɪɠɞɟɧɨ ɧɚɭɱɧɨ-ɦɟɬɨɞɢɱɟɫɤɢɦ 13 ɫɟɧɬɹɛɪɹ 2007 ɝ., ɩɪɨɬɨɤɨɥ ʋ 5
ɫɨɜɟɬɨɦ
ɯɢɦɢɱɟɫɤɨɝɨ
ɮɚɤɭɥɶɬɟɬɚ
ɏɂɆɂɑȿɋɄȺə ɄɂɇȿɌɂɄȺ ɍɱɟɛɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ ɋɨɫɬɚɜɢɬɟɥɶ Ⱥ.ȼ. ɇɚɭɦɨɜ
ɍɱɟɛɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɩɨɞɝɨɬɨɜɥɟɧɨ ɧɚ ɤɚɮɟɞɪɟ ɨɛɳɟɣ ɯɢɦɢɢ ɯɢɦɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ.
Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɞɥɹ ɫɬɭɞɟɧɬɨɜ 1 ɤɭɪɫɚ.
ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ 2007
Ⱦɥɹ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ 010700 – Ɏɢɡɢɤɚ, 010801 – Ɋɚɞɢɨɮɢɡɢɤɚ ɢ ɷɥɟɤɬɪɨɧɢɤɚ, 010803 – Ɇɢɤɪɨɷɥɟɤɬɪɨɧɢɤɚ ɢ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɟ ɩɪɢɛɨɪɵ
2
I. ɗɅȿɆȿɇɌɕ ȽɈɆɈȽȿɇɇɈɃ ɄɂɇȿɌɂɄɂ
ɉɪɟɞɢɫɥɨɜɢɟ ɉɪɢ ɩɨɞɝɨɬɨɜɤɟ ɤ ɫɟɦɢɧɚɪɫɤɢɦ ɢ ɩɪɚɤɬɢɱɟɫɤɢɦ ɡɚɧɹɬɢɹɦ ɩɨɥɟɡɧɨ ɢɦɟɬɶ ɩɨɫɨɛɢɟ, ɤɨɬɨɪɨɟ ɫɨɞɟɪɠɚɥɨ ɛɵ ɜ ɫɠɚɬɨɣ ɮɨɪɦɟ ɨɫɧɨɜɧɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɫɜɟɞɟɧɢɹ ɢ ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɩɢɫɚɧɢɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɛɨɬ. ɉɨɷɬɨɦɭ ɜ ɧɚɫɬɨɹɳɟɟ ɢɡɞɚɧɢɟ ɜɤɥɸɱɟɧɵ ɨɞɧɨɜɪɟɦɟɧɧɨ ɪɚɡɞɟɥɵ ɩɨ ɤɢɧɟɬɢɤɟ ɝɨɦɨɝɟɧɧɵɯ ɪɟɚɤɰɢɣ ɢ ɪɚɛɨɬɵ ɞɥɹ ɫɬɭɞɟɧɱɟɫɤɨɝɨ ɩɪɚɤɬɢɤɭɦɚ. Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɱɚɫɬɶ ɫɨɞɟɪɠɢɬ ɦɚɬɟɪɢɚɥ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɩɨ ɮɨɪɦɚɥɶɧɨɣ ɤɢɧɟɬɢɤɟ ɢ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɥɟɤɰɢɨɧɧɨɝɨ ɤɭɪɫɚ ɪɚɫɫɦɨɬɪɟɧɢɟɦ ɪɹɞɚ ɡɚɞɚɱ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɤ ɪɟɲɟɧɢɸ ɧɚ ɫɟɦɢɧɚɪɚɯ. ɋɸɞɚ ɨɬɧɨɫɹɬɫɹ ɤɢɧɟɬɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ ɩɪɨɫɬɵɯ ɪɟɚɤɰɢɣ, ɹɜɧɨɟ ɪɟɲɟɧɢɟ ɞɥɹ ɨɛɪɚɬɢɦɨɣ ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɪɟɚɤɰɢɣ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ. ɏɨɬɹ ɯɢɦɢɱɟɫɤɨɟ ɪɚɜɧɨɜɟɫɢɟ ɢɡɭɱɚɟɬɫɹ ɜ ɬɟɦɟ «ɏɢɦɢɱɟɫɤɚɹ ɬɟɪɦɨɞɢɧɚɦɢɤɚ», ɦɵ ɫɨɱɥɢ ɧɭɠɧɵɦ ɪɚɫɫɦɨɬɪɟɬɶ ɢɦɟɧɧɨ ɡɞɟɫɶ ɨɫɧɨɜɧɵɟ ɫɜɨɣɫɬɜɚ ɤɨɧɫɬɚɧɬɵ ɪɚɜɧɨɜɟɫɢɹ, ɩɨɞɯɨɞɹ ɤ ɷɬɨɦɭ ɜɨɩɪɨɫɭ ɫɨ ɫɬɨɪɨɧɵ ɤɢɧɟɬɢɤɢ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɢ. ȼ ɩɨɫɨɛɢɢ ɞɚɧɵ ɥɢɲɶ ɷɥɟɦɟɧɬɚɪɧɵɟ ɫɜɟɞɟɧɢɹ ɨ ɬɟɨɪɢɢ ɚɤɬɢɜɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫ ɬɟɦ, ɱɬɨɛɵ ɩɨɹɫɧɢɬɶ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɷɧɟɪɝɢɢ ɚɤɬɢɜɚɰɢɢ. Ɇɵ ɨɛɯɨɞɢɦ ɜɵɱɢɫɥɟɧɢɹ ɧɚ ɨɫɧɨɜɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ, ɚ ɬɚɤɠɟ ɩɨɥɧɨɫɬɶɸ ɨɛɯɨɞɢɦ ɩɨɧɹɬɢɟ ɨɛ ɚɤɬɢɜɢɪɨɜɚɧɧɨɦ ɤɨɦɩɥɟɤɫɟ, ɱɬɨ ɞɨɥɠɧɨ ɫɨɫɬɚɜɢɬɶ ɩɪɟɞɦɟɬ ɨɬɞɟɥɶɧɨɝɨ ɩɨɫɨɛɢɹ. ȼɦɟɫɬɟ ɫ ɬɟɦ ɜ ɧɚɱɚɥɟ ɩɟɪɜɨɝɨ ɪɚɡɞɟɥɚ ɤɨɪɨɬɤɨ ɨɛɫɭɠɞɚɟɬɫɹ ɫɬɟɯɢɨɦɟɬɪɢɹ ɪɟɚɤɰɢɣ, ɩɪɟɞɜɚɪɹɸɳɚɹ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ. Ɇɚɬɟɪɢɚɥ ɪɚɫɫɱɢɬɚɧ ɧɚ ɫɥɭɲɚɬɟɥɟɣ, ɡɧɚɤɨɦɵɯ ɫ ɩɪɨɫɬɵɦɢ ɩɪɢɟɦɚɦɢ ɪɟɲɟɧɢɹ ɥɢɧɟɣɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ. ɉɪɚɤɬɢɱɟɫɤɚɹ ɱɚɫɬɶ ɩɨɫɜɹɳɟɧɚ ɢɫɫɥɟɞɨɜɚɧɢɸ ɪɚɜɧɨɜɟɫɢɹ ɢ ɤɢɧɟɬɢɤɢ ɪɟɚɤɰɢɣ ɫ ɩɨɦɨɳɶɸ ɫɩɟɤɬɪɨɮɨɬɨɦɟɬɪɢɱɟɫɤɨɝɨ ɦɟɬɨɞɚ. ɉɨɫɤɨɥɶɤɭ ɪɚɛɨɬɵ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɩɟɪɜɨɝɨ ɤɭɪɫɚ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ, ɨɤɚɡɚɥɨɫɶ ɧɟɨɛɯɨɞɢɦɵɦ ɪɚɫɫɦɨɬɪɟɬɶ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɨɫɧɨɜɵ ɷɬɨɝɨ ɦɟɬɨɞɚ. Ɍɚɤɨɣ ɦɚɬɟɪɢɚɥ, ɪɚɡɭɦɟɟɬɫɹ, ɧɟ ɜɯɨɞɢɬ ɜ ɨɛɳɢɣ ɤɭɪɫ ɯɢɦɢɢ ɢ ɩɪɟɞɧɚɡɧɚɱɟɧ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɢɡɭɱɟɧɢɹ ɫɬɭɞɟɧɬɚɦɢ, ɚ ɬɚɤɠɟ ɨɛɫɭɠɞɟɧɢɹ ɧɚ ɫɟɦɢɧɚɪɚɯ.
ɏɢɦɢɱɟɫɤɚɹ ɤɢɧɟɬɢɤɚ – ɨɬɞɟɥ ɮɢɡɢɱɟɫɤɨɣ ɯɢɦɢɢ, ɜ ɤɨɬɨɪɨɦ ɢɡɭɱɚɸɬɫɹ ɫ ɤ ɨ ɪ ɨ ɫ ɬ ɶ ɢ ɦ ɟ ɯ ɚ ɧ ɢ ɡ ɦ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ. Ɉɛɵɱɧɨ ɜɵɞɟɥɹɸɬ ɞɜɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɨɛɥɚɫɬɢ: ɮɨɪɦɚɥɶɧɭɸ ɤɢɧɟɬɢɤɭ ɢ ɭɱɟɧɢɟ ɨ ɦɟɯɚɧɢɡɦɚɯ. Ɂɚɞɚɱɟɣ ɮɨɪɦɚɥɶɧɨɣ ɤɢɧɟɬɢɤɢ ɹɜɥɹɟɬɫɹ ɭɫɬɚɧɨɜɥɟɧɢɟ ɜɪɟɦɟɧɧɵѱѳɯ ɡɚɤɨɧɨɜ, ɩɨ ɤɨɬɨɪɵɦ ɷɜɨɥɸɰɢɨɧɢɪɭɸɬ ɪɟɚɝɢɪɭɸɳɢɟ ɫɢɫɬɟɦɵ *). ɉɨɞ ɦɟɯɚɧɢɡɦɨɦ ɪɟɚɤɰɢɢ ɩɨɧɢɦɚɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɩɪɨɫɬɟɣɲɢɯ ɫɬɚɞɢɣ (ɚɤɬɨɜ), ɱɟɪɟɡ ɤɨɬɨɪɵɟ ɢɫɯɨɞɧɵɟ ɜɟɳɟɫɬɜɚ ɩɪɟɜɪɚɳɚɸɬɫɹ ɜ ɩɪɨɞɭɤɬɵ ɪɟɚɤɰɢɢ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɦɟɯɚɧɢɡɦɨɜ ɩɪɟɞɩɨɥɚɝɚɟɬ ɩɨɫɬɪɨɟɧɢɟ ɩɨɞɨɛɧɵɯ ɪɟɚɤɰɢɨɧɧɵɯ ɫɯɟɦ, ɜɤɥɸɱɚɹ ɢɯ ɦɨɥɟɤɭɥɹɪɧɵɟ ɦɨɞɟɥɢ. ɋɸɞɚ ɠɟ ɨɬɧɨɫɹɬɫɹ ɬɪɚɞɢɰɢɨɧɧɵɟ ɜɨɩɪɨɫɵ ɨ ɜɥɢɹɧɢɢ ɭɫɥɨɜɢɣ (ɬɟɦɩɟɪɚɬɭɪɵ, ɞɚɜɥɟɧɢɹ ɢ ɞɪ.) ɧɚ ɩɪɨɬɟɤɚɧɢɟ ɪɟɚɤɰɢɣ. Ʉɪɭɩɧɵɦɢ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɦɢ ɪɚɡɞɟɥɚɦɢ ɹɜɥɹɸɬɫɹ ɤɢɧɟɬɢɤɚ ɝɟɬɟɪɨɝɟɧɧɵɯ ɩɪɨɰɟɫɫɨɜ ɢ ɭɱɟɧɢɟ ɨ ɤɚɬɚɥɢɡɟ. 1. Ɉɫɧɨɜɧɨɣ ɡɚɤɨɧ ɫɬɟɯɢɨɦɟɬɪɢɢ ɏɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ – ɷɬɨ ɹɜɥɟɧɢɟ, ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢ ɧɚɛɥɸɞɚɟɦɨɟ ɤɚɤ ɜɡɚɢɦɧɨɟ ɩɪɟɜɪɚɳɟɧɢɟ ɜɟɳɟɫɬɜ. ɋ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɪɟɚɤɰɢɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɨɰɟɫɫ, ɜ ɤɨɬɨɪɨɦ ɨɞɧɢ ɜɟɳɟɫɬɜɚ ɢɫɱɟɡɚɸɬ, ɞɪɭɝɢɟ ɩɨɹɜɥɹɸɬɫɹ. ɗɬɨɬ ɩɪɨɰɟɫɫ ɩɨɞɱɢɧɹɟɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɦ ɡɚɤɨɧɚɦ ɫɨɯɪɚɧɟɧɢɹ – ɬɚɤ ɧɚɡɵɜɚɟɦɵɦ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɡɚɤɨɧɚɦ (ɨɬ ɝɪɟɱ. ıIJȠȚȤİȚҔȠȞ – ɷɥɟɦɟɧɬ, ɧɚɱɚɥɨ ɢ ȝİIJȡȑȦ – ɢɡɦɟɪɹɸ). ȼ ɨɫɧɨɜɚɧɢɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɯ ɡɚɤɨɧɨɜ ɥɟɠɚɬ ɫɥɟɞɭɸɳɢɟ ɞɜɚ ɮɚɤɬɚ, ɢɦɟɸɳɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ ɢ ɹɜɥɹɸɳɢɟɫɹ ɨɛɨɛɳɟɧɢɟɦ ɦɧɨɝɨɱɢɫɥɟɧɧɵɯ ɧɚɛɥɸɞɟɧɢɣ. 1. Ɇɚɫɫɚ ɫɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɯɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ, ɹɜɥɹɟɬɫɹ ɫ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɶɸ ɫɨɯɪɚɧɹɸɳɟɣɫɹ ɜɟɥɢɱɢɧɨɣ (Ɇ. ȼ. Ʌɨɦɨɧɨɫɨɜ, 1756, Ⱥ. Ʌ. Ʌɚɜɭɚɡɶɟ (A. L. Lavoisier), 1774). ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɷɬɨɬ ɡɚɤɨɧ – ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɚɫɫɵ – ɫɩɪɚɜɟɞɥɢɜ ɞɥɹ ɫɢɫɬɟɦɵ, ɧɟ ɨɛɦɟɧɢɜɚɸɳɟɣɫɹ ɜɟɳɟɫɬɜɨɦ ɫ ɜɧɟɲɧɢɦɢ ɬɟɥɚɦɢ. Ɍɚɤɭɸ ɫɢɫɬɟɦɭ ɧɚɡɵɜɚɸɬ ɡɚɤɪɵɬɨɣ; ɢɡɦɟɧɟɧɢɟ ɱɢɫɥɚ ɱɚɫɬɢɰ ɜ ɧɟɣ ɜɨɡɦɨɠɧɨ ɥɢɲɶ ɡɚ ɫɱɟɬ ɤɚɤɨɝɨ-ɬɨ ɜɧɭɬɪɟɧɧɟɝɨ ɩɪɨɰɟɫɫɚ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɷɬɨɬ ɩɪɨɰɟɫɫ – ɯɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ. Ɇ ɚ ɫ ɫ ɚ ɪɟɚɝɢɪɭɸɳɟɣ ɫɢɫɬɟɦɵ ɫɨɯɪɚɧɹɟɬɫɹ. Ɉɞɧɚɤɨ ɱ ɢ ɫ ɥ ɨ ɱ ɚ ɫ ɬ ɢ ɰ (ɦɨɥɟɤɭɥ, ɦɨɥɟɤɭɥɹɪɧɵɯ ɢɨɧɨɜ, ɢɯ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɤɨɦɩɥɟɤɫɨɜ ɢ ɚɫɫɨɰɢɚɬɨɜ) ɫɨɯɪɚɧɹɬɶɫɹ ɧɟ ɨɛɹɡɚɧɨ. ɇɚɩɪɨɬɢɜ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɚɤɰɢɢ ɢɡ ɛɨɥɶɲɟɝɨ ɱɢɫɥɚ ɱɚɫɬɢɰ ɦɨɠɟɬ ɩɨɥɭɱɚɬɶɫɹ ɦɟɧɶɲɟɟ (ɪɟɚɤɰɢɢ ɫɨɟɞɢɧɟɧɢɹ), ɢɡ ɦɟɧɶɲɟɝɨ – ɛɨɥɶɲɟɟ (ɪɚɫɩɚɞɚ ɢɥɢ ɪɚɡɥɨɠɟɧɢɹ), ɱɢɫɥɨ ɱɚɫɬɢɰ ɦɨɠɟɬ ɢ ɧɟ ɢɡɦɟɧɹɬɶɫɹ (ɪɟɚɤɰɢɢ ɡɚɦɟɳɟɧɢɹ ɢ ɨɛɦɟɧɚ). ____________________ *)
3
Ɍɟɪɦɢɧ «ɤɢɧɟɬɢɤɚ» ɩɪɨɢɫɯɨɞɢɬ ɨɬ ɝɪɟɱ. țȓȞȘıȚȢ – ɞɜɢɠɟɧɢɟ. 4
2. ɇɚ ɷɬɨɬ ɫɱɟɬ ɟɫɬɶ ɨɞɧɨ ɩɪɢɧɰɢɩɢɚɥɶɧɨɟ ɨɝɪɚɧɢɱɟɧɢɟ: ɜ ɤɚɠɞɨɣ ɪɟɚɤɰɢɢ ɫɭɳɟɫɬɜɭɸɬ ɢɧɜɚɪɢɚɧɬɧɵɟ ɱɚɫɬɢɰɵ, ɬɨ ɟɫɬɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɟɜɪɚɳɟɧɢɹ ɧɟ ɩɟɪɟɯɨɞɹɳɢɟ ɧɢ ɜ ɤɚɤɢɟ ɞɪɭɝɢɟ ɱɚɫɬɢɰɵ ɢ ɨɫɬɚɸɳɢɟɫɹ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɫɜɨɟɝɨ ɪɨɞɚ. ȿɫɥɢ ɩɪɢɧɹɬɶ ɜɨ ɜɧɢɦɚɧɢɟ ɨɛɚ ɮɚɤɬɚ, ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɚɫɫɵ ɩɨɥɭɱɚɟɬ ɬɪɚɤɬɨɜɤɭ ɫ ɨ ɯ ɪ ɚ ɧ ɟ ɧ ɢ ɹ ɱ ɢ ɫ ɥ ɚ ɢ ɧ ɜ ɚ ɪ ɢ ɚ ɧ ɬ ɧ ɵ ɯ ɱ ɚ ɫ ɬ ɢ ɰ . ȼ ɫɚɦɨɦ ɞɟɥɟ, ɤɨɥɶ ɫɤɨɪɨ ɫɭɳɟɫɬɜɭɸɬ ɬɚɤɢɟ ɱɚɫɬɢɰɵ, ɚ ɦɚɫɫɚ ɜ ɰɟɥɨɦ ɫɨɯɪɚɧɹɟɬɫɹ, ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɹɟɬɫɹ ɢ ɱɢɫɥɨ ɢɧɜɚɪɢɚɧɬɧɵɯ ɱɚɫɬɢɰ. ɇɚɢɛɨɥɶɲɚɹ ɢɧɜɚɪɢɚɧɬɧɚɹ ɱɚɫɬɢɰɚ – ɷɬɨ ɚɬɨɦ. Ɋɨɞ ɚɬɨɦɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɚɪɹɞɨɜɵɦ ɱɢɫɥɨɦ ɚɬɨɦɧɨɝɨ ɹɞɪɚ Za, ɚ ɫɨɜɨɤɭɩɧɨɫɬɶ ɜɫɟɯ ɚɬɨɦɨɜ ɨɞɧɨɝɨ ɪɨɞɚ (ɜ ɭɤɚɡɚɧɧɨɦ ɫɦɵɫɥɟ ɷɬɨɝɨ ɫɥɨɜɚ) ɧɚɡɵɜɚɟɬɫɹ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɯɢɦɢɱɟɫɤɢɦ ɷɥɟɦɟɧɬɨɦ. ɂɬɚɤ, ɩɨɫɤɨɥɶɤɭ ɢɧɜɚɪɢɚɧɬɧɵɟ ɱɚɫɬɢɰɵ ɫɨɯɪɚɧɹɸɬɫɹ, ɦɟɠɞɭ ɤɨɥɢɱɟɫɬɜɚɦɢ ɱɚɫɬɢɰ ɩɪɟɜɪɚɳɚɸɳɢɯɫɹ ɞɨɥɠɧɨ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɧɨɟ ɫɨɨɬɧɨɲɟɧɢɟ. ɇɚɩɪɢɦɟɪ, ɩɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɯɥɨɪɢɫɬɨɝɨ ɜɨɞɨɪɨɞɚ, ɦɨɥɟɤɭɥɚ ɤɨɬɨɪɨɝɨ ɢɦɟɟɬ ɫɨɫɬɚɜ HCl, ɫ ɤɢɫɥɨɪɨɞɨɦ O2 ɨɛɪɚɡɭɸɬɫɹ ɯɥɨɪ Cl2 ɢ ɜɨɞɚ H2O. ȼɨɡɦɨɠɧɚɹ ɤɨɦɛɢɧɚɰɢɹ ɷɬɢɯ ɱɚɫɬɢɰ, ɨɫɬɚɜɥɹɸɳɚɹ ɧɟɢɡɦɟɧɧɵɦ ɱɢɫɥɨ ɢɧɜɚɪɢɚɧɬɨɜ H, Cl ɢ O, ɢɦɟɟɬ ɜɢɞ: 4HCl + O2 = 2Cl2 + 2H2O. ɉɨɞɯɨɞɹɳɟɣ ɛɭɞɟɬ ɬɚɤɠɟ ɥɸɛɚɹ ɤɪɚɬɧɚɹ ɤɨɦɛɢɧɚɰɢɹ, ɟɫɥɢ ɭɪɚɜɧɟɧɢɟ ɭɦɧɨɠɢɬɶ ɧɚ ɰɟɥɨɟ ɱɢɫɥɨ D > 0, ɨɞɧɚɤɨ ɧɢɤɚɤɨɣ ɞɪɭɝɨɣ ɧɚɛɨɪ ɱɢɫɟɥ, ɤɪɨɦɟ (4, 1; 2, 2) ɢ ɤɪɚɬɧɵɯ ɢɦ, ɧɟɜɨɡɦɨɠɟɧ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɢɦɟɸɬɫɹ N ɪɟɚɝɢɪɭɸɳɢɯ ɜɟɳɟɫɬɜ, ɦɨɥɟɤɭɥɵ ɤɨɬɨɪɵɯ ɦɵ ɛɭɞɟɦ ɨɛɨɡɧɚɱɚɬɶ A1, A2, …, AN, ɬɨ ɭɪɚɜɧɟɧɢɟ ɫɨɯɪɚɧɟɧɢɹ ɢɦɟɟɬ ɜɢɞ: Q1A1 + … + QmAm = Qm+1Am+1 + … + QNAN, ɢɥɢ ɤɨɪɨɬɤɨ m
N
¦ Qi Ai
¦ Q j Aj .
(I.1)
j m1
i 1
ɐɟɥɵɟ ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɱɢɫɥɚ Q1, Q2, …, QN, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɱɢɫɥɚ ɢɧɜɚɪɢɚɧɬɧɵɯ ɱɚɫɬɢɰ, ɧɚɡɵɜɚɸɬɫɹ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ, ɚ ɫɚɦɚ ɬɚɤɚɹ ɡɚɩɢɫɶ – ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɭɪɚɜɧɟɧɢɟɦ. Ⱦɚɥɟɟ ɦɵ ɭɫɥɨɜɢɦɫɹ ɢɧɞɟɤɫɨɦ i ɨɛɨɡɧɚɱɚɬɶ ɢɫɯɨɞɧɵɟ ɜɟɳɟɫɬɜɚ, ɡɚɩɢɫɚɧɧɵɟ ɜ ɭɪɚɜɧɟɧɢɢ (I.1) ɫɥɟɜɚ, ɢɧɞɟɤɫɨɦ j – ɩɪɨɞɭɤɬɵ, ɡɚɩɢɫɚɧɧɵɟ ɫɩɪɚɜɚ. ɉɟɪɟɣɞɟɦ ɬɟɩɟɪɶ ɤ ɨɩɢɫɚɧɢɸ ɪɟɚɤɰɢɢ ɜ ɬɟɪɦɢɧɚɯ ɤɨɥɢɱɟɫɬɜ ɜɟɳɟɫɬɜ. ɉɭɫɬɶ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɜ ɫɢɫɬɟɦɟ ɫɨɞɟɪɠɚɥɢɫɶ ɜɟɳɟɫɬɜɚ ɜ ɤɨɥɢɱɟɫɬɜɚɯ (ɦɨɥɶ) n10, n20, …, nN0. Ɍɨɝɞɚ ɤ ɩɪɨɢɡɜɨɥɶɧɨɦɭ ɦɨɦɟɧɬɭ ɤɨɥɢɱɟɫɬɜɚ ɜɟɳɟɫɬɜ ɛɭɞɭɬ n1, n2, …, nN. ɉɪɢɪɚɳɟɧɢɹ ɤɨɥɢɱɟɫɬɜ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɫɜɹɡɚɧɵ ɩɪɨɩɨɪɰɢɟɣ
n nm0 n n0 1 1 m Q1 Qm ɢɫɯɨɞɧɵɟ ɜɟɳɟɫɬɜɚ
nm1 nm0 1 nN nN0 , (I.2) Q m1 QN
ɩɪɨɞɭɤɬɵ
5
ɬɨ ɟɫɬɶ ɩɪɢɪɚɳɟɧɢɹ 'nk ɦɟɠɞɭ ɫɨɛɨɣ ɨɬɧɨɫɹɬɫɹ ɬɚɤ ɠɟ, ɤɚɤ ɨɬɧɨɫɹɬɫɹ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ. ɗɬɨ ɭɬɜɟɪɠɞɟɧɢɟ ɢ ɫɨɫɬɚɜɥɹɟɬ ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɫɬɟɯɢɨɦɟɬɪɢɢ. Ɂɧɚɤ «–» ɩɟɪɟɞ ɤɚɠɞɨɣ ɞɪɨɛɶɸ ɞɥɹ ɢɫɯɨɞɧɵɯ ɜɟɳɟɫɬɜ ɫɜɹɡɚɧ ɫ ɬɟɦ, ɱɬɨ ɷɬɢ ɜɟɳɟɫɬɜɚ ɢɫɱɟɡɚɸɬ ('ni < 0), ɬɚɤ ɱɬɨ ɜɫɟ ɱɥɟɧɵ ɧɚɲɟɣ N-ɱɥɟɧɧɨɣ ɩɪɨɩɨɪɰɢɢ ɛɭɞɭɬ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ. ɇɚ ɡɚɤɨɧɟ (I.2) ɨɫɧɨɜɚɧɵ ɩɪɨɫɬɟɣɲɢɟ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɟ ɪɚɫɱɟɬɵ. Ɏɨɪɦɭɥɭ (I.2) ɧɟɬɪɭɞɧɨ ɩɟɪɟɩɢɫɚɬɶ ɬɚɤ, ɱɬɨɛɵ ɜ ɧɟɟ ɜɦɟɫɬɨ ɤɨɥɢɱɟɫɬɜ ɜɯɨɞɢɥɢ ɦɚɫɫɵ ɪɟɚɝɢɪɭɸɳɢɯ ɜɟɳɟɫɬɜ. ȿɫɥɢ Mk = mk/nk – ɦɨɥɹɪɧɚɹ ɦɚɫɫɚ k-ɝɨ ɜɟɳɟɫɬɜɚ, ɬɨ
'mi Qi M i
'm j Q jM j
.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɫɫɵ ɜɟɳɟɫɬɜ, ɜɫɬɭɩɢɜɲɢɯ ɜ ɪɟɚɤɰɢɸ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɤɪɚɬɧɵɦ ɢɯ ɦɨɥɹɪɧɵɯ ɦɚɫɫ.
2. ɋɤɨɪɨɫɬɶ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ Ɋɚɫɫɦɨɬɪɢɦ ɪɚɡɜɢɬɢɟ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɜɨ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɷɬɨɝɨ ɩɪɟɞɫɬɚɜɢɦ ɫɟɛɟ, ɱɬɨ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ W ɦɵ ɢɦɟɟɦ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɫɪɟɞɫɬɜɚ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɢɡɦɟɪɹɬɶ ɤɨɥɢɱɟɫɬɜɚ ɜɫɟɯ ɜɟɳɟɫɬɜ ɜ ɫɢɫɬɟɦɟ. Ɍɨɝɞɚ ɦɵ ɨɛɧɚɪɭɠɢɦ, ɱɬɨ ɷɬɢ ɤɨɥɢɱɟɫɬɜɚ – ɫɭɬɶ ɮɭɧɤɰɢɢ ɜɪɟɦɟɧɢ ni(W). ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɩɪɨɩɨɪɰɢɹ (I.2) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɨɬɧɨɲɟɧɢɟ 'ni/Qi ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɨɞɢɧɚɤɨɜɨ ɞɥɹ ɜɫɟɯ ɭɱɚɫɬɧɢɤɨɜ ɪɟɚɤɰɢɢ. ɗɬɨ ɨɬɧɨɲɟɧɢɟ, ɡɚɜɢɫɹɳɟɟ ɨɬ ɜɪɟɦɟɧɢ, ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɢɧɞɟɤɫɨɜ (i, j). ɂɦɟɸɬɫɹ N ɮɭɧɤɰɢɣ, ɩɪɢɧɢɦɚɸɳɢɯ ɨɞɢɧɚɤɨɜɵɟ ɡɧɚɱɟɧɢɹ ɩɪɢ ɥɸɛɨɦ ɡɧɚɱɟɧɢɢ ɚɪɝɭɦɟɧɬɚ:
'n1 (W) 'n ( W ) m Q1 Qm
'nm1 (W) 'n N ( W ) { [ ( W) . Q m1 QN
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɦɨɠɧɨ ɜɜɟɫɬɢ ɩɚɪɚɦɟɬɪ – ɮɭɧɤɰɢɸ [(W), ɧɚɡɵɜɚɟɦɭɸ ɯɢɦɢɱɟɫɤɨɣ ɩɟɪɟɦɟɧɧɨɣ (ɢɥɢ ɤɨɨɪɞɢɧɚɬɨɣ ɪɟɚɤɰɢɢ). ɗɬɚ ɜɟɥɢɱɢɧɚ ɩɨɤɚɡɵɜɚɟɬ ɫɬɟɩɟɧɶ ɩɪɨɬɟɤɚɧɢɹ ɪɟɚɤɰɢɢ ɧɚ ɩɭɬɢ ɨɬ ɢɫɯɨɞɧɵɯ ɜɟɳɟɫɬɜ ɤ ɩɪɨɞɭɤɬɚɦ ɤ ɥɸɛɨɦɭ ɦɨɦɟɧɬɭ ɜɪɟɦɟɧɢ. ɋ ɩɨɦɨɳɶɸ ɯɢɦɢɱɟɫɤɨɣ ɩɟɪɟɦɟɧɧɨɣ ɦɨɠɧɨ ɞɚɬɶ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ. ȼ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɩɟɪɟɦɟɧɧɚɹ [ ɨɩɪɟɞɟɥɹɟɬ ɫɨɫɬɨɹɧɢɟ ɪɟɚɝɢɪɭɸɳɟɣ ɫɢɫɬɟɦɵ, ɩɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶɸ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɧɚɡɵɜɚɟɬɫɹ ɩɪɨɢɡɜɨɞɧɚɹ ɩɨ ɜɪɟɦɟɧɢ w [ (I.3) (ɬɨɱɤɚ ɧɚɞ ɫɢɦɜɨɥɨɦ, ɤɚɤ ɨɛɵɱɧɨ, ɨɛɨɡɧɚɱɚɟɬ ɩɪɨɢɡɜɨɞɧɭɸ). Ɉɩɪɟɞɟɥɟɧɢɟ (I.3) – ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɤɚɧɨɧɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɢ – ɭɞɨɛɧɨ ɩɪɢɜɟɫɬɢ ɤ ɜɵɪɚɠɟɧɢɸ ɱɟɪɟɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɩɪɟɞɟɥɹɟ1 ɦɵɟ ɜɟɥɢɱɢɧɵ. əɫɧɨ, ɱɬɨ w ni , ɨɞɧɚɤɨ ɢɡɦɟɪɟɧɢɟ ɤɨɥɢɱɟɫɬɜɚ ɜɟQi 6
ɳɟɫɬɜɚ ɜ ɫɢɫɬɟɦɟ ɜ ɰɟɥɨɦ, ɞɚ ɟɳɟ ɜ ɨɬɞɟɥɶɧɨ ɜɡɹɬɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɬɪɭɞɧɭɸ ɢ ɧɟɧɭɠɧɭɸ ɡɚɞɚɱɭ. Ɇɵ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɬɨɥɶɤɨ ɝ ɨ ɦ ɨ ɝ ɟ ɧ ɧ ɵ ɟ ɫɢɫɬɟɦɵ, ɬɨ ɟɫɬɶ ɫɢɫɬɟɦɵ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɫɨɛɨɣ ɫɩɥóɲɧɨɟ ɬɟɥɨ, ɧɟ ɢɦɟɸɳɟɟ ɝɪɚɧɢɰ ɪɚɡɞɟɥɚ ɦɟɠɞɭ ɫɜɨɢɦɢ ɨɞɧɨɪɨɞɧɵɦɢ ɱɚɫɬɹɦɢ. Ɍɨɝɞɚ, ɪɚɡɞɟɥɢɜ (I.3) ɧɚ ɨɛɴɟɦ ɫɢɫɬɟɦɵ V, ɩɨɥɭɱɢɦ ɨɛɴɟɦɧɭɸ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ
v
w V
1 Ci . Qi
(I.4)
Ɂɞɟɫɶ Ci = ni/V – ɤɨɧɰɟɧɬɪɚɰɢɹ i-ɝɨ ɜɟɳɟɫɬɜɚ – ɜɟɥɢɱɢɧɚ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ * ɢɡɦɟɪɹɟɦɚɹ ) . ɉɪɢ ɷɬɨɦ ɦɵ ɩɪɢɧɢɦɚɟɦ ɨɫɧɨɜɧɨɟ ɞɨɩɭɳɟɧɢɟ, ɫɨɫɬɨɹɳɟɟ ɜ ɬɨɦ, ɱɬɨ ɫɢɫɬɟɦɚ ɪɟɚɝɢɪɭɟɬ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɨɛɴɟɦɚ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɬɨɥɶɤɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɜɟɥɢɱɢɧɚ (I.4) ɞɚɟɬ ɩɪɚɜɢɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ ɫɤɨɪɨɫɬɢ. ɂɧɚɱɟ, ɟɫɥɢ ɫɢɫɬɟɦɚ ɪɟɚɝɢɪɭɟɬ ɧɟɢɡɨɯɨɪɧɨ (V z const), ɩɪɨɢɡɜɨɞɧɚɹ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɪɚɜɧɚ
C i
1 1 ni CiV . V V
ȼɬɨɪɨɣ ɱɥɟɧ ɫɜɹɡɚɧ ɫ ɢɡɦɟɧɟɧɢɟɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ ɨɛɴɟɦɚ, ɚ ɧɟ ɪɟɚɤɰɢɢ (ɟɝɨ ɧɚɡɵɜɚɸɬ ɢɧɨɝɞɚ ɪɚɡɛɚɜɥɟɧɢɟɦ). ȿɫɥɢ ɢɡɦɟɧɟɧɢɟ ɨɛɴɟɦɚ ɢɡɜɟɫɬɧɨ, ɬɨ ɪɚɡɛɚɜɥɟɧɢɟ Ci V V ɦɨɠɧɨ ɜɩɨɫɥɟɞɫɬɜɢɢ ɢɫɤɥɸɱɢɬɶ. Ɍɟɩɟɪɶ ɦɵ ɢɦɟɟɦ ɪɚɛɨɱɟɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɢ, ɤɨɬɨɪɵɦ ɢ ɛɭɞɟɦ ɩɨɥɶɡɨɜɚɬɶɫɹ ɜ ɞɚɥɶɧɟɣɲɟɦ. Ɉɛɵɱɧɨ ɡɚ ɯɨɞɨɦ ɪɟɚɤɰɢɢ ɫɥɟɞɹɬ, ɜɵɛɢɪɚɹ ɨɞɢɧ ɢɡ ɪɟɚɝɟɧɬɨɜ (ɫɤɚɠɟɦ, ɨɞɢɧ ɢɡ ɢɫɯɨɞɧɵɯ ɪɟɚɝɟɧɬɨɜ Ai) ɢ ɢɡɦɟɪɹɹ ɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɸ ɜ ɨɬɞɟɥɶɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ. ɗɬɨɬ ɪɟɚɝɟɧɬ ɞɨɥɠɟɧ ɨɛɥɚɞɚɬɶ ɬɚɤɢɦɢ ɫɜɨɣɫɬɜɚɦɢ, ɤɨɬɨɪɵɟ ɞɟɥɚɸɬ ɜɨɡɦɨɠɧɵɦ ɢ ɭɞɨɛɧɵɦ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɢ. ɉɪɨɢɡɜɨɞɧɭɸ vi C i , ɜɵɱɢɫɥɹɟɦɭɸ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɤɢɧɟɬɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ Ci(W), ɧɚɡɵɜɚɸɬ ɫɤɨɪɨɫɬɶɸ ɩɨ ɪɟɚɝɟɧɬɭ. Ⱦɥɹ ɪɚɡɧɵɯ ɭɱɚɫɬɧɢɤɨɜ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɪɟɚɤɰɢɢ ɷɬɚ ɜɟɥɢɱɢɧɚ, ɜ ɨɬɥɢɱɢɟ ɨɬ v, ɪɚɡɥɢɱɧɚ. ɉɨɷɬɨɦɭ ɜɨ ɜɫɟɯ ɭɪɚɜɧɟɧɢɹɯ ɯɢɦɢɱɟɫɤɨɣ ɤɢɧɟɬɢɤɢ ɫɤɨɪɨɫɬɶ ɮɢɝɭɪɢɪɭɟɬ ɜ ɜɢɞɟ (I.4) ɢɥɢ (I.3). Ɉɩɪɟɞɟɥɟɧɢɟ (I.4) ɡɚɩɢɫɚɧɨ ɞɥɹ ɢɫɯɨɞɧɨɝɨ i-ɝɨ ɜɟɳɟɫɬɜɚ. ȿɫɥɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɩɪɨɬɟɤɚɧɢɟ ɪɟɚɤɰɢɢ ɩɨ ɭɪɚɜɧɟɧɢɸ (I.1) ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɞɥɹ ɧɟɝɨ C i 0 , ɚ ɩɨɬɨɦɭ v > 0. Ɉɬɧɨɫɢɬɟɥɶɧɨ ɥɸɛɨɝɨ ɢɡ ɩɪɨɞɭɤɬɨɜ ɮɨɪɦɭɥɚ (I.4) ɞɨɥɠɧɚ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɜ ɜɢɞɟ:
1 Cj . Qj
v
*)
Ɉɛ ɨɞɧɨɦ ɢɡ ɫɩɨɫɨɛɨɜ ɟɟ ɢɡɦɟɪɟɧɢɹ ɪɟɱɶ ɛɭɞɟɬ ɢɞɬɢ ɧɢɠɟ, ɜɨ II ɱɚɫɬɢ ɧɚɲɟɝɨ ɩɨɫɨɛɢɹ. 7
ɉɨɤɚ ɦɵ ɫɨɯɪɚɧɹɟɦ ɹɜɧɨɟ ɪɚɡɥɢɱɢɟ ɦɟɠɞɭ ɢɫɯɨɞɧɵɦɢ ɜɟɳɟɫɬɜɚɦɢ ɢ ɩɪɨɞɭɤɬɚɦɢ, ɯɨɬɹ ɜɩɨɫɥɟɞɫɬɜɢɢ ɭɜɢɞɢɦ, ɱɬɨ ɷɬɨ ɜɨɩɪɨɫ ɫɨɝɥɚɲɟɧɢɹ. 3. Ɂɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ȼ ɫɚɦɨɦ ɧɚɱɚɥɟ ɦɵ ɭɩɨɦɹɧɭɥɢ ɨɛ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟ ɮɨɪɦɚɥɶɧɨɣ ɤɢɧɟɬɢɤɢ. Ɍɟɩɟɪɶ ɟɟ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɞɥɹ ɞɚɧɧɨɣ ɪɟɚɤɰɢɢ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɡɚɤɨɧ Ck(W), ɩɨ ɤɨɬɨɪɨɦɭ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɫɟɯ ɭɱɚɫɬɧɢɤɨɜ ɪɟɚɤɰɢɢ ɢɡɦɟɧɹɸɬɫɹ ɜɨ ɜɪɟɦɟɧɢ. ȼɜɢɞɭ ɫɨɨɬɧɨɲɟɧɢɹ (I.2) ɹɫɧɨ, ɱɬɨ ɛɭɞɟɬ ɞɨɫɬɚɬɨɱɧɨ ɫɞɟɥɚɬɶ ɷɬɨ ɞɥɹ ɨɞɧɨɝɨ ɢɡ ɪɟɚɝɟɧɬɨɜ; ɞɥɹ ɜɫɟɯ ɨɫɬɚɥɶɧɵɯ ɡɚɜɢɫɢɦɨɫɬɢ ɜɵɱɢɫɥɹɸɬɫɹ ɩɨ ɫɬɟɯɢɨɦɟɬɪɢɢ. Ɏɭɧɤɰɢɹ Ck(W) ɧɚɡɵɜɚɟɬɫɹ ɤɢɧɟɬɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ ɪɟɚɤɰɢɢ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ ɡɧɚɬɶ, ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɫɤɨɪɨɫɬɶ ɫɜɹɡɚɧɚ ɫ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɜɟɳɟɫɬɜ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. ȿɫɥɢ ɬɚɤɭɸ ɫɜɹɡɶ ɭɞɚɫɬɫɹ ɧɚɣɬɢ ɜ ɹɜɧɨɦ ɜɢɞɟ, ɬɨ ɡɚɞɚɱɚ ɫɜɟɞɟɬɫɹ ɤ ɪɟɲɟɧɢɸ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ 1 Ci f C1 (W),, C N (W) . Qi ɍɫɬɚɧɨɜɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ f, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɦɨɠɧɨ ɥɢɛɨ ɷɦɩɢɪɢɱɟɫɤɢɦ ɩɭɬɟɦ, ɥɢɛɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɦɨɞɟɥɢ, ɨɩɪɟɞɟɥɟɧɧɵɦ ɨɛɪɚɡɨɦ ɬɨɥɤɭɸɳɟɣ ɦɟɯɚɧɢɡɦ ɪɟɚɤɰɢɢ. Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɬɚɤɨɣ ɦɨɞɟɥɢ ɪɟɚɝɢɪɭɸɳɭɸ ɫɦɟɫɶ ɢɞɟɚɥɶɧɵɯ ɝɚɡɨɜ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɩɪɨɢɡɨɲɟɥ ɚɤɬ ɩɪɟɜɪɚɳɟɧɢɹ, ɨɧɢ ɞɨɥɠɧɵ ɫɛɥɢɡɢɬɶɫɹ ɩɨ ɦɟɧɶɲɟɣ ɦɟɪɟ ɧɚ ɪɚɫɫɬɨɹɧɢɟ, ɫɪɚɜɧɢɦɨɟ ɫ ɢɯ ɫɨɛɫɬɜɟɧɧɵɦɢ ɪɚɡɦɟɪɚɦɢ. ɗɬɭ ɫɢɬɭɚɰɢɸ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɭɞɚɪɨɦ. ȼ ɬɚɤɨɦ ɫɥɭɱɚɟ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɛɭɞɟɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɚɫɬɨɬɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ, ɩɪɢɱɟɦ ɧɚɫ ɭɫɬɪɚɢɜɚɸɬ ɧɟ ɤɚɤɢɟ ɭɝɨɞɧɨ ɫɬɨɥɤɧɨɜɟɧɢɹ, ɚ ɬɨɥɶɤɨ ɜ ɞɚɧɧɨɣ ɤɨɦɛɢɧɚɰɢɢ. ɂɦɟɟɬɫɹ ɜ ɜɢɞɭ, ɱɬɨ ɜ ɤɚɠɞɨɦ ɚɤɬɟ ɞɨɥɠɧɵ ɩɪɢɣɬɢ ɜ ɫɨɭɞɚɪɟɧɢɟ ɧɭɠɧɵɟ ɦɨɥɟɤɭɥɵ ɜ ɧɭɠɧɨɦ ɱɢɫɥɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɭɪɚɜɧɟɧɢɟɦ. ɑɚɫɬɨɬɚ ɩ ɚ ɪ ɧ ɵ ɯ ɫɨɭɞɚɪɟɧɢɣ z ɨɞɢɧɚɤɨɜɵɯ ɱɚɫɬɢɰ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɜɚɞɪɚɬɭ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ:
z
2 A
1 2
C
16ɤT 2Sr N SP 2
2
,
(I.5)
ɝɞɟ r – ɪɚɞɢɭɫ ɱɚɫɬɢɰɵ; P – ɟɟ ɦɚɫɫɚ; NA – ɱɢɫɥɨ Ⱥɜɨɝɚɞɪɨ; ɤ – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ. ɗɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɩɚɪɧɨɟ ɫɨɭɞɚɪɟɧɢɟ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ ɫɨɛɵɬɢɟɦ, ɢ ɟɝɨ ɦɨɠɧɨ ɩɪɨɤɨɦɦɟɧɬɢɪɨɜɚɬɶ ɬɚɤ. ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɧɚɪɭɠɢɬɶ ɱɚɫɬɢɰɭ ɜ ɦɚɥɨɦ ɨɛɴɟɦɟ (ɩɨɪɹɞɤɚ r3), ɨɤɪɭɠɚɸɳɟɦ ɜɵɞɟɥɟɧɧɭɸ ɬɨɱɤɭ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ C. ɋɬɨɥɤɧɨɜɟɧɢɟ – ɟɫɬɶ ɫɨɛɵɬɢɟ, ɫɨɫɬɨɹɳɢɟ ɜ ɩɨɩɚɞɚɧɢɢ ɫɪɚɡɭ 2-ɯ ɱɚɫɬɢɰ ɜ ɷɬɨɬ ɨɛɴɟɦ, ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɟɝɨ ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɷɥɟɦɟɧɬɚɪɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ, ɬɨ ɟɫɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ C2. 8
ɇɚɤɨɧɟɰ, ɫɪɟɞɧɹɹ ɱɚɫɬɨɬɚ ɫɨɭɞɚɪɟɧɢɣ, ɤɚɤ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɬɚɬɢɫɬɢɱɟɫɤɚɹ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɦɟɧɧɨ ɷɬɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ. ȿɫɥɢ ɫɬɚɥɤɢɜɚɸɬɫɹ ɞɜɟ ɪɚɡɧɵɟ ɱɚɫɬɢɰɵ A1 ɢ A2, ɬɨ z C1C2. Ɍɟɩɟɪɶ ɦɵ ɦɨɠɟɦ ɨɰɟɧɢɬɶ ɱɚɫɬɨɬɭ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɪɟɚɤɰɢɨɧɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ. Ʉɚɤ ɦɵ ɫɤɚɡɚɥɢ, ɨɧɢ ɞɨɥɠɧɵ ɢɦɟɬɶ ɤɨɧɮɢɝɭɪɚɰɢɸ Q1A1 + Q2A2 + … + QmAm, Q Q Q ɩɨɷɬɨɦɭ z C1 1 C2 2 Cmm . ɍɱɢɬɵɜɚɹ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ v z, ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ: m
v(W) k CiQi (W) ,
(I.6)
ɫɯɟɦɭ, ɨɧɢ ɦɨɝɭɬ ɧɚ ɩɨɪɹɞɤɢ ɢɡɦɟɧɹɬɶ (ɭɜɟɥɢɱɢɜɚɬɶ ɢɥɢ, ɜ ɧɟɤɨɬɨɪɵɯ ɫɥɭɱɚɹɯ, ɭɦɟɧɶɲɚɬɶ) ɤɨɧɫɬɚɧɬɭ ɫɤɨɪɨɫɬɢ, ɯɨɬɹ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ ɦɨɝɭɬ ɧɟ ɜɯɨɞɢɬɶ ɜ ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ. Ⱥɝɟɧɬɵ, ɡɚɦɟɞɥɹɸɳɢɟ ɪɟɚɤɰɢɸ, ɧɨɫɹɬ ɧɚɡɜɚɧɢɟ ɢɧɝɢɛɢɬɨɪɨɜ. 4. ɉɨɪɹɞɨɤ ɢ ɦɨɥɟɤɭɥɹɪɧɨɫɬɶ
ȼɟɪɧɟɦɫɹ ɤ ɨɛɵɱɧɨɣ ɧɟɤɚɬɚɥɢɬɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ. ɂɡ ɜɟɪɨɹɬɧɨɫɬɧɵɯ ɫɨɨɛɪɚɠɟɧɢɣ ɹɫɧɨ, ɱɬɨ ɫɨɛɵɬɢɟ ɜɫɬɪɟɱɢ ɞɜɭɯ ɱɚɫɬɢɰ ɛɨɥɟɟ ɜɟɪɨɹɬɧɨ, ɱɟɦ ɬɪɟɯ, ɬɪɟɯ – ɱɟɦ ɱɟɬɵɪɟɯ ɢ ɬ. ɞ. Ɍɨɱɧɟɟ, ɢɦɟɸɬɫɹ ɜɚɪɢɚɧɬɵ:
i 1
ɝɞɟ k – ɫɜɨɞɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɤɥɸɱɚɸɳɢɣ ɜ ɫɟɛɟ ɜɫɟ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ . ɍɪɚɜɧɟɧɢɟ (I.6) ɜɵɪɚɠɚɟɬ ɨɞɢɧ ɢɡ ɨɫɧɨɜɧɵɯ ɡɚɤɨɧɨɜ ɤɢɧɟɬɢɤɢ – ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ [ɨɬɤɪɵɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ Ƚɭɥɶɞɛɟɪɝɨɦ ɢ ȼɚɚɝɟ (C. Guldberg, P. Waage), 1864–67]. Ɉɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɩɪɨɬɟɤɚɧɢɹ ɪɟɚɤɰɢɢ ɜ «ɩɨɥɨɠɢɬɟɥɶɧɨɦ» ɧɚɩɪɚɜɥɟɧɢɢ (ɫɥɟɜɚ ɧɚɩɪɚɜɨ ɫɨɝɥɚɫɧɨ ɩɪɢɧɹɬɨɣ ɨɪɢɟɧɬɚɰɢɢ) ɨ ɩ ɪ ɟ ɞ ɟ ɥ ɹ ɟ ɬ ɫ ɹ ɤ ɨ ɧ ɰ ɟ ɧ ɬ ɪ ɚ ɰ ɢ ɹ ɦ ɢ ɬ ɨ ɥ ɶ ɤ ɨ ɢ ɫ ɯ ɨ ɞ ɧ ɵ ɯ ɜ ɟ ɳ ɟ ɫ ɬ ɜ . ɉɪɢ ɷɬɨɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɨɥɠɧɵ ɜɯɨɞɢɬɶ ɜ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɫɤɨɪɨɫɬɢ ɜ ɫɬɟɩɟɧɹɯ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ * ɤɨɷɮɮɢɰɢɟɧɬɚɦ ) . ɉɪɢ ɨɩɟɪɢɪɨɜɚɧɢɢ ɫ ɡɚɤɨɧɨɦ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɧɭɠɧɨ ɢɦɟɬɶ ɜ ɜɢɞɭ ɞɜɚ ɨɛɫɬɨɹɬɟɥɶɫɬɜɚ. ȼ ɨ - ɩ ɟ ɪ ɜ ɵ ɯ , ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ (I.6), ɡɚɜɢɫɢɬ ɨɬ ɜɪɟɦɟɧɢ; ɜɟɞɶ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɫɬɨɢɬ ɩɪɨɢɡɜɟɞɟɧɢɟ ɮɭɧɤɰɢɣ ɜɪɟɦɟɧɢ Ci(W). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɟɚɤɰɢɹ – ɩɪɨɰɟɫɫ ɧɟɪɚɜɧɨɦɟɪɧɵɣ, ɩɪɨɬɟɤɚɸɳɢɣ ɫ ɩɟɪɟɦɟɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɂɫɤɥɸɱɟɧɢɹ, ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɪɟɚɤɰɢɢ ɧɭɥɟɜɨɝɨ ɩɨɪɹɞɤɚ, ɫɭɳɟɫɬɜɭɸɬ, ɧɨ ɷɬɨ ɞɨɜɨɥɶɧɨ ɪɟɞɤɢɣ ɫɥɭɱɚɣ. Ʉɚɤ ɛɭɞɟɬ ɩɨɤɚɡɚɧɨ ɜ ɩ. 5, ɫɤɨɪɨɫɬɶ ɩɪɨɫɬɵɯ ɪɟɚɤɰɢɣ ɫɨ ɜɪɟɦɟɧɟɦ ɡɚɬɭɯɚɟɬ, ɫɬɪɟɦɹɫɶ ɩɪɢ W ĺ f ɤ ɧɭɥɸ. ȼ ɨ - ɜ ɬ ɨ ɪ ɵ ɯ , ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ k ɧɟ ɡɚɜɢɫɢɬ ɧɢ ɨɬ ɜɪɟɦɟɧɢ, ɧɢ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɣ. ɉɨɷɬɨɦɭ ɜɟɥɢɱɢɧɭ k ɧɚɡɵɜɚɸɬ ɤɨɧɫɬɚɧɬɨɣ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ. Ʉɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ – ɨɫɧɨɜɧɚɹ ɞɢɧɚɦɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɪɟɚɤɰɢɢ, ɩɨɫɤɨɥɶɤɭ ɢɦɟɧɧɨ ɨɧɚ ɨɩɪɟɞɟɥɹɟɬ ɫɤɨɪɨɫɬɶ ɩɪɢ ɩɪɨɱɢɯ ɪɚɜɧɵɯ ɭɫɥɨɜɢɹɯ. Ƚɥɚɜɧɵɦ ɫɜɨɣɫɬɜɨɦ ɤɨɧɫɬɚɧɬɵ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɨɧɚ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ ɢ ɨɱɟɧɶ ɱɭɜɫɬɜɢɬɟɥɶɧɚ ɤ ɦɚɥɵɦ ɞɨɛɚɜɤɚɦ ɜɟɳɟɫɬɜ, ɜɥɢɹɸɳɢɦ ɧɚ ɦɟɯɚɧɢɡɦ ɪɟɚɤɰɢɢ. ɗɬɢ ɜɟɳɟɫɬɜɚ, ɧɚɡɵɜɚɟɦɵɟ ɤɚɬɚɥɢɡɚɬɨɪɚɦɢ, ɢɡɦɟɧɹɸɬ ɪɟɚɤɰɢɨɧɧɵɣ ɩɭɬɶ ɩɪɨɰɟɫɫɚ, ɭɱɚɫɬɜɭɹ ɜ ɧɟɦ ɧɚ ɧɟɤɨɬɨɪɵɯ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɫɬɚɞɢɹɯ. «ȼɫɬɪɚɢɜɚɹɫɶ» ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɜ ɪɟɚɤɰɢɨɧɧɭɸ *)
Ʉɨɧɰɟɧɬɪɚɰɢɸ ɜɟɳɟɫɬɜɚ ɪɚɧɶɲɟ ɧɚɡɵɜɚɥɢ «ɞɟɣɫɬɜɭɸɳɟɣ ɦɚɫɫɨɣ». Ɉɬɫɸɞɚ ɧɚɡɜɚɧɢɟ ɡɚɤɨɧɚ, ɤɨɬɨɪɨɟ ɫɨɯɪɚɧɹɟɬɫɹ ɩɨ ɬɪɚɞɢɰɢɢ. 9
Ɋɟɚɤɰɢɹ 2-ɯ ɱɚɫɬɢɰ
3-ɯ ɱɚɫɬɢɰ
Ɍɢɩ (20) (11) (300) (210) (111) ɢ ɬ. ɞ.
ɋɯɟɦɚ 2A ĺ A+Bĺ 3A ĺ 2A + B ĺ A+B+Cĺ
ɑɢɫɥɨ ɱɚɫɬɢɰ, ɭɱɚɫɬɜɭɸɳɢɯ ɟɞɢɧɨɜɪɟɦɟɧɧɨ ɜ ɷɥɟɦɟɧɬɚɪɧɨɦ ɚɤɬɟ ɩɪɟɜɪɚɳɟɧɢɹ, ɧɚɡɵɜɚɟɬɫɹ ɦɨɥɟɤɭɥɹɪɧɨɫɬɶɸ ɩɪɨɰɟɫɫɚ. Ɉɰɟɧɢɜɚɹ ɷɬɢ ɜɚɪɢɚɧɬɵ ɦɵ ɩɨɧɢɦɚɟɦ, ɱɬɨ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɯɨɠɞɟɧɢɹ ɪɟɚɤɰɢɢ ɱɟɪɟɡ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ ɛɵɫɬɪɨ ɭɛɵɜɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɦɨɥɟɤɭɥɹɪɧɨɫɬɢ. ɇɚ ɞɟɥɟ ɨɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɛɨɥɟɟ ɱɟɦ ɬɪɢɦɨɥɟɤɭɥɹɪɧɵɟ ɩɪɨɰɟɫɫɵ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɨɫɭɳɟɫɬɜɢɦɵ, ɚ ɛɨɥɶɲɢɧɫɬɜɨ ɪɟɚɤɰɢɣ ɹɜɥɹɸɬɫɹ ɛɢɦɨɥɟɤɭɥɹɪɧɵɦɢ. Ɋɟɚɤɰɢɹ, ɜ ɤɨɬɨɪɨɣ ɤɚɠɞɨɟ ɩɪɟɜɪɚɳɟɧɢɟ ɢɫɯɨɞɧɵɯ ɱɚɫɬɢɰ ɜ ɤɨɧɟɱɧɵɟ ɩɪɨɞɭɤɬɵ ɫɨɫɬɨɢɬ ɢɡ ɨɞɧɨɝɨ ɚɤɬɚ, ɧɚɡɵɜɚɟɬɫɹ ɩɪɨɫɬɨɣ. Ɍɚɤɨɜɚ, ɧɚɩɪɢɦɟɪ, ɛɢɦɨɥɟɤɭɥɹɪɧɚɹ ɪɟɚɤɰɢɹ H2 + I2 ĺ 2HI. ɑɢɫɥɨ ɢɡɜɟɫɬɧɵɯ ɩɪɨɫɬɵɯ ɪɟɚɤɰɢɣ ɧɟɜɟɥɢɤɨ. Ʉ ɧɢɦ ɨɬɧɨɫɹɬɫɹ ɧɟɦɧɨɝɢɟ ɪɟɚɤɰɢɢ ɜ ɝɚɡɚɯ, ɢɨɧɧɵɟ ɪɟɚɤɰɢɢ ɜ ɪɚɫɬɜɨɪɚɯ. ȿɫɥɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɬɪɟɛɭɟɬ ɭɱɚɫɬɢɹ ɛɨɥɟɟ ɬɪɟɯ ɱɚɫɬɢɰ, ɬɨ ɞɟɣɫɬɜɢɬɟɥɶɧɵɣ ɦɟɯɚɧɢɡɦ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɫɬɚɞɢɣ, ɤɚɠɞɚɹ ɢɡ ɤɨɬɨɪɵɯ ɧɟ ɛɨɥɟɟ ɱɟɦ ɬɪɢɦɨɥɟɤɭɥɹɪɧɚ (ɚ ɱɚɳɟ ɜɫɟɝɨ ɢɦɟɧɧɨ ɛɢɦɨɥɟɤɭɥɹɪɧɚ). Ɍɚɤɚɹ ɪɟɚɤɰɢɹ ɧɚɡɵɜɚɟɬɫɹ ɫɥɨɠɧɨɣ. Ɉɞɧɚɤɨ ɩɪɨɫɬɚɹ ɫɬɟɯɢɨɦɟɬɪɢɹ ɧɟ ɹɜɥɹɟɬɫɹ ɟɳɟ ɞɨɫɬɚɬɨɱɧɵɦ ɩɪɢɡɧɚɤɨɦ ɬɨɝɨ, ɱɬɨ ɪɟɚɤɰɢɹ ɩɪɨɫɬɚ. ɇɚɩɪɢɦɟɪ, ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɜɨɞɨɪɨɞɚ ɫ ɯɥɨɪɨɦ ɨɩɢɫɵɜɚɟɬɫɹ ɬɚɤɢɦ ɠɟ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɭɪɚɜɧɟɧɢɟɦ, ɤɚɤ ɢ ɜɨɞɨɪɨɞɚ ɫ ɢɨɞɨɦ: H2 + Cl2 ĺ 2HCl. ɇɨ ɟɝɨ ɦɟɯɚɧɢɡɦ ɡɧɚɱɢɬɟɥɶɧɨ ɫɥɨɠɧɟɟ ɢ ɫɨɫɬɨɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɫɬɚɞɢɣ: Cl2 ĺ 2Cl, Cl + H2ĺ HCl + H, H + Cl2 ĺ HCl + Cl ɢ ɬ. ɞ. 10
ɉɟɪɜɚɹ ɹɜɥɹɟɬɫɹ ɦɨɧɨɦɨɥɟɤɭɥɹɪɧɨɣ, ɨɫɬɚɥɶɧɵɟ – ɛɢɦɨɥɟɤɭɥɹɪɧɵɦɢ. ɉɨɞɨɛɧɵɣ ɦɟɯɚɧɢɡɦ ɧɚɡɵɜɚɟɬɫɹ ɰɟɩɧɵɦ. ɉɪɚɜɢɥɨ ɨ ɝ ɪ ɚ ɧ ɢ ɱ ɟ ɧ ɢ ɹ ɦ ɨ ɥ ɟ ɤ ɭ ɥ ɹ ɪ ɧ ɨ ɫ ɬ ɢ ɩ ɨ ɜ ɟ ɪ ɨ ɹ ɬ ɧ ɨ ɫ ɬ ɢ ɩɪɢɜɨɞɢɬ ɤ ɜɵɜɨɞɭ, ɱɬɨ ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɜ ɮɨɪɦɟ (I.6) ɫɩɪɚ-
AA* ĺ ɩɪɨɞɭɤɬɵ + A,
A* ĺ ɩɪɨɞɭɤɬɵ.
ȼɨɡɛɭɠɞɟɧɢɟ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɡɚ ɫɱɟɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɨɥɟɤɭɥɵ ɫ ɢɡɥɭɱɟɧɢɟɦ. Ɍɚɤ ɢɧɢɰɢɢɪɭɟɬɫɹ, ɧɚɩɪɢɦɟɪ, ɰɟɩɧɚɹ ɪɟɚɤɰɢɹ ɨɛɪɚɡɨɜɚɧɢɹ ɯɥɨɪɢɫɬɨɝɨ ɜɨɞɨɪɨɞɚ, ɩɪɢɜɟɞɟɧɧɚɹ ɧɚ ɫɬɪ. 11:
m
ɜɟɞɥɢɜ ɞɥɹ ɩɪɨɫɬɨɣ ɪɟɚɤɰɢɢ, ɢ, ɜ ɱɚɫɬɧɨɫɬɢ, ɟɫɥɢ ¦ Q i ¶ 3 . Ⱦɥɹ ɫɥɨɠɧɵɯ
Cl2 + hQ ĺ Cl2* ĺ Cl + Cl.
i 1
ɪɟɚɤɰɢɣ ɷɬɨɬ ɡɚɤɨɧ, ɫɬɪɨɝɨ ɝɨɜɨɪɹ, ɧɟɩɪɢɦɟɧɢɦ. Ɍɟɦ ɧɟ ɦɟɧɟɟ ɜ ɛɨɥɶɲɨɦ ɱɢɫɥɟ ɫɥɭɱɚɟɜ ɭɞɚɟɬɫɹ ɫɨɯɪɚɧɢɬɶ ɫɬɟɩɟɧɧýɸ ɮɨɪɦɭ ɡɚɤɨɧɚ, ɜɜɟɞɹ ɜ ɧɟɝɨ ɷɦɩɢɪɢɱɟɫɤɢɟ ɩɨɩɪɚɜɤɢ. ɉɨɩɪɚɜɤɢ ɫɨɫɬɨɹɬ ɜ ɡɚɦɟɧɟ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ Qi ɧɟɤɨɬɨɪɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ pi, ɬɚɤ ɱɬɨ m
v k Cipi . i 1
ɉɚɪɚɦɟɬɪɵ pi ɧɚɡɵɜɚɸɬ ɩɨɪɹɞɤɚɦɢ ɩɨ ɪɟɚɝɟɧɬɚɦ, ɚ ɫɭɦɦɭ ɷɬɢɯ ɱɢɫɟɥ – ɨɛɳɢɦ ɩɨɪɹɞɤɨɦ ɪɟɚɤɰɢɢ. ɉɨɪɹɞɤɢ, ɨɩɪɟɞɟɥɹɟɦɵɟ ɫɭɝɭɛɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ, ɦɨɝɭɬ ɛɵɬɶ ɧɟɰɟɥɵɦɢ ɢ ɞɚɠɟ ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ ɱɢɫɥɚɦɢ. Ɂɚ ɤɨɧɫɬɚɧɬɨɣ ɫɤɨɪɨɫɬɢ ɜ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɨɦ ɡɚɤɨɧɟ ɫɨɯɪɚɧɹɟɬɫɹ ɜ ɰɟɥɨɦ ɟɟ ɩɟɪɜɨɧɚɱɚɥɶɧɵɣ ɫɦɵɫɥ, ɯɨɬɹ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɟɟ ɩɪɟɞɩɨɱɢɬɚɸɬ ɧɚɡɵɜɚɬɶ ɷɮɮɟɤɬɢɜɧɨɣ ɤɨɧɫɬɚɧɬɨɣ. ɂɡɜɟɫɬɧɵ ɪɟɚɤɰɢɢ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɚɤɨɝɨ-ɥɢɛɨ ɪɟɚɝɟɧɬɚ (pi = 0) – ɪɟɚɤɰɢɢ ɧɭɥɟɜɨɝɨ ɩɨɪɹɞɤɚ. ȿɫɥɢ ɫɭɦɦɚɪɧɵɣ ɩɨɪɹɞɨɤ ɪɚɜɟɧ ɧɭɥɸ, ɬɨ ɷɬɨ, ɤɚɤ ɪɚɡ, ɬɨɬ ɫɥɭɱɚɣ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ ɩɨɫɬɨɹɧɧɚ.
5. Ʉɢɧɟɬɢɤɚ ɧɟɤɨɬɨɪɵɯ ɩɪɨɫɬɵɯ ɪɟɚɤɰɢɣ
Ɂɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɩɨɡɜɨɥɹɟɬ ɪɟɲɢɬɶ ɨɫɧɨɜɧɭɸ ɡɚɞɚɱɭ ɤɢɧɟɬɢɤɢ. ɉɨɤɚɠɟɦ, ɤɚɤ ɷɬɨ ɩɪɨɢɫɯɨɞɢɬ ɧɚ ɞɜɭɯ ɩɪɢɦɟɪɚɯ. 1. ɉɪɢɦɟɪ ɦɨɧɨɦɨɥɟɤɭɥɹɪɧɨɣ ɪɟɚɤɰɢɢ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɣ ɫɨɛɨɣ ɪɚɫɩɚɞ ɦɨɥɟɤɭɥ ɜɟɳɟɫɬɜɚ A: A ĺ ɩɪɨɞɭɤɬɵ. ɉɨɫɤɨɥɶɤɭ ɜ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɫɤɨɪɨɫɬɢ ɜɯɨɞɹɬ ɬɨɥɶɤɨ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢɫɯɨɞɧɵɯ ɜɟɳɟɫɬɜ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɨɞɧɨɝɨ ɜɟɳɟɫɬɜɚ A), ɯɚɪɚɤɬɟɪ ɩɪɨɞɭɤɬɨɜ ɧɚɦ ɧɟ ɜɚɠɟɧ. ɇɚ ɫɚɦɨɦ ɞɟɥɟ ɩɨɞɨɛɧɵɟ ɪɟɚɤɰɢɢ ɜɫɟɝɞɚ ɹɜɥɹɸɬɫɹ ɛɢɦɨɥɟɤɭɥɹɪɧɵɦɢ. ɂɯ ɦɟɯɚɧɢɡɦ ɫɨɫɬɨɢɬ ɜ ɚɤɬɢɜɚɰɢɢ (ɫɦ. ɞɚɥɟɟ, ɩ. 8) ɱɚɫɬɢɰɵ A ɤɚɤɨɣ-ɥɢɛɨ ɞɪɭɝɨɣ ɱɚɫɬɢɰɟɣ, ɧɚɩɪɢɦɟɪ, ɜɬɨɪɨɣ ɱɚɫɬɢɰɟɣ A: A + A ĺ AA* ɢɥɢ
A + A ĺ A* + A.
ȼɬɨɪɚɹ ɫɯɟɦɚ ɨɡɧɚɱɚɟɬ ɫɬɨɥɤɧɨɜɟɧɢɟ ɢ ɪɚɡɥɟɬ ɱɚɫɬɢɰ, ɩɪɢɱɟɦ ɨɞɧɚ ɢɡ ɧɢɯ ɩɟɪɟɯɨɞɢɬ ɜ ɜɨɡɛɭɠɞɟɧɧɨɟ (ɚɤɬɢɜɢɪɨɜɚɧɧɨɟ) ɫɨɫɬɨɹɧɢɟ A*, ɧɚɩɪɢɦɟɪ, ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɢɹ ɱɚɫɬɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɞɪɭɝɨɣ ɱɚɫɬɢɰɵ. Ⱦɚɥɟɟ ɧɚɫɬɭɩɚɟɬ ɪɚɫɩɚɞ ɚɤɬɢɜɢɪɨɜɚɧɧɨɣ ɱɚɫɬɢɰɵ: 11
Ɉɩɢɫɚɧɢɟ, ɤɨɬɨɪɨɟ ɦɵ ɞɚɞɢɦ ɫɟɣɱɚɫ, ɹɜɥɹɟɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɦ ɢ ɩɪɢɦɟɧɢɦɨ, ɤɨɝɞɚ ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɪɚɫɩɚɞɚ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ.
ɂɬɚɤ, ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɫɤɨɪɨɫɬɢ ɛɭɞɟɬ, ɫɨɝɥɚɫɧɨ (I.6), ɢɦɟɬɶ ɜɢɞ: C A kC A . ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɫ ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ ɧɭɠɧɨ ɪɟɲɢɬɶ ɩɪɢ ɧɚɱɚɥɶɧɨɦ ɭɫɥɨɜɢɢ CA|W = 0 = CA0. ɍɫɥɨɜɢɟ ɜɵɪɚɠɚɟɬ ɩɪɨɫɬɨɣ ɮɚɤɬ, ɱɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, ɤɨɝɞɚ ɧɚɱɚɥɢ ɫɥɟɞɢɬɶ ɡɚ ɫɢɫɬɟɦɨɣ, ɜɟɳɟɫɬɜɨ ɫɨɞɟɪɠɚɥɨɫɶ ɜ ɤɨɧɰɟɧɬɪɚɰɢɢ CA0. Ɋɚɡɞɟɥɹɹ ɩɟɪɟɦɟɧɧɵɟ ɢ ɢɧɬɟɝɪɢɪɭɹ, ɩɨɥɭɱɢɦ: dC A k d W const , ɬɨ ɟɫɬɶ ln CA = – kW + const. CA ɇɟɨɩɪɟɞɟɥɟɧɧɭɸ ɤɨɧɫɬɚɧɬɭ (const) ɧɚɣɞɟɦ, ɢɫɩɨɥɶɡɭɹ ɧɚɱɚɥɶɧɨɟ ɭɫɥɨɜɢɟ. ɉɨɫɥɟ ɨɱɟɜɢɞɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɛɭɞɟɦ ɢɦɟɬɶ: CA(W) = CA0e–kW. (I.7-1) ɉɟɪɟɞ ɧɚɦɢ ɤɢɧɟɬɢɱɟɫɤɢɣ ɡɚɤɨɧ ɪɟɚɤɰɢɢ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ. Ɉɬɫɸɞɚ ɜɢɞɧɨ, ɱɬɨ ɤɢɧɟɬɢɤɚ ɩɪɨɰɟɫɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ, ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ, ɤɨɧɫɬɚɧɬɨɣ ɫɤɨɪɨɫɬɢ. ȿɫɥɢ ɤɨɧɫɬɚɧɬɚ ɦɚɥɚ, ɩɪɨɰɟɫɫ ɦɨɠɟɬ ɛɵɬɶ ɱɪɟɡɜɵɱɚɣɧɨ ɦɟɞɥɟɧɧɵɦ; ɟɫɥɢ ɜɟɥɢɤɚ – ɩɪɚɤɬɢɱɟɫɤɢ ɦɝɧɨɜɟɧɧɵɦ. ȼɜɨɞɹɬ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɜɪɟɦɹ (ɩɟɪɢɨɞ) ɩɨɥɭɩɪɟɜɪɚɳɟɧɢɹ W1/2 – ɜɪɟɦɹ, ɡɚ ɤɨɬɨɪɨɟ ɜɟɳɟɫɬɜɨ ɪɚɫɩɚɞɟɬɫɹ ɧɚɩɨɥɨɜɢɧɭ: CA(W1/2) = 1e2CA0. Ⱦɥɹ ɪɟɚɤɰɢɢ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɨɧɨ ɫɜɹɡɚɧɨ ɬɨɥɶɤɨ ɫ ɤɨɧɫɬɚɧɬɨɣ:
y
y
ln 2 . k
W1/ 2
Ɉɩɪɟɞɟɥɹɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɟɪɢɨɞ W1/2, ɦɨɠɧɨ ɧɚɣɬɢ ɤɨɧɫɬɚɧɬɭ ɫɤɨɪɨɫɬɢ. ɉɭɫɬɶ ɬɟɩɟɪɶ ɩɪɨɞɭɤɬɵ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɞɜɚ «ɨɫɤɨɥɤɚ» ɦɨɥɟɤɭɥɵ A, ɬɨ ɟɫɬɶ ɩɪɨɰɟɫɫ ɢɦɟɟɬ ɜɢɞ: A ĺ B1 + B2. Ʉɢɧɟɬɢɱɟɫɤɢɣ ɡɚɤɨɧ ɞɥɹ CA ɧɟ ɢɡɦɟɧɢɬɫɹ. Ⱦɥɹ ɩɪɨɞɭɤɬɨɜ Bj ɟɝɨ ɧɟɫɥɨɠɧɨ ɧɚɣɬɢ ɩɨ ɫɬɟɯɢɨɦɟɬɪɢɢ. ȼɨ-ɩɟɪɜɵɯ, ɹɫɧɨ, ɱɬɨ CB1 = CB2 ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ W. ȼɨ-ɜɬɨɪɵɯ, CBj = CA0 – CA, ɩɨɷɬɨɦɭ CBj(W) = CA0(1 – e–kW). (I.7-2) ɇɚɤɨɧɟɰ, ɞɥɹ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɩɨɥɭɱɢɦ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣ ɡɚɬɭɯɚɸɳɢɣ ɡɚɤɨɧ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɪɟɦɟɧɢ: B
B
B
12
v(W) = kCA0e–kW. ɉɨɫɬɚɜɥɟɧɧɚɹ ɡɚɞɚɱɚ ɩɨɥɧɨɫɬɶɸ ɪɟɲɟɧɚ. 2. Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɛɢɦɨɥɟɤɭɥɹɪɧɭɸ ɪɟɚɤɰɢɸ ɬɢɩɚ (11): A + B ĺ ɩɪɨɞɭɤɬɵ. Ɉɫɧɨɜɧɨɟ ɤɢɧɟɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɢɦɟɟɬ ɜɢɞ:
C A
6. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɪɟɚɤɰɢɢ
Ʉɚɤ ɦɵ ɨɬɦɟɱɚɥɢ, ɛɨɥɶɲɢɧɫɬɜɨ ɪɟɚɤɰɢɣ ɢɞɭɬ ɧɟ ɨɞɧɨɚɤɬɧɨ, ɚ ɜ ɧɟɫɤɨɥɶɤɨ ɫɬɚɞɢɣ. ȼɨɡɦɨɠɧɵ ɩɪɨɰɟɫɫɵ, ɪɚɡɜɢɜɚɸɳɢɟɫɹ ɫɪɚɡɭ ɩɨ ɞɜɭɦ ɢɥɢ ɧɟɫɤɨɥɶɤɢɦ ɩɭɬɹɦ. ɇɚɩɪɢɦɟɪ,
kC ACB
(I.8) ɫ ɧɚɱɚɥɶɧɵɦ ɭɫɥɨɜɢɟɦ CA|W = 0 = CA ɢ CB|W = 0 = CB . ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ ɫɤɨɪɨɫɬɢ (I.4) ɭɪɚɜɧɟɧɢɟ (I.8) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɤɚɤ ɨɬɧɨɫɢɬɟɥɶɧɨ CA, ɬɚɤ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨ CB ɜ ɥɟɜɨɣ ɱɚɫɬɢ. Ɏɭɧɤɰɢɢ CA ɢ CB ɧɟ ɹɜɥɹɸɬɫɹ ɧɟɡɚɜɢɫɢɦɵɦɢ, ɚ ɢɦɟɧɧɨ, ɩɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɦɭ ɡɚɤɨɧɭ (I.2) CA – CA0 = CB – CB0. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ (I.8) ɩɪɢɜɨɞɢɬɫɹ ɤ ɜɢɞɭ: C A kC A (CB0 C A0 C A ) . ɗɬɨ ɧɟɨɞɧɨɪɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ ɭɠɟ ɧɟɥɶɡɹ ɪɟɲɢɬɶ ɩɪɹɦɵɦ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ. Ɍɚɤɢɟ ɭɪɚɜɧɟɧɢɹ ɪɟɲɚɸɬ ɦɟɬɨɞɨɦ ɜɚɪɢɚɰɢɢ ɩɪɨɢɡɜɨɥɶɧɨɣ ɩɨɫɬɨɹɧɧɨɣ. Ɉɞɧɚɤɨ ɨɧɨ ɭɩɪɨɳɚɟɬɫɹ ɢ ɫɜɨɞɢɬɫɹ ɤ ɭɪɚɜɧɟɧɢɸ ɫ ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ, ɟɫɥɢ ɩɨɥɨɠɢɬɶ CA0 = CB0: C A kC A2 . ȼɵɱɢɫɥɹɹ ɢɧɬɟɝɪɚɥ ɢ ɩɪɢɦɟɧɹɹ ɧɚɱɚɥɶɧɨɟ ɭɫɥɨɜɢɟ, ɩɨɥɭɱɢɦ: 0
.
0
C A (W)
C A0 . 1 kC A0 W
ɗɬɨ ɦɨɧɨɬɨɧɧɨ ɭɛɵɜɚɸɳɚɹ ɮɭɧɤɰɢɹ, ɢɦɟɸɳɚɹ ɩɪɟɞɟɥ ɩɪɢ W ĺ f, ɪɚɜɧɵɣ 0. ɂɧɬɟɪɟɫɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɫɨɝɥɚɫɧɨ ɜɵɜɟɞɟɧɧɵɦ ɤɢɧɟɬɢɱɟɫɤɢɦ ɭɪɚɜɧɟɧɢɹɦ ɡɚɜɢɫɢɦɨɫɬɢ Ci(W) ɧɟ ɞɨɫɬɢɝɚɸɬ ɫɜɨɟɣ ɧɢɠɧɟɣ ɝɪɚɧɢ – ɧɭɥɹ. ɗɬɨ ɞɨɥɠɧɨ ɨɡɧɚɱɚɬɶ, ɱɬɨ ɩɪɟɜɪɚɳɚɸɳɟɟɫɹ ɜɟɳɟɫɬɜɨ ɧɢɤɨɝɞɚ ɧɟ ɢɫɱɟɪɩɚɟɬɫɹ, ɚ ɫɚɦɚ ɪɟɚɤɰɢɹ ɧɢɤɨɝɞɚ ɧɟ ɡɚɤɨɧɱɢɬɫɹ. Ʉɚɠɟɬɫɹ, ɱɬɨ ɷɬɨ ɹɜɧɨ ɩɪɨɬɢɜɨɪɟɱɢɬ ɧɚɛɥɸɞɟɧɢɹɦ ɢ ɡɞɪɚɜɨɦɭ ɫɦɵɫɥɭ. Ⱦɟɥɨ ɠɟ ɨɛɫɬɨɢɬ ɬɚɤ. ȼɨ-ɩɟɪɜɵɯ, ɤɚɤ ɦɵ ɭɜɢɞɢɦ ɞɚɥɟɟ, ɜɫɟ ɪɟɚɤɰɢɢ ɹɜɥɹɸɬɫɹ ɜ ɬɨɣ ɢɥɢ ɢɧɨɣ ɫɬɟɩɟɧɢ ɨɛɪɚɬɢɦɵɦɢ, ɢ ɮɢɧɚɥɨɦ ɩɪɨɰɟɫɫɚ ɛɭɞɟɬ ɫɨɫɬɨɹɧɢɟ ɪɚɜɧɨɜɟɫɢɹ, ɜ ɤɨɬɨɪɨɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɫɟɯ ɜɟɳɟɫɬɜ (ɢ ɢɫɯɨɞɧɵɯ ɢ ɩɪɨɞɭɤɬɨɜ) ɨɬɥɢɱɧɵ ɨɬ ɧɭɥɹ. ȼɨ-ɜɬɨɪɵɯ, ɟɫɥɢ ɪɟɚɤɰɢɹ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɨɛɪɚɬɢɦɚ, ɬɨ ɧɚɛɥɸɞɚɟɦɵɣ «ɦɨɦɟɧɬ» ɡɚɜɟɪɲɟɧɢɹ ɪɟɚɤɰɢɢ ɫɨɜɩɚɞɚɟɬ ɫ ɬɟɦ ɦɨɦɟɧɬɨɦ (Wf), ɤɨɝɞɚ ɜ ɫɢɫɬɟɦɟ ɩɟɪɟɫɬɚɟɬ ɨɛɧɚɪɭɠɢɜɚɬɶɫɹ ɜɟɳɟɫɬɜɨ. ɗɬɨ ɫɨɫɬɨɹɧɢɟ ɧɚɫɬɭɩɢɬ, ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ CA ɫɬɚɧɟɬ ɦɟɧɶɲɟ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɢ ɩɪɢɛɨɪɚ GCA, ɢɡɦɟɪɹɸɳɟɝɨ ɷɬɭ ɤɨɧɰɟɧɬɪɚɰɢɸ. Ⱦɥɹ ɪɟɚɤɰɢɢ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ 0 A
1 C Wf · ln . k GC A ɇɚɩɪɢɦɟɪ, ɟɫɥɢ ɩɟɪɢɨɞ ɩɨɥɭɩɪɟɜɪɚɳɟɧɢɹ W1/2 = 10 ɫ, ɚ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ GCA = 10–5 ɦɨɥɶeɥ, ɬɨ Wf · 166 ɫ ɩɪɢ ɧɚɱɚɥɶɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ 1 ɦɨɥɶeɥ.
13
Ɍɚɤɢɟ ɩɪɨɰɟɫɫɵ ɧɚɡɵɜɚɸɬ ɩɚɪɚɥɥɟɥɶɧɵɦɢ. Ⱦɪɭɝɨɣ ɬɢɩ ɫɥɨɠɧɵɯ ɪɟɚɤɰɢɣ – ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ, ɜ ɤɨɬɨɪɵɯ ɜɟɳɟɫɬɜɚ ɩɟɪɟɯɨɞɹɬ ɞɪɭɝ ɜ ɞɪɭɝɚ ɩɨ ɰɟɩɨɱɤɟ ɩɪɟɜɪɚɳɟɧɢɣ. Ɋɚɫɫɦɨɬɪɢɦ ɞɜɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɦɨɧɨɦɨɥɟɤɭɥɹɪɧɵɟ ɪɟɚɤɰɢɢ, ɢɞɭɳɢɟ ɩɨ ɫɯɟɦɟ: A' I ' B . 1
2
ȼɟɳɟɫɬɜɨ I, ɨɛɪɚɡɭɸɳɟɟɫɹ ɜ ɩɟɪɜɨɣ ɪɟɚɤɰɢɢ A ĺ I ɢ ɪɚɫɯɨɞɭɸɳɟɟɫɹ ɜɨ ɜɬɨɪɨɣ I ĺ B, ɧɚɡɵɜɚɸɬ ɩɪɨɦɟɠɭɬɨɱɧɵɦ. ɋɥɟɞɭɟɬ ɩɨɞɱɟɪɤɧɭɬɶ: ɩɨɞɨɛɧɚɹ ɪɟɚɤɰɢɨɧɧɚɹ ɫɯɟɦɚ ɧɟ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɧɚɱɚɥɚ ɡɚɜɟɪɲɚɟɬɫɹ ɩɪɟɜɪɚɳɟɧɢɟ 1, ɚ ɩɨɫɥɟ ɬɨɝɨ ɧɚɱɢɧɚɟɬɫɹ ɩɪɟɜɪɚɳɟɧɢɟ 2. Ʉɚɤ ɬɨɥɶɤɨ ɜ ɫɢɫɬɟɦɟ ɩɨɹɜɢɬɫɹ ɜɟɳɟɫɬɜɨ I, ɨɧɨ ɜɫɬɭɩɚɟɬ ɜ ɫɥɟɞɭɸɳɭɸ ɪɟɚɤɰɢɸ, ɢ ɨɛɚ ɩɪɨɰɟɫɫɚ ɢɞɭɬ ɨɞɧɨɜɪɟɦɟɧɧɨ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɤɢɧɟɬɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɢɫɯɨɞɧɨɝɨ ɜɟɳɟɫɬɜɚ A ɢ ɮɢɧɚɥɶɧɨɝɨ ɩɪɨɞɭɤɬɚ B ɢɦɟɸɬ ɜɢɞ: C A k1C A , C B k2CI , ɝɞɟ k1 ɢ k2 – ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɟɣ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɪɟɚɤɰɢɣ. Ɋɟɲɟɧɢɟ ɩɟɪɜɨɝɨ ɭɪɚɜɧɟɧɢɹ ɧɟ ɜɵɡɵɜɚɟɬ ɡɚɬɪɭɞɧɟɧɢɣ: ɨɧɨ ɭɠɟ ɩɨɥɭɱɟɧɨ ɩɨɞ ɧɨɦɟɪɨɦ (I.7-1). ɑɬɨɛɵ ɪɟɲɢɬɶ ɜɬɨɪɨɟ ɭɪɚɜɧɟɧɢɟ ɬɪɟɛɭɟɬɫɹ ɡɧɚɬɶ ɮɭɧɤɰɢɸ CI(W), ɩɨ ɤɨɬɨɪɨɣ ɢɡɦɟɧɹɟɬɫɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɜɟɳɟɫɬɜɚ. Ⱦɥɹ ɷɬɨɣ ɩɨɫɥɟɞɧɟɣ ɦɨɠɟɦ ɡɚɩɢɫɚɬɶ: C I v1 v2 k1C A k2CI . ɉɨɞɫɬɚɜɥɹɹ ɫɸɞɚ ɮɭɧɤɰɢɸ (I.7-1), ɩɨɥɭɱɢɦ: C I k2CI k1C A0 e k1W . ɗɬɨ ɧɟɨɞɧɨɪɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɫɨɞɟɪɠɚɳɟɟ ɹɜɧɭɸ ɮɭɧɤɰɢɸ ɜɪɟɦɟɧɢ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ, ɢɦɟɟɬ ɪɟɲɟɧɢɟ
CI (W) C A0
k1 e k1W e k2W k2 k1
(I.9)
ɩɪɢ ɧɚɱɚɥɶɧɨɦ ɭɫɥɨɜɢɢ CI|W = 0 = 0. Ɍɨɝɞɚ ɞɥɹ ɩɪɨɞɭɤɬɚ ɪɟɚɤɰɢɢ B ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ (I.9) ɜ ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɫɤɨɪɨɫɬɢ ɟɝɨ ɧɚɤɨɩɥɟɧɢɹ ɢɦɟɟɦ:
C B
C A0
k1k2 e k1W e k2W . k2 k1 14
ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɢɧɬɟɝɪɢɪɭɟɬɫɹ ɭɠɟ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ, ɩɨɫɤɨɥɶɤɭ ɩɟɪɟɦɟɧɧɵɟ CB ɢ W ɜ ɧɟɦ ɪɚɡɞɟɥɟɧɵ: ɩɪɢ ɧɚɱɚɥɶɧɨɦ ɭɫɥɨɜɢɢ CI|W = 0 = 0 CB ( W )
y
dCB
0
C A0
k1k2 k2 k1
W
y e
k1W
e k2W d W .
0
ɉɨɫɥɟ ɜɵɱɢɫɥɟɧɢɹ ɢɧɬɟɝɪɚɥɚ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɩɨɥɭɱɚɟɬɫɹ:
k2 k1 CB (W) C A0 §¨1 e k1W e k2W ·¸ . k2 k1 © k2 k1 ¹
(I.10)
ɉɪɨɚɧɚɥɢɡɢɪɭɟɦ ɩɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ. ɇɚɢɛɨɥɟɟ ɢɧɬɟɪɟɫɧɨ ɩɨɜɟɞɟɧɢɟ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɜɟɳɟɫɬɜɚ I, ɤɨɧɰɟɧɬɪɚɰɢɹ ɤɨɬɨɪɨɝɨ ɧɟɦɨɧɨɬɨɧɧɨ ɢɡɦɟɧɹɟɬɫɹ ɫɨ ɜɪɟɦɟɧɟɦ. Ɏɭɧɤɰɢɹ (I.9) ɹɜɥɹɟɬɫɹ ɤɨɦɛɢɧɚɰɢɟɣ ɞɜɭɯ ɷɤɫɩɨɧɟɧɬ ɢ ɢɦɟɟɬ ɦɚɤɫɢɦɭɦ ɜ ɬɨɱɤɟ
Wmax
1 ln K , ɝɞɟ k2 k1
K
k2 k1
ɗɬɨ ɡɧɚɱɢɬ, ɱɬɨ ɩɪɨɞɭɤɬ ɧɚɤɚɩɥɢɜɚɟɬɫɹ ɬɚɤ, ɤɚɤ ɟɫɥɢ ɛɵ ɲɥɚ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɪɟɚɤɰɢɹ A ĺ B ɫ ɤɨɧɫɬɚɧɬɨɣ k2. 2. ɉɭɫɬɶ ɬɟɩɟɪɶ k1 " k2. Ɍɨɝɞɚ, ɩɪɟɧɟɛɪɟɝɚɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɱɥɟɧɚɦɢ ɜ (I.10), ɦɨɠɟɦ ɡɚɩɢɫɚɬɶ: CB(W) = CA0(1 – e–k1W). Ɉɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɪɚɡɨɜɚɧɢɟ ɜɟɳɟɫɬɜɚ B ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɦɟɞɥɟɧɧɨɣ ɪɟɚɤɰɢɢ 1, ɚ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɜɟɳɟɫɬɜɨ ɧɚɫɬɨɥɶɤɨ ɚɤɬɢɜɧɨ, ɱɬɨ ɜɫɬɭɩɚɟɬ ɜ ɪɟɚɤɰɢɸ, ɧɟ ɭɫɩɟɜɚɹ ɨɛɪɚɡɨɜɚɬɶɫɹ. ɗɬɢ ɩɪɟɞɟɥɶɧɵɟ ɫɥɭɱɚɢ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɩɪɢ ɡɧɚɱɢɬɟɥɶɧɨɦ ɧɟɪɚɜɟɧɫɬɜɟ ɤɨɧɫɬɚɧɬ ɫɤɨɪɨɫɬɶ ɨɛɪɚɡɨɜɚɧɢɹ ɩɨɫɥɟɞɧɟɝɨ ɜɟɳɟɫɬɜɚ ɜ ɰɟɩɨɱɤɟ ɩɪɟɜɪɚɳɟɧɢɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫ ɚ ɦ ɨ ɣ ɦ ɟ ɞ ɥ ɟ ɧ ɧ ɨ ɣ ɫ ɬ ɚ ɞ ɢ ɟ ɣ . Ɉɛ ɷɬɨɦ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɦ ɹɜɥɟɧɢɢ ɝɨɜɨɪɹɬ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɣ ɪɟɚɤɰɢɢ ɥɢɦɢɬɢɪɭɟɬɫɹ ɦɟɞɥɟɧɧɨɣ ɫɬɚɞɢɟɣ. 7. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ
ɹɜɥɹɟɬɫɹ ɨɬɧɨɲɟɧɢɟɦ ɤɨɧɫɬɚɧɬ ɫɤɨɪɨɫɬɟɣ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɜɟɳɟɫɬɜɨ ɞɨ ɧɟɤɨɬɨɪɨɝɨ ɦɨɦɟɧɬɚ ɧɚɤɚɩɥɢɜɚɟɬɫɹ, ɚ ɞɚɥɟɟ ɢɫɱɟɡɚɟɬ. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɤɪɢɜɚɹ ɞɥɹ ɧɟɝɨ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 1. ȼɟɳɟɫɬɜɨ B ɜɟɞɟɬ ɫɟɛɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɧɚ ɟɝɨ ɤɢɧɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ ɢɦɟɟɬɫɹ ɩɟɪɟɝɢɛ, ɫɨɜɩɚɞɚɸɳɢɣ ɩɨ ɜɪɟɦɟɧɢ ɫ ɬɨɱɤɨɣ ɦɚɤɫɢɦɭɦɚ ɧɚ ɤɪɢɜɨɣ CI (ɪɢɫ. 1). ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɪɨɞɭɤɬɚ B ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ ɢ, ɯɨɬɹ ɪɚɫɬɟɬ ɫ ɜɨɡɪɚɫɬɚɸɳɟɣ ɫɤɨɪɨɫɬɶɸ, ɦɨɠɟɬ ɜɨɨɛɳɟ ɧɟ ɨɛɧɚɪɭɠɢɜɚɬɶɫɹ. ȼɪɟɦɹ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɩɪɨɞɭɤɬ ɧɟɜɨɡɦɨɠɧɨ ɨɛɧɚɪɭɠɢɬɶ, ɧɚɡɵɜɚɟɬɫɹ ɢɧɞɭɤɰɢɨɧɧɵɦ ɩɟɪɢɨɞɨɦ. Ʉɪɨɦɟ ɫɨɨɬɧɨɲɟɧɢɹ ɤɨɧɫɬɚɧɬ ɫɤɨɪɨɫɬɟɣ ɨɧ ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶɸ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ. Ɋɚɫɫɦɨɬɪɢɦ ɜ ɫɜɹɡɢ ɫ ɷɬɢɦ ɞɜɚ ɩɪɟɞɟɥɶɧɵɯ ɪɟɠɢɦɚ, ɜ ɤɨɬɨɪɵɯ ɦɨɝɭɬ ɩɪɨɬɟɤɚɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɪɟɚɤɰɢɢ. Ɋɢɫ. 1 1. ɉɨɫɤɨɥɶɤɭ ɦɚɤɫɢɦɭɦ ɤɨɧɰɟɧɬɪɚɰɢɢ I ɫɨɜɩɚɞɚɟɬ ɩɨ ɜɪɟɦɟɧɢ ɫ ɬɨɱɤɨɣ ɩɟɪɟɝɢɛɚ ɧɚ ɤɪɢɜɨɣ CB, ɢɧɞɭɤɰɢɨɧɧɵɣ ɩɟɪɢɨɞ ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɦɟɧɶɲɟ ɨɬɧɨɲɟɧɢɟ ɤɨɧɫɬɚɧɬ K, ɬɨ ɟɫɬɶ, ɱɟɦ ɦɟɞɥɟɧɧɟɟ ɜɬɨɪɚɹ ɫɬɚɞɢɹ. ȼ ɩɪɟɞɟɥɟ, ɤɨɝɞɚ k2 ĺ 0, ɩɪɨɞɭɤɬ ɜɨɨɛɳɟ ɧɟ ɩɨɹɜɥɹɟɬɫɹ – ɜɬɨɪɚɹ ɪɟɚɤɰɢɹ ɩɪɨɫɬɨ ɧɟ ɢɞɟɬ. ȿɫɥɢ ɠɟ k2 " k1 (ɧɨ ɤɨɧɟɱɧɨ!), ɬɨ ɜ ɭɪɚɜɧɟɧɢɢ (I.10) ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɱɥɟɧɨɦ, ɫɨɞɟɪɠɚɳɢɦ e–k1W, ɢ ɜɟɥɢɱɢɧɨɣ k2 ɜ ɡɧɚɦɟɧɚɬɟɥɟ. Ɍɨɝɞɚ ɜɦɟɫɬɨ (I.10) ɩɨɥɭɱɢɬɫɹ ɮɭɧɤɰɢɹ, ɩɪɢɛɥɢɠɟɧɧɨ ɫɨɜɩɚɞɚɸɳɚɹ ɫ (I.7-2): CB(W) = CA0(1 – e–k2W).
ȼ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ ɡɚɤɨɧɚ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɜɟɥɢɱɢɧɨɣ, ɡɚɜɢɫɹɳɟɣ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɹɜɥɹɟɬɫɹ ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ. Ɇɨɠɧɨ ɫɤɚɡɚɬɶ, ɱɬɨ ɜ ɷɬɨɦ ɭɪɚɜɧɟɧɢɢ ɪɚɡɞɟɥɟɧɵ ɩɟɪɟɦɟɧɧɵɟ: v = k(T)f(C), ɝɞɟ k – ɮɭɧɤɰɢɹ ɬɨɥɶɤɨ ɬɟɦɩɟɪɚɬɭɪɵ, f – ɮɭɧɤɰɢɹ ɬɨɥɶɤɨ ɤɨɧɰɟɧɬɪɚɰɢɣ. ɉɨɷɬɨɦɭ ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɮɨɪɦɭɥɢɪɭɟɬɫɹ ɢɦɟɧɧɨ ɞɥɹ ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɢ. Ɉɩɢɲɟɦ ɜ ɧɚɱɚɥɟ ɞɜɟ ɷɦɩɢɪɢɱɟɫɤɢɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ. 1. ɋɨɝɥɚɫɧɨ ɩɪɚɜɢɥɭ ȼɚɧɬ-Ƚɨɮɮɚ (J. H. van’t Hoff, 1884) ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɜ ɨɞɧɨ ɢ ɬɨ ɠɟ ɱɢɫɥɨ ɪɚɡ ɩɪɢ ɤɚɠɞɨɦ ɭɜɟɥɢɱɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ ɨɞɧɭ ɢ ɬɭ ɠɟ ɜɟɥɢɱɢɧɭ 'T:
15
16
k(T 'T ) k(T )
J ( 'T ) .
(I.11)
Ʉɨɷɮɮɢɰɢɟɧɬ J ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ T, ɧɨ ɡɚɜɢɫɢɬ ɨɬ ɟɟ ɩ ɪ ɢ ɪ ɚ ɳ ɟ ɧ ɢ ɹ 'T. Ɇɵ ɧɚɡɨɜɟɦ ɟɝɨ ɝɪɚɞɭɫɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ȼɚɧɬ-Ƚɨɮɮɚ. Ⱦɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɪɟɚɤɰɢɣ ɜɟɥɢɱɢɧɚ J (10 Ʉ) ɥɟɠɢɬ ɜ ɢɧɬɟɪɜɚɥɟ ɨɬ 2 ɞɨ 4, ɬɨ ɟɫɬɶ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ 10 Ʉ ɫɤɨɪɨɫɬɶ ɜɨɡɪɚɫɬɚɟɬ ɜ 2–4 ɪɚɡɚ. ɋɭɳɟɫɬɜɭɸɬ, ɨɞɧɚɤɨ, ɪɟɚɤɰɢɢ, ɞɟɫɹɬɢɝɪɚɞɭɫɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɬɨɪɵɯ ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɹ J (10 Ʉ) 10 . 2. ɏɨɪɨɲɨ ɨɩɢɫɵɜɚɸɳɢɦ ɬɟɦɩɟɪɚɬɭɪɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɛɨɥɶɲɢɧɫɬɜɚ ɪɟɚɤɰɢɣ ɨɤɚɡɚɥɨɫɶ ɭɪɚɜɧɟɧɢɟ, ɩɪɟɞɥɨɠɟɧɧɨɟ Ⱥɪɪɟɧɢɭɫɨɦ (S. A. Arrhenius, 1889): k(T ) k0 e Ea RT . (I.12) Ɂɞɟɫɶ k0 ɢ Ea – ɩɚɪɚɦɟɬɪɵ, ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɹɳɢɟ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. ȼɟɥɢɱɢɧɚ Ea, ɢɦɟɸɳɚɹ ɪɚɡɦɟɪɧɨɫɬɶ ɷɧɟɪɝɢɢ, ɧɚɡɵɜɚɟɬɫɹ ɷɧɟɪɝɢɟɣ ɚɤɬɢɜɚɰɢɢ,
ɟɟ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɫɬɚɧɟɬ ɹɫɟɧ ɩɨɡɞɧɟɟ. Ʉɚɤ ɩɪɚɜɢɥɨ, ɷɧɟɪɝɢɹ ɚɤɬɢɜɚɰɢɢ ɫɨɫɬɚɜɥɹɟɬ ɨɬ 50 ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɫɨɬɟɧ ɤȾɠeɦɨɥɶ. Ƚɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ k(T) ɩɨ ɭɪɚɜɧɟɧɢɸ Ⱥɪɪɟɧɢɭɫɚ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫ. 2. ɇɚ ɧɟɦ ɜ ɤɚɱɟɫɬɜɟ ɤɨɨɪɞɢɧɚɬ ɢɫɩɨɥɶɡɨɜɚɧɵ ɛɟɡɪɚɡɦɟɪɧɵɟ ɨɬɧɨɲɟɧɢɹ k/k0 ɢ T/Ta, ɝɞɟ Ta = Ea/R – ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɚɤɬɢɜɚɰɢɢ. Ɂɚɜɢɫɢɦɨɫɬɶ ɛɵɫɬɪɨ ɜɨɡɪɚɫɬɚɟɬ ɧɚ ɧɚɱɚɥɶɧɨɦ ɭɱɚɫɬɤɟ ɢ ɢɦɟɟɬ ɩɟɪɟɝɢɛ ɩɪɢ T = 1e2Ta. ȿɫɥɢ Ea = 50 ɤȾɠeɦɨɥɶ, ɬɨ ɬɟɦɩɟɪɚɬɭɪɚ ɩɟɪɟɝɢɛɚ ɫɨɫɬɚɜɥɹɟɬ ɨɤɨɥɨ 3000 Ʉ. ɉɨɷɬɨɦɭ ɨɛɵɱɧɵɟ ɭɫɥɨɜɢɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɩɪɨɢɫɯɨɞɢɬ ɛɨɥɶɲɢɧɫɬɜɨ ɪɟɚɤɰɢɣ, ɩɪɢɯɨɞɹɬɫɹ ɧɚ ɛɵɫɬɪɨɜɨɡɪɚɫɬɚɸɳɭɸ ɱɚɫɬɶ. ɋɜɟɪɯɭ ɮɭɧɤɰɢɹ (I.12) ɨɝɪɚɧɢɱɟɧɚ ɩɪɟɞɟɥɨɦ k0 lim e Ta T k0 . T 'f
ɇɚɣɞɟɦ ɫɜɹɡɶ ɦɟɠɞɭ ɭɪɚɜɧɟɧɢɟɦ Ⱥɪɪɟɧɢɭɫɚ ɢ ɩɪɚɜɢɥɨɦ ȼɚɧɬ-Ƚɨɮɮɚ. Ⱦɥɹ ɷɬɨɝɨ ɢɡ ɮɨɪɦɭɥɵ (I.11) ɜɵɪɚɡɢɦ ɩɪɨɢɡɜɨɞɧɭɸ ɩɨ ɬɟɦɩɟɪɚɬɭɪɟ:
dk dT
ɉɪɟɞɟɥ J
lim
lim
'T '0
k(T 'T ) k(T ) 'T
k(T ) lim
'T '0
J ('T ) 1 . 'T
J ( 'T ) 1
ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɜɵɪɚɠɟɧɢɹ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. ɗɬɭ ɜɟ'T ɥɢɱɢɧɭ ɦɵ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ȼɚɧɬ-Ƚɨɮɮɚ. Ɉɬɫɸɞɚ 'T '0
dk dT
Jk(T )
ɢɥɢ
k(T ) ae JT
(I.13)
ɩɨɫɥɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ (a – ɩɨɫɬɨɹɧɧɚɹ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɝɥɚɫɧɨ ɩɪɚɜɢɥɭ ȼɚɧɬ-Ƚɨɮɮɚ, ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɪɚɫɬɟɬ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ. ɋɜɹɡɶ ɦɟɠɞɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɢ ɝɪɚɞɭɫɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɢɦɟɟɬ ɜɢɞ:
J ('T )
k(T 'T ) k(T )
e J'T .
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɞɢɮɮɟɪɟɧɰɢɪɭɹ ɭɪɚɜɧɟɧɢɟ Ⱥɪɪɟɧɢɭɫɚ, ɧɚɣɞɟɦ:
ɢɥɢ
Ɋɢɫ. 2
Ɋɢɫ. 3
ɗɧɟɪɝɢɹ ɚɤɬɢɜɚɰɢɢ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ, ɫ ɨɞɧɨɣ ɫɬɨɪɨɧɵ ɨɩɪɟɞɟɥɹɸɳɟɣ ɬɟɦɩɟɪɚɬɭɪɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ, ɫ ɞɪɭɝɨɣ – ɩɪɢɧɰɢɩɢɚɥɶɧɵɦ ɨɛɪɚɡɨɦ ɫɜɹɡɚɧɧɨɣ ɫ ɦɟɯɚɧɢɡɦɨɦ ɪɟɚɤɰɢɢ. ɉɨɷɬɨɦɭ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɯɢɦɢɢ ɨɱɟɧɶ ɜɚɠɧɨ ɨɩɪɟɞɟɥɟɧɢɟ ɷɧɟɪɝɢɣ ɚɤɬɢɜɚɰɢɢ ɪɚɡɥɢɱɧɵɯ ɪɟɚɤɰɢɣ. Ɉɛɵɱɧɨ ɞɥɹ ɷɬɨɝɨ ɩɪɢɦɟɧɹɟɬɫɹ ɫɥɟɞɭɸɳɢɣ ɩɪɢɟɦ. ɍɪɚɜɧɟɧɢɟ (I.12) ɩɨɫɥɟ ɥɨɝɚɪɢɮɦɢɪɨɜɚɧɢɹ ɦɨɠɧɨ ɩɟɪɟɩɢɫɚɬɶ ɜ ɜɢɞɟ:
ln k ln k0
Ea 1 . R T
dk dT
k0e Ea
dk dT
k
RT
Ea RT 2
Ea . RT 2
(I.14)
ɋɪɚɜɧɢɦ ɬɟɩɟɪɶ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɭɸ ɮɨɪɦɭ ɩɪɚɜɢɥɚ ȼɚɧɬ-Ƚɨɮɮɚ (I.13) ɫ ɭɪɚɜɧɟɧɢɟɦ Ⱥɪɪɟɧɢɭɫɚ. ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɭɪɚɜɧɟɧɢɹ (I.13) ɜ (I.14) ɩɨɥɭɱɚɟɬɫɹ, ɱɬɨ J = Ea/RT2. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɤɨɷɮɮɢɰɢɟɧɬ ȼɚɧɬ-Ƚɨɮɮɚ ɧɟ ɹɜɥɹɟɬɫɹ ɫɬɪɨɝɨ ɩɨɫɬɨɹɧɧɵɦ. ɇɨ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɜɵɊɢɫ. 4 ɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ (ɤɨɦɧɚɬɧɨɣ ɢ ɜɵɲɟ) ɜɟɥɢɱɢɧɚ Ea/RT2 ɦɟɧɹɟɬɫɹ ɦɟɞɥɟɧɧɨ. ɗɬɨ ɢ ɩɪɢɜɨɞɢɬ ɤ ɩɪɢɛɥɢɠɟɧɧɨɦɭ ɜɵɩɨɥɧɟɧɢɸ ɩɪɚɜɢɥɚ ȼɚɧɬ-Ƚɨɮɮɚ. ȿɫɥɢ ɷɧɟɪɝɢɹ ɚɤɬɢɜɚɰɢɢ ɥɟɠɢɬ ɜ ɢɧɬɟɪɜɚɥɟ ɨɬ 50 ɞɨ 100 ɤȾɠ/ɦɨɥɶ, ɬɨ 10-ɝɪɚɞɭɫɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ J (10 Ʉ) ɨɫɬɚɟɬɫɹ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 2 ɞɨ 4 ɩɪɢ 298 Ʉ. ɋɪɚɜɧɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɟɣ ɩɨ ȼɚɧɬ-Ƚɨɮɮɭ ɢ Ⱥɪɪɟɧɢɭɫɭ ɞɚɧɨ ɧɚ ɪɢɫ. 4.
8. Ɉ ɬɟɨɪɢɢ ɚɤɬɢɜɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ
k(T) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɹɦɭɸ ɜɨ ɜɫɟɣ ɨɛɥɚɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ T > 0 (ɪɢɫ. 3). Ɉɩɪɟɞɟɥɹɹ ɟɟ ɩɚɪɚɦɟɬɪɵ ɥɟɝɤɨ ɜɵɱɢɫɥɢɬɶ ɷɧɟɪɝɢɸ ɚɤɬɢɜɚɰɢɢ ɢ ɩɪɟɞɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣ ɦɧɨɠɢɬɟɥɶ k0. ɉɨɞɨɛɧɵɣ ɩɪɢɟɦ ɧɚɡɵɜɚɟɬɫɹ ɥɢɧɟɚɪɢɡɚɰɢɟɣ.
Ɇɵ ɩɪɢɞɟɪɠɢɜɚɟɦɫɹ ɬɚɤɨɝɨ ɜɡɝɥɹɞɚ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɣ ɚɤɬ ɪɟɚɤɰɢɢ, ɱɬɨ ɨɧ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɧɚɦ ɩɪɨɢɫɯɨɞɹɳɢɦ ɜ ɦɨɦɟɧɬ ɫɨɭɞɚɪɟɧɢɹ ɱɚɫɬɢɰ. ɗɬɚ ɬɨɱɤɚ ɡɪɟɧɢɹ ɩɨɡɜɨɥɹɟɬ ɨɛɨɫɧɨɜɚɬɶ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɭɫɬɚɧɨɜɥɟɧɧɵɣ ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ, ɨɞɧɚɤɨ ɨɧɚ ɧɟ ɝɨɞɢɬɫɹ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɫɤɨɪɨɫɬɢ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɱɚɫɬɨɬɚ ɫɨɭɞɚɪɟɧɢɣ ɜɨɡɪɚɫɬɚɟɬ ɤɚɤ z T1/2 (ɮɨɪɦɭɥɚ (I.5)), ɬɨ ɟɫɬɶ ɦɟɧɹɟɬɫɹ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ ɞɨɜɨɥɶɧɨ ɦɟɞɥɟɧɧɨ. ɋɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ, ɧɚɩɪɨɬɢɜ, ɨɱɟɧɶ ɪɟɡɤɨ ɡɚɜɢɫɢɬ ɨɬ T. ɍɠɟ ɢɡ ɨɛɳɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɩɨɧɹɬɧɨ, ɱɬɨ ɧɟ ɤɚɠɞɨɟ ɫɬɨɥɤɧɨɜɟɧɢɟ ɩɪɢɜɨɞɢɬ ɤ ɪɟɚɝɢɪɨɜɚɧɢɸ ɱɚɫɬɢɰ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɫɤɨɪɨɫɬɶ, ɪɚɫɫɱɢɬɚɧɧɚɹ
17
18
ȿɫɥɢ ɡɚɦɟɧɢɬɶ ɩɟɪɟɦɟɧɧɵɟ y = ln k, x = 1/T, ɬɨ ɭɪɚɜɧɟɧɢɟ ɫɬɚɧɟɬ ɥɢɧɟɣɧɵɦ:
y
b
Ea R
x . Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɧɨɜɵɯ ɤɨɨɪɞɢɧɚɬɚɯ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ
ɩɨ ɮɨɪɦɭɥɟ ɬɢɩɚ (I.5), ɛɵɥɚ ɛɵ ɧɟɩɨɦɟɪɧɨ ɜɵɫɨɤɚ. Ⱥɪɪɟɧɢɭɫ ɩɪɟɞɩɨɥɨɠɢɥ, ɱɬɨ ɪɟɚɤɰɢɨɧɧɵɦɢ ɹɜɥɹɸɬɫɹ ɬɨɥɶɤɨ ɬɟ ɫɬɨɥɤɧɨɜɟɧɢɹ, ɤɨɬɨɪɵɟ ɩɪɨɢɫɯɨɞɹɬ ɫ ɷɧɟɪɝɢɟɣ, ɩɪɟɜɵɲɚɸɳɟɣ ɧɟɤɨɬɨɪɵɣ ɩɨɪɨɝ Ea. ȼɫɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɫ ɷɧɟɪɝɢɟɣ E < Ea ɨɤɚɡɵɜɚɸɬɫɹ ɧɟɷɮɮɟɤɬɢɜɧɵɦɢ: ɫɨɭɞɚɪɹɸɳɢɟɫɹ «ɦɟɞɥɟɧɧɵɟ» ɱɚɫɬɢɰɵ ɧɟ ɪɟɚɝɢɪɭɸɬ. ɗɬɨɬ ɩɨɪɨɝ ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɷ ɧ ɟ ɪ ɝ ɢ ɸ ɚ ɤ ɬ ɢ ɜ ɚ ɰ ɢ ɢ, ɚ ɫɬɨɥɤɧɨɜɟɧɢɹ ɫ ɭɫɥɨɜɢɟɦ E · Ea ɧɚɡɵɜɚɸɬ ɚɤɬɢɜɧɵɦɢ. ɋɬɚɬɢɫɬɢɱɟɫɤɢɣ ɩɨɞɫɱɟɬ ɱɚɫɬɨɬɵ za ɛɢɧɚɪɧɵɯ ɚɤɬɢɜɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɜ ɢɞɟɚɥɶɧɨɦ ɝɚɡɟ, ɨɫɧɨɜɚɧɧɵɣ ɧɚ ɪ ɚ ɫ ɩ ɪ ɟ ɞ ɟ ɥ ɟ ɧ ɢ ɢ Ɇ ɚ ɤ ɫ ɜ ɟ ɥ ɥ ɚ ɦɨɥɟɤɭɥ ɝɚɡɚ ɩɨ ɫɤɨɪɨɫɬɹɦ, ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ
za
2
S(r1 r2 ) N
2 A
8ɤT SP*
1 2
e
Ea RT
C1C2
(I.15)
(ɫɦ. ɥɢɬɟɪɚɬɭɪɭ [2, 4, 5]). Ɂɞɟɫɶ r1 ɢ r2 – ɪɚɞɢɭɫɵ ɫɬɚɥɤɢɜɚɸɳɢɯɫɹ ɱɚɫɬɢɰ; P* – ɢɯ ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ: 1 1 1 , P* P 1 P 2 ɚ ɦɧɨɠɢɬɟɥɶ V = S(r1 + r2)2 ɧɚɡɵɜɚɟɬɫɹ ɫɟɱɟɧɢɟɦ ɫɨɭɞɚɪɟɧɢɹ. Ɉɧɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɟɱɟɧɢɟ ɰɢɥɢɧɞɪɚ, ɜ ɤɨɬɨɪɨɦ ɞɨɥɠɧɵ ɨɤɚɡɚɬɶɫɹ ɰɟɧɬɪɵ ɦɚɫɫ ɫɮɟɪɢɱɟɫɤɢɯ ɱɚɫɬɢɰ, ɱɬɨɛɵ ɫɥɭɱɢɥɨɫɶ ɫɨɭɞɚɪɟɧɢɟ. ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɭ (I.5), ɤɨɬɨ*) ɪɚɹ ɞɥɹ ɱɚɫɬɨɬɵ ɜɫɟɯ ɞɜɨɣɧɵɯ ɫɨɭɞɚɪɟɧɢɣ ɪɚɡɥɢɱɧɵɯ ɱɚɫɬɢɰ ɢɦɟɟɬ ɜɢɞ
z
2
S(r1 r2 ) N
2 A
1 2
CC 8ɤT SP*
1
–Ea/RT
ze
1/ 2
8ɤT SP*
,
ɬɨ ɟɦɭ ɦɨɠɧɨ ɩɪɢɞɚɬɶ ɮɨɪɦɭ
za
uVN A2 e
Ea RT
C1C2 .
ɉɪɨɢɡɜɟɞɟɧɢɟ z0 = uV ɧɚɡɵɜɚɟɬɫɹ ɮɚɤɬɨɪɨɦ ɫɨɭɞɚɪɟɧɢɣ. Ɉɧ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɱɚɫɬɨɬɭ ɜɫɬɪɟɱ ɞɜɭɯ ɞɚɧɧɵɯ ɱɚɫɬɢɰ 1 ɢ 2, ɞɜɢɠɭɳɢɯɫɹ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ. ɇɚɤɨɧɟɰ, ɧɭɠɧɨ ɩɪɢɧɹɬɶ ɜɨ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɞɚɠɟ ɚɤɬɢɜɧɨɟ ɫɨɭɞɚɪɟɧɢɟ ɧɟ ɜɫɟɝɞɚ ɪɟɚɤɰɢɨɧɧɨ ɷɮɮɟɤɬɢɜɧɨ. Ⱦɥɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɨɥɟɤɭɥ, ɨɛɥɚɞɚɸɳɢɯ ɧɟɤɨɬɨɪɵɦ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɫɬɪɨɟɧɢɟɦ, ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɢɯ ɜɡɚɢɦɧɚɹ ɨɪɢɟɧɬɚɰɢɹ ɜ ɦɨɦɟɧɬ ɫɬɨɥɤɧɨɜɟɧɢɹ (ɢɥɢ, ɤɚɤ ɝɨɜɨɪɹɬ ɤɨɧɮɢɝɭɪɚɰɢɹ ɫɬɨɥɤɧɨɜɟɧɢɹ) ɛɵɥɚ ɩɨɞɯɨɞɹɳɟɣ. ɉɨɷɬɨɦɭ ɞɥɹ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɩɪɢɧɢɦɚɸɬ:
v
pza
pze
Ea RT
C1C2 , ɢɥɢ k
pze
Ea RT
ɞɥɹ ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɢ. Ɇɧɨɠɢɬɟɥɶ p, ɩɨɤɚɡɵɜɚɸɳɢɣ ɞɨɥɸ ɷɮɮɟɤɬɢɜɧɵɯ ɜ ɧɚɡɜɚɧɧɨɦ ɫɦɵɫɥɟ ɫɬɨɥɤɧɨɜɟɧɢɣ, ɧɚɡɵɜɚɟɬɫɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɢɥɢ ɫɬɟɪɢɱɟɫɤɢɦ * ) ɮɚɤɬɨɪɨɦ. 9. Ɉɛɪɚɬɢɦɵɟ ɪɟɚɤɰɢɢ
2,
ɩɨɥɭɱɢɦ:
za
u
Ea RT
Ⱦɨ ɫɢɯ ɩɨɪ ɪɚɫɫɦɚɬɪɢɜɚɥɢɫɶ ɪɟɚɤɰɢɢ, ɩɪɨɬɟɤɚɸɳɢɟ ɜ ɨɞɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ɗɬɨ ɹɜɥɹɟɬɫɹ ɩɪɢɛɥɢɠɟɧɢɟɦ ɢ ɨɩɪɚɜɞɚɧɨ ɜ ɬɨɣ ɢɥɢ ɢɧɨɣ ɫɬɟɩɟɧɢ ɞɥɹ ɧɚɱɚɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɩɪɨɰɟɫɫɚ. ɉɭɫɬɶ ɢɦɟɟɬɫɹ ɩɪɨɫɬɚɹ ɪɟɚɤɰɢɹ ɫ ɭɪɚɜɧɟɧɢɟɦ
. ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɨɥɸ ɚɤɬɢɜɧɵɯ ɫɬɨɥɤɧɨ-
Ɍɟɦ ɫɚɦɵɦ ɦɧɨɠɢɬɟɥɶ e ɜɟɧɢɣ ɫ ɷɧɟɪɝɢɟɣ E > Ea. Ʉɚɤ ɜɢɞɧɨ, ɩɨɫɥɟɞɧɟɟ ɭɪɚɜɧɟɧɢɟ ɫɨɜɩɚɞɚɟɬ ɩɨ ɮɨɪɦɟ ɫ ɭɪɚɜɧɟɧɢɟɦ Ⱥɪɪɟɧɢɭɫɚ. Ɉɬɥɢɱɢɟ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɩɪɟɞɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣ ɦɧɨɠɢɬɟɥɶ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ, ɜɩɪɨɱɟɦ, ɨɫɬɚɟɬɫɹ ɫɥɚɛɨɣ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ T1/2, ɱɬɨ ɜ ɧɟɛɨɥɶɲɨɦ ɢɧɬɟɪɜɚɥɟ ɬɟɦɩɟɪɚɬɭɪ ɧɟɫɭɳɟɫɬɜɟɧɧɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɛɵɫɬɪɨɪɚɫɬɭɳɟɣ ɮɭɧɤɰɢɟɣ e–Ea/RT. ɍɪɚɜɧɟɧɢɟ (I.15) – ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɬɟɨɪɢɢ ɚɤɬɢɜɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ – ɫɨɞɟɪɠɢɬ ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ (ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɶ C1C2). ȿɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɫɪɟɞɧɹɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ
m
n
i 1
j 1
¦ Qi Ai ' ¦ Q j B j ,
(I.16)
ɢ ɩɭɫɬɶ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɜ ɫɢɫɬɟɦɟ ɨɬɫɭɬɫɬɜɨɜɚɥɢ ɜɟɳɟɫɬɜɚ Bj. Ʉɚɤ ɬɨɥɶɤɨ ɜɟɳɟɫɬɜɚ Bj ɩɨɹɜɹɬɫɹ ɢ ɫɬɚɧɭɬ ɧɚɤɚɩɥɢɜɚɬɶɫɹ, ɜɨɡɧɢɤɧɟɬ ɢ ɫɬɚɧɟɬ ɪɚɡɜɢɜɚɬɶɫɹ ɜɫɬɪɟɱɧɵɣ ɩɪɨɰɟɫɫ ɩɪɟɜɪɚɳɟɧɢɹ, ɨɬɜɟɱɚɸɳɢɣ ɬɨɦɭ ɠɟ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɦɭ ɭɪɚɜɧɟɧɢɸ, ɧɨ ɩɪɨɱɢɬɚɧɧɨɦɭ ɫɩɪɚɜɚ ɧɚɥɟɜɨ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ, ɱɬɨ ɪɟɚɤɰɢɹ ɹɜɥɹɟɬɫɹ ɨɛɪɚɬɢɦɨɣ ɢ, ɱɬɨɛɵ ɩɨɞɱɟɪɤɧɭɬɶ ɷɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ, ɩɢɲɭɬ: B
B
m
n
i 1
j 1
' ¦ Q j Bj . ¦ Qi Ai &
ɉɪɢ ɬɚɤɨɦ ɩɨɥɨɠɟɧɢɢ ɞɟɥɚ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɦɵ ɩɨ-ɩɪɟɠɧɟɦɭ ɨɩɪɟɞɟɥɹɟɦ ɮɨɪɦɭɥɨɣ (I.4) ɢ ɫɥɟɞɢɦ ɡɚ ɪɚɡɜɢɬɢɟɦ ɩɪɨɰɟɫɫɚ ɩɨ ɨɞɧɨɦɭ ɢɡ ɤɨɦɩɨ-
*)
Ɏɨɪɦɭɥɚ (I.5) ɩɨɥɭɱɚɟɬɫɹ, ɟɫɥɢ ɩɨɥɨɠɢɬɶ r1 = r2, P1 = P2 ɢ C1 = C2, ɚ ɬɚɤɠɟ ɭɱɟɫɬɶ, ɱɬɨ ɩɪɢ ɨɬɨɠɞɟɫɬɜɥɟɧɢɢ ɱɚɫɬɢɰ (1 { 2) ɩɨɥɭɱɢɬɫɹ ɭɞɜɨɟɧɧɨɟ ɱɢɫɥɨ ɫɨɭɞɚɪɟɧɢɣ. Ɉɬɫɸɞɚ – ɤɨɷɮɮɢɰɢɟɧɬ 2 ɜ (I.5). 19
*)
Ɉɬ ɝɪɟɱ. ıIJİȡȩȢ – ɬɜɟɪɞɵɣ, ɜ ɩɟɪɟɧɨɫɧɨɦ ɫɦɵɫɥɟ – ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ, ɨɛɴɟɦɧɵɣ. 20
ɧɟɧɬɨɜ. ɉɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɞɨɥɠɧɚ ɛɵɬɶ ɜɵɱɢɫɥɟɧɚ ɤɚɤ ɪɚɡɧɨɫɬɶ 1
ɤɨɬɨɪɵɟ ɦɵ ɛɭɞɟɦ ɨɛɨɡɧɚɱɚɬɶ ɫɩɟɰɢɚɥɶɧɵɦɢ ɫɢɦɜɨɥɚɦɢ [A], [B]. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɫɢɫɬɟɦɟ ɫ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɟɣ ɜɫɟɝɞɚ ɨɫɬɚɸɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɟ ɤɨɥɢɱɟɫɬɜɚ ɢ ɢɫɯɨɞɧɨɝɨ ɜɟɳɟɫɬɜɚ, ɢ ɩɪɨɞɭɤɬɚ.
Qi ɫɤɨɪɨɫɬɟɣ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɟɜɪɚɳɟɧɢɣ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɪɚɡɞɟɥɢɬɶ ɞɜɚ ɷɬɢɯ ɜɫɬɪɟɱɧɵɯ ɩɨɬɨɤɚ ɧɟɜɨɡɦɨɠɧɨ, ɨɞɧɚɤɨ ɞɥɹ v+ ɢ v– ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɹ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ:
10. ɏɢɦɢɱɟɫɤɨɟ ɪɚɜɧɨɜɟɫɢɟ
v{
Ci
v v
m
n
i 1
j 1
Q
v(W) k CiQi (W) k C j j (W) .
(I.17)
ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɫɨ ɜɫɟɣ ɨɩɪɟɞɟɥɟɧɧɨɫɬɶɸ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɟɫɥɢ ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɨɛɪɚɬɧɨɣ ɪɟɚɤɰɢɢ k– z 0, ɬɨ ɜɫɬɪɟɱɧɨɟ ɩɪɟɜɪɚɳɟɧɢɟ ɞɨɥɠɧɨ ɫɭɳɟɫɬɜɨɜɚɬɶ. Ɉɧɨ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɜ ɤɪɚɣɧɟ ɧɟɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɢɥɢ ɧɚɨɛɨɪɨɬ – ɛɵɬɶ ɜɟɫɶɦɚ ɫɭɳɟɫɬɜɟɧɧɵɦ. ɗɬɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɫɨɨɬɧɨɲɟɧɢɟɦ ɤɨɧɫɬɚɧɬ. ȿɫɥɢ k– " k+, ɬɨ ɝɨɜɨɪɹɬ, ɱɬɨ ɪɟɚɤɰɢɹ ɹɜɥɹɟɬɫɹ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɨɛɪɚɬɢɦɨɣ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɤɨɧɫɬɚɧɬɵ k+ ɢ k– ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɜ ɤɢɧɟɬɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ ɪɚɡɧɵɟ ɩɪɨɰɟɫɫɵ ɢ ɩɨɷɬɨɦɭ ɧɟɡɚɜɢɫɢɦɵ. ɍɪɚɜɧɟɧɢɟ (I.17) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɤɢɧɟɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ, ɩɨɞɨɛɧɨɟ ɬɟɦ, ɤɚɤɢɟ ɦɵ ɪɟɲɚɥɢ ɜ ɩɩ. 5, 6. ɉɨɥɭɱɢɦ ɟɝɨ ɪɟɲɟɧɢɟ ɞɥɹ ɫɚɦɨɣ ɩɪɨɫɬɨɣ ɪɟɚɤɰɢɢ, ɢɞɭɳɟɣ ɩɨ ɩɟɪɜɨɦɭ ɩɨɪɹɞɤɭ ɜ ɨɛɨɢɯ ɧɚɩɪɚɜɥɟɧɢɹɯ: Aĺ (I.18) ĸ B. ɍɪɚɜɧɟɧɢɟ (I.17) ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ:
C A
kC A kCB
ɢɥɢ, ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɣ ɫɜɹɡɢ ɦɟɠɞɭ CA ɢ CB, C A (k k )C A k (C A0 CB0 ) . ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɟɝɨ ɜ ɤɨɧɟɱɧɨɦ ɫɱɟɬɟ ɞɚɟɬ ɤɢɧɟɬɢɱɟɫɤɢɣ ɡɚɤɨɧ 0 0 0 0 C A CB C A CB ( k k ) W
CA
k
k
k k
e
k k
0
k
0
C A CB k k
0
k
W'f
W'f
0.
ȼ ɨɛɳɟɦ ɜɢɞɟ ɞɥɹ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɢ m-ɝɨ ɩɨɪɹɞɤɚ ɜ ɩɪɹɦɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɢ n-ɝɨ – ɜ ɨɛɪɚɬɧɨɦ ɫɭɳɟɫɬɜɭɟɬ ɫɨɫɬɨɹɧɢɟ, ɩɪɢ ɤɨɬɨɪɨɦ v = 0, v+, v– z 0. (I.20) ɗɬɨ ɫɨɫɬɨɹɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɞɢɧɚɦɢɱɟɫɤɢɦ ɯɢɦɢɱɟɫɤɢɦ ɪɚɜɧɨɜɟɫɢɟɦ, ɚ ɭɫɥɨɜɢɟ (I.20) – ɤɢɧɟɬɢɱɟɫɤɢɦ ɭɫɥɨɜɢɟɦ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɋɥɨɜɨ «ɞɢɧɚɦɢɱɟɫɤɨɟ» ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɜɫɟɝɞɚ, ɢ ɫ ɪɚɜɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ, ɫɭɳɟɫɬɜɭɸɬ ɜɫɬɪɟɱɧɵɟ ɩɨɬɨɤɢ: ɩɪɹɦɨɣ «» ɢ ɨɛɪɚɬɧɵɣ «–». Ʉɨɧɰɟɧɬɪɚɰɢɢ ɜɟɳɟɫɬɜ, ɭɫɬɚɧɨɜɢɜɲɢɟɫɹ ɜ ɯɢɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɧɚɡɵɜɚɸɬɫɹ ɪɚɜɧɨɜɟɫɧɵɦɢ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɢ ɨɛɨɡɧɚɱɚɸɬɫɹ [Ai], [Bj]. ɉɪɢɦɟɧɢɦ ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɞɥɹ ɫɨɫɬɨɹɧɢɹ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɉɨɫɤɨɥɶɤɭ ɜɟɳɟɫɬɜɚ ɫɨɞɟɪɠɚɬɫɹ ɜ ɫɜɨɢɯ ɪɚɜɧɨɜɟɫɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ, ɫɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ (I.20) B
m
n
i 1
j 1
(I.19)
0
e ( k k ) W
ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ B. ɗɬɨɬ ɜɵɜɨɞ ɢɧɬɟɪɟɫɟɧ ɬɟɦ, ɱɬɨ ɩɪɢ W ĺ f ɨɛɟ ɮɭɧɤɰɢɢ CA(W) ɢ CB(W) ɢɦɟɸɬ ɤɨɧɟɱɧɵɟ ɩɪɟɞɟɥɵ: 0 0 0 0 C CB C CB lim C A k A { [ A] , lim CB k A { [ B] , W'f W'f k k k k
0.
(I.21)
Ɉɛɚ ɱɥɟɧɚ ɫɥɟɜɚ, ɜ ɨɬɥɢɱɢɟ ɨɬ (I.17), ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɜɪɟɦɟɧɢ, ɢ ɨɛɚ ɱɥɟɧɚ (ɟɫɥɢ k+ ɢ k– ɤɨɧɟɱɧɵ) ɧɟ ɪɚɜɧɵ ɧɭɥɸ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɟ (I.21) ɢɦɟɥɨ ɛɵ ɬɪɢɜɢɚɥɶɧɨɟ ɪɟɲɟɧɢɟ: [Ai] = 0 ɢ [Bj] = 0 ɨɞɧɨɜɪɟɦɟɧɧɨ. Ɍɟɦ ɫɚɦɵɦ, ɫɨɫɬɨɹɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɦɨɠɧɨ ɨɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɬɚɤ, ɱɬɨ ɜ ɧɟɦ ɨɞɧɨɜɪɟɦɟɧɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ, ɫɨɫɭɳɟɫɬɜɭɸɬ ɜ ɤɨɧɟɱɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɜɫɟ ɭɱɚɫɬɧɢɤɢ ɪɟɚɤɰɢɢ. ɇɚɛɥɸɞɚɬɟɥɶ, ɢɡɦɟɪɹɸɳɢɣ ɜ ɪɚɡɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɧɟ ɨɛɧɚɪɭɠɢɬ ɧɢɤɚɤɢɯ ɢɡɦɟɧɟɧɢɣ ɢ ɭɫɬɚɧɨɜɢɬ, ɱɬɨ C i 0 . ɍɪɚɜɧɟɧɢɟ (I.21) ɩɨɥɟɡɧɨ ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɬɚɤ, ɱɬɨɛɵ ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɨɦɩɨɧɟɧɬɨɜ ɨɫɬɚɜɚɥɢɫɶ ɜ ɨɞɧɨɣ ɱɚɫɬɢ: n
Qj
[Bj ] j 1 m
Qi
[ Ai ] i 1
21
Qj
B
C A CB k k
W'f
ɲɟɧɢɹ (I.19), lim C A
k [ Ai ]Qi k [ B j ]
ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ A, ɢ
CB
Ɂɚɞɚɱɚ, ɪɟɲɟɧɧɚɹ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɭɧɤɬɟ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɢɫɬɟɦɚ ɫ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɟɣ ɩɪɢɯɨɞɢɬ ɜ ɫɨɫɬɨɹɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɨɛɳɚɹ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ v = 0 ɩɪɢ ɨɬɥɢɱɧɵɯ ɨɬ ɧɭɥɹ ɫɤɨɪɨɫɬɹɯ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɟɜɪɚɳɟɧɢɣ. ȼ ɫɚɦɨɦ ɞɟɥɟ, ɤɨɥɶ ɫɤɨɪɨ ɧɢ ɨɞɧɨ ɢɡ ɜɟɳɟɫɬɜ ɧɟ ɢɫɱɟɡɚɟɬ, lim v k [ A] ɢ lim v k [ B ] . ȼ ɬɨ ɠɟ ɫɚɦɨɟ ɜɪɟɦɹ, ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ ɪɟ-
22
k { K. k
(I.22)
Ɍɨɝɞɚ ɜ ɞɪɭɝɨɣ ɱɚɫɬɢ ɨɤɚɠɟɬɫɹ ɨɬɧɨɲɟɧɢɟ ɤɨɧɫɬɚɧɬ ɫɤɨɪɨɫɬɟɣ. ɉɨɫɤɨɥɶɤɭ kr ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɣ, ɩɨɫɬɨɥɶɤɭ ɢ ɢɯ ɨɬɧɨɲɟɧɢɟ K ɹɜɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɩɨɫɬɨɹɧɧɨɣ. ɗɬɨ ɨɬɧɨɲɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɤɨɧɫɬɚɧɬɨɣ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɋɭɳɟɫɬɜɨɜɚɧɢɟ ɤɨɧɫɬɚɧɬɵ K – ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ (ɟɝɨ ɬɚɤ ɠɟ ɧɚɡɵɜɚɸɬ ɡɚɤɨɧɨɦ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ; ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɞɬɜɟɪɠɞɟɧ Ƚɭɥɶɞɛɟɪɝɨɦ ɢ ȼɚɚɝɟ). Ɉɧ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɦɨɝɭɬ ɛɵɬɶ ɥɸɛɵɦɢ, ɧɨ ɬɚɤɢɦɢ, ɱɬɨɛɵ ɭɞɨɜɥɟɬɜɨɪɹɥɨɫɶ ɫɨɨɬɧɨɲɟɧɢɟ (I.22), ɜ ɤɨɬɨɪɨɦ K – ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɚɹ ɜɟɥɢɱɢɧɚ ɩɪɢ ɞɚɧɧɵɯ ɭɫɥɨɜɢɹɯ (ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɞɚɜɥɟɧɢɢ). ɋɨɨɬɧɨɲɟɧɢɟ (I.22) ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɫɜɹɡɶ ɦɟɠɞɭ m + n = N ɩɟɪɟɦɟɧɧɵɦɢ [A1], …, [Am], [B1], …, [Bn], B
B
(I.23)
0
[ A]
0
C A CB
K
[ B] , CA0 – [A] = [B] – CB0. [ A]
ȼɬɨɪɨɟ ɢɡ ɧɢɯ, ɡɚɩɢɫɚɧɧɨɟ ɞɥɹ ɫɨɫɬɨɹɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɜɵɪɚɠɚɟɬ ɫ ɨ ɯ ɪ ɚ ɧ ɟ ɧ ɢ ɟ ɜɟɳɟɫɬɜɚ, ɩɟɪɜɨɟ – ɪ ɚ ɫ ɩ ɪ ɟ ɞ ɟ ɥ ɟ ɧ ɢ ɟ ɜɟɳɟɫɬɜɚ ɦɟɠɞɭ ɟɝɨ ɪɚɜɧɨɜɟɫɧɵɦɢ ɮɨɪɦɚɦɢ. ɂɯ ɫɨɜɦɟɫɬɧɨɟ ɪɟɲɟɧɢɟ ɞɚɟɬ: 23
[ B] K
0
C A CB
, K 1 K 1 ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫɨ ɡɧɚɱɟɧɢɹɦɢ [A] ɢ [B], ɩɨɥɭɱɟɧɧɵɦɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɦ ɪɟɲɟɧɢɟɦ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ. Ɋɚɫɫɦɨɬɪɢɦ ɟɳɟ ɨɞɢɧ ɩɪɢɦɟɪ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɨ ɪɚɜɧɨɜɟɫɢɢ. ɉɭɫɬɶ ɢɦɟɟɬɫɹ ɨɛɪɚɬɢɦɵɣ ɪɚɫɩɚɞ ɫɨɟɞɢɧɟɧɢɹ XY ɩɨ ɭɪɚɜɧɟɧɢɸ XY ĺ ĸ X + Y. ȿɫɥɢ ɨɛɨɡɧɚɱɢɬɶ ɱɟɪɟɡ D ɞɨɥɸ ɪɚɫɩɚɜɲɢɯɫɹ ɱɚɫɬɢɰ ɜ ɪɚɜɧɨɜɟɫɢɢ, ɬɨ 0 0 [ X ] [Y ] DC XY ɢ [ XY ] (1 D)C XY . ȼɬɨɪɨɟ ɭɪɚɜɧɟɧɢɟ, ɤɚɤ ɢ ɪɚɜɟɧɫɬɜɨ [X] = [Y], ɜɵɪɚɠɚɟɬ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɟ ɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɭɱɚɫɬɧɢɤɚɦɢ ɪɟɚɤɰɢɢ. ɉɨ ɡɚɤɨɧɭ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ
K ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɬɨɥɶɤɨ N – 1 ɢɡ ɧɢɯ ɦɨɝɭɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɤɚɤ ɧɟɡɚɜɢɫɢɦɵɟ. ȼɫɟ ɫɨɫɬɨɹɧɢɹ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɷɬɨɣ ɫɜɹɡɢ, ɛɭɞɭɬ ɪɚɜɧɨɜɟɫɧɵɦɢ; ɥɸɛɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɡɧɚɱɟɧɢɣ (I.23), ɧɟ ɭɞɨɜɥɟɬɜɨɪɹɸɳɚɹ ɟɣ, ɨɬɦɟɱɚɟɬ ɧɟɪɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ. ɉɭɫɬɶ ɦɵ ɢɦɟɟɦ ɫɢɫɬɟɦɭ, ɧɚɯɨɞɹɳɭɸɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ. ȼɧɟɫɟɦ ɫɸɞɚ ɦɝɧɨɜɟɧɧɨ ɧɟɤɨɬɨɪɭɸ ɞɨɛɚɜɤɭ ɨɞɧɨɝɨ ɢɡ ɜɟɳɟɫɬɜ, ɭɱɚɫɬɜɭɸɳɢɯ ɜ ɪɟɚɤɰɢɢ, ɫɤɚɠɟɦ, ɨɞɧɨɝɨ ɢɡ ɜɟɳɟɫɬɜ Ai (ɫɢɫɬɟɦɚ ɜ ɤɚɤɨɣ-ɬɨ ɦɨɦɟɧɬ ɞɨɥɠɧɚ ɛɵɬɶ ɨ ɬ ɤ ɪ ɵ ɬ ɨ ɣ , ɬɨ ɟɫɬɶ ɞɨɩɭɫɤɚɬɶ ɩɟɪɟɧɨɫ ɜɟɳɟɫɬɜɚ ɢɡɜɧɟ). ȼ ɷɬɨɬ ɦɨɦɟɧɬ ɫɨɨɬɧɨɲɟɧɢɟ (I.22) ɩɟɪɟɫɬɚɧɟɬ ɭɞɨɜɥɟɬɜɨɪɹɬɶɫɹ, ɢ ɪɚɜɧɨɜɟɫɢɟ ɧɚɪɭɲɢɬɫɹ. ȼ ɫɢɫɬɟɦɟ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ ɞɨɥɠɧɵ ɩɪɨɢɡɨɣɬɢ ɢɡɦɟɧɟɧɢɹ, ɜɟɞɭɳɢɟ ɤ ɬɨɦɭ, ɱɬɨɛɵ ɜɨɫɫɬɚɧɨɜɢɥɨɫɶ ɢɫɯɨɞɧɨɟ ɨɬɧɨɲɟɧɢɟ (I.22). ɋ ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɜɜɟɞɟɧɢɟ ɥɸɛɨɝɨ ɢɡ ɢɫɯɨɞɧɵɯ ɜɟɳɟɫɬɜ ɜɨɡɛɭɠɞɚɟɬ ɩɪɹɦɭɸ ɪɟɚɤɰɢɸ (I.16), ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɨɣ ɱɚɫɬɶ ɜɟɳɟɫɬɜ Ai ɢɡɪɚɫɯɨɞɭɟɬɫɹ ɢ ɭɫɬɚɧɨɜɢɬɫɹ ɧɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɫ ɧɨɜɵɦɢ ɡɧɚɱɟɧɢɹɦɢ (I.23). ɉɪɢ ɭɞɚɥɟɧɢɢ ɥɸɛɨɝɨ ɜɟɳɟɫɬɜɚ ɢɡ ɫɢɫɬɟɦɵ ɪɟɚɤɰɢɹ ɩɨɣɞɟɬ ɜ ɫɬɨɪɨɧɭ ɨɛɪɚɡɨɜɚɧɢɹ ɷɬɨɝɨ ɜɟɳɟɫɬɜɚ, ɢ ɛɭɞɟɬ ɢɞɬɢ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɭɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɨɜɟɫɢɟ. ɗɬɭ ɫɢɬɭɚɰɢɸ ɧɚɡɵɜɚɸɬ ɫɦɟɳɟɧɢɟɦ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɍɪɚɜɧɟɧɢɟ (I.22) ɫɨɜɦɟɫɬɧɨ ɫɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ (I.2) ɩɨɡɜɨɥɹɟɬ ɜɵɱɢɫɥɢɬɶ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɫɟɯ ɭɱɚɫɬɧɢɤɨɜ ɪɟɚɤɰɢɢ ɩɪɢ ɥɸɛɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ CA10, …, CAm0, CB10, …, CBn0. Ɉɩɢɲɟɦ ɨɛɳɢɣ ɦɟɬɨɞ ɧɚ ɩɪɢɦɟɪɟ ɪɟɚɤɰɢɢ (I.18). ɍɪɚɜɧɟɧɢɹ ɡɚɤɨɧɚ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɡɚɤɨɧɚ ɢɦɟɸɬ ɜɢɞ:
0
,
D2 0 C XY . 1 D
ɂɡ ɞɜɭɯ ɤɨɪɧɟɣ ɷɬɨɝɨ ɤɜɚɞɪɚɬɧɨɝɨ ɩɨ D ɭɪɚɜɧɟɧɢɹ ɧɭɠɧɨ, ɪɚɡɭɦɟɟɬɫɹ, ɜɵɛɪɚɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɤɨɪɟɧɶ:
D
1 0 2C XY
0 K 2 4 KC XY K .
ɉɨɫɥɟɞɧɹɹ ɮɨɪɦɭɥɚ ɩɪɢɦɟɧɢɦɚ, ɜ ɱɚɫɬɧɨɫɬɢ, ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɥɢɬɨɜ, ɤɨɝɞɚ ɨɛɪɚɡɭɸɬɫɹ ɤɚɬɢɨɧɵ X + ɢ ɚɧɢɨɧɵ Y –. Ɉɧɚ ɢɡɜɟɫɬɧɚ ɩɨɞ ɢɦɟɧɟɦ ɡɚɤɨɧɚ ɪɚɡɛɚɜɥɟɧɢɹ Ɉɫɬɜɚɥɶɞɚ (W. Ostwald, 1888). ɂɡ ɡɚɤɨɧɚ ɪɚɡɛɚɜɥɟɧɢɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɜɧɨɜɟɫɧɚɹ ɫɬɟɩɟɧɶ ɞɢɫɫɨɰɢɚɰɢɢ (ɢɨɧɢɡɚɰɢɢ) D ɡɚɜɢɫɢɬ ɨɬ ɧɚɱɚɥɶɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɪɚɫɩɚɞɚɸɳɟɝɨɫɹ ɜɟɳɟɫɬɜɚ. ɍɛɵɜɚɹ ɦɨɧɨɬɨɧɧɨ, ɨɧɚ 0 0 ɢɡɦɟɧɹɟɬɫɹ ɨɬ 1 ɜ ɩɪɟɞɟɥɟ ɩɪɢ C XY ' 0 ɞɨ ɧɭɥɹ ɜ ɩɪɟɞɟɥɟ C XY ' f . Ɍɟɦ ɫɚɦɵɦ ɩɨɤɚɡɚ0
ɧɨ, ɱɬɨ ɩɪɢ ɛɟɫɤɨɧɟɱɧɨɦ ɪɚɡɛɚɜɥɟɧɢɢ ( C XY ' 0 ) ɩɪɨɢɫɯɨɞɢɬ ɩɨɥɧɵɣ ɪɚɫɩɚɞ ɜɟɳɟɫɬɜɚ.
Ɍɟɩɟɪɶ ɫɬɚɧɨɜɢɬɫɹ ɹɫɧɨ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɢ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɥɢɛɨ ɤɪɚɣɧɟ ɜɟɥɢɤɚ, ɟɫɥɢ k+ # k–, ɥɢɛɨ ɤɪɚɣɧɟ ɦɚɥɚ, ɟɫɥɢ k+ " k–. ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɪɟɚɤɰɢɹ ɩɨɱɬɢ ɞɨɯɨɞɢɬ ɞɨ ɤɨɧɰɚ (ɫɥɟɜɚ ɧɚɩɪɚɜɨ ɢɥɢ ɫɩɪɚɜɚ ɧɚɥɟɜɨ). ɇɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɥɢɬ ɫɱɢɬɚɟɬɫɹ ɫɢɥɶɧɵɦ, ɟɫɥɢ ɟɝɨ ɤɨɧɫɬɚɧɬɚ ɢɨɧɢɡɚɰɢɢ K ~ 102. Ʉɚɤ ɦɨɠɧɨ ɭɛɟɞɢɬɶɫɹ ɩɨ ɮɨɪɦɭɥɟ Ɉɫɬɜɚɥɶɞɚ, ɬɚɤɨɣ ɷɥɟɤɬɪɨɥɢɬ ɞɢɫɫɨɰɢɢɪɭɟɬ ɩɨɱɬɢ ɧɚɰɟɥɨ (D ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ 1). ɇɚɤɨɧɟɰ, ɦɨɠɧɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɜ ɫɢɬɭɚɰɢɢ ɪɚɜɧɨɜɟɫɢɹ ɜɫɟ ɧɚɲɢ ɭɪɚɜɧɟɧɢɹ ɞɨɩɭɫɤɚɸɬ ɩɪɨɱɬɟɧɢɟ ɤɚɤ ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɬɚɤ ɢ ɫɩɪɚɜɚ ɧɚɥɟɜɨ, ɩɨɫɤɨɥɶɤɭ ɬɭɬ ɧɟɬ ɜɵɞɟɥɟɧɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɩɪɟɜɪɚɳɟɧɢɹ. ɗɬɨ ɞɟɥɚɟɬ ɜ ɢɡɜɟɫɬɧɨɦ ɫɦɵɫɥɟ ɭɫɥɨɜɧɵɦɢ ɩɨɧɹɬɢɹ «ɢɫɯɨɞɧɨɟ ɜɟɳɟɫɬɜɨ» ɢ «ɩɪɨɞɭɤɬ» ɪɟɚɤɰɢɢ. ɂ ɬɟ, ɢ ɞɪɭɝɢɟ, ɤɚɤ ɭɠɟ ɡɚɦɟɱɟɧɨ, ɫɨɫɭɳɟɫɬɜɭɸɬ ɜ ɪɚɜɧɨɜɟɫɧɨɣ ɫɢɫɬɟɦɟ, ɢ ɱɬɨ ɫɱɢɬɚɬɶ ɢɫɯɨɞɧɵɦ, ɚ ɱɬɨ ɩɪɨɞɭɤɬɨɦ – ɜɨɩɪɨɫ ɫɨɝɥɚɲɟɧɢɹ. ȿɫɥɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɩɟɪɟɩɢɫɚɬɶ ɜ ɞɪɭɝɨɣ ɨɪɢɟɧɬɚɰɢɢ, ɬɨ ɤɨɧɫɬɚɧɬɭ ɪɚɜɧɨɜɟɫɢɹ ɫɥɟɞɭɟɬ ɡɚɦɟɧɢɬɶ ɨɛɪɚɬɧɨɣ ɜɟɥɢɱɢɧɨɣ K –1.
24
11. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɧɫɬɚɧɬɵ ɪɚɜɧɨɜɟɫɢɹ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ. ɉɪɢɧɰɢɩ Ʌɟ ɒɚɬɟɥɶɟ
w ln K wp
Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ (I.22), ɨ ɡɚɜɢɫɢɦɨɫɬɢ K ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɦɨɠɧɨ ɫɭɞɢɬɶ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɡɚɜɢɫɢɦɨɫɬɹɦ ɤɨɧɫɬɚɧɬ ɫɤɨɪɨɫɬɟɣ k+, k–. ɉɨ ɭɪɚɜɧɟɧɢɸ Ⱥɪɪɟɧɢɭɫɚ ɩɨɥɭɱɚɟɬɫɹ, ɱɬɨ
K (T )
k0 EaRT Ea e , k0
ɝɞɟ Ea+ ɢ Ea– – ɷɧɟɪɝɢɢ ɚɤɬɢɜɚɰɢɢ ɩɪɹɦɨɣ ɢ ɨɛɪɚɬɧɨɣ ɪɟɚɤɰɢɣ. Ɉɬɧɨɲɟɧɢɟ ɩɪɟɞɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɯ ɦɧɨɠɢɬɟɥɟɣ, ɤɚɤ ɧɚɦ ɢɡɜɟɫɬɧɨ, ɩɨɱɬɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. Ɍɨɝɞɚ, ɨɛɨɡɧɚɱɚɹ ɷɬɨ ɨɬɧɨɲɟɧɢɟ ɱɟɪɟɡ K0, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
K (T )
K 0e
'H RT
(I.24) ɝɞɟ ɪɚɡɧɨɫɬɶ ɷɧɟɪɝɢɣ ɚɤɬɢɜɚɰɢɢ 'H = Ea+ – Ea– ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɬɟɩɥɨɬɭ ɪɟɚɤɰɢɢ. Ɏɨɪɦɭɥɚ (I.24) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ K(T) ɨɩɪɟɞɟɥɹɟɬɫɹ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɜɟɥɢɱɢɧɨɣ 'H. ȼ ɨɬɥɢɱɢɟ ɨɬ ɷɧɟɪɝɢɢ ɚɤɬɢɜɚɰɢɢ ɷɬɚ ɜɟɥɢɱɢɧɚ ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɩɨɥɨɠɢɬɟɥɶɧɨɣ, ɬɚɤ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨɣ. ɉɨɷɬɨɦɭ ɮɭɧɤɰɢɹ K(T) ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɜɨɡɪɚɫɬɚɸɳɟɣ, ɬɚɤ ɢ ɭɛɵɜɚɸɳɟɣ. ɉɪɨɞɢɮɮɟɪɟɧɰɢɪɭɟɦ (I.24) ɩɨ ɬɟɦɩɟɪɚɬɭɪɟ:
ɢɧɚɱɟ
wK wT
K 0e
w ln K wT
'H RT
,
'H , RT 2
'H RT 2
(I.25)
(ɫɪ. ɫ (I.14)). Ɇɵ ɢɫɩɨɥɶɡɭɟɦ ɡɞɟɫɶ ɫɢɦɜɨɥ ɱɚɫɬɧɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨɬɨɦɭ, ɱɬɨ ɛɭɞɟɦ ɢɫɫɥɟɞɨɜɚɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɧɫɬɚɧɬɵ ɧɟ ɬɨɥɶɤɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɧɨ ɢ ɨɬ ɞɚɜɥɟɧɢɹ, ɬɚɤ ɱɬɨ K ɜɵɫɬɭɩɚɟɬ ɤɚɤ ɮɭɧɤɰɢɹ ɞɜɭɯ ɩɟɪɟɦɟɧɧɵɯ K(T, p). ɍɪɚɜɧɟɧɢɟ (I.25) ɢɡɜɟɫɬɧɨ ɤɚɤ ɭɪɚɜɧɟɧɢɟ ȼɚɧɬ-Ƚɨɮɮɚ (1884). ɂɡ ɧɟɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ
wK ! 0 , ɟɫɥɢ 'H > 0, ɬɨ ɟɫɬɶ ɬɟɩɥɨɬɚ ɩɨɝɥɨɳɚɟɬɫɹ, wT wK 0 , ɟɫɥɢ 'H < 0, ɬɨ ɟɫɬɶ ɬɟɩɥɨɬɚ ɜɵɞɟɥɹɟɬɫɹ wT
ɩɪɢ ɩɪɨɯɨɞɟ ɪɟɚɤɰɢɢ ɫɥɟɜɚ ɧɚɩɪɚɜɨ ɫɨɝɥɚɫɧɨ ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɣ ɡɚɩɢɫɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɪɚɜɧɨɜɟɫɢɟ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɫɦɟɳɚɟɬɫɹ ɜɩɪɚɜɨ, ɬɨ ɟɫɬɶ ɫɨɝɥɚɫɧɨ ɫɨɨɬɧɨɲɟɧɢɸ (I.22) ɜɟɳɟɫɬɜɚ Bj ɧɚɤɚɩɥɢɜɚɸɬɫɹ, ɚ ɜɟɳɟɫɬɜɚ Ai ɢɫɱɟɡɚɸɬ; ɜɨ ɜɬɨɪɨɦ – ɫɦɟɳɚɟɬɫɹ ɜɥɟɜɨ. Ɇɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɧɫɬɚɧɬɵ ɨɬ ɞɚɜɥɟɧɢɹ ɜɵɪɚɠɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ, ɩɨɞɨɛɧɵɦ (I.25):
'V , RT
(I.26)
ɝɞɟ 'V – ɢɡɦɟɧɟɧɢɟ ɨɛɴɟɦɚ ɜ ɪɟɚɤɰɢɢ. ȼ ɩɥɚɧɟ ɫɦɟɳɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɷɬɨ ɩɪɢɜɨɞɢɬ ɤ ɚɧɚɥɨɝɢɱɧɨɦɭ ɩɪɚɜɢɥɭ, ɭɫɬɚɧɚɜɥɢɜɚɸɳɟɦɭ ɧɚɩɪɚɜɥɟɧɢɟ ɫɦɟɳɟɧɢɹ, ɫɦɨɬɪɹ ɩɨ ɡɧɚɤɭ 'V. ɉɨɥɭɱɢɦ ɹɜɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɧɫɬɚɧɬɵ ɨɬ ɞɚɜɥɟɧɢɹ ɞɥɹ ɝɚɡɨɜɨɣ ɪɟɚɤɰɢɢ. ɋɢɫɬɟɦɚ ɪɟɚɝɢɪɭɸɳɢɯ ɢɞɟɚɥɶɧɵɯ ɝɚɡɨɜ ɯɨɪɨɲɚ ɬɟɦ, ɱɬɨ ɞɥɹ ɧɟɟ ɥɟɝɤɨ ɜɵɱɢɫɥɢɬɶ ɢɡɦɟɧɟɧɢɟ ɨɛɴɟɦɚ. ȿɫɥɢ ɪɟɚɤɰɢɹ ɨɬɜɟɱɚɟɬ ɭɪɚɜɧɟɧɢɸ (I.16), ɬɨ
'V
m RT n ¦ Q j ¦ Qi . i 1 p j1
ȼɯɨɞɹɳɭɸ ɫɸɞɚ ɪɚɡɧɨɫɬɶ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɨɛɵɱɧɨ ɨɛɨɡɧɚɱɚɸɬ ɤɚɤ 'Q. Ɍɨɝɞɚ K ( p)
y K0
1 dK K
p
y
'Q
p0
1 dp , ɚ ɨɬɫɸɞɚ p
K
K0
p p0
'Q
.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɨɧɫɬɚɧɬɚ ɝɚɡɨɜɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɨɛɧɚɪɭɠɢɜɚɟɬ ɫɬɟɩɟɧɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɞɚɜɥɟɧɢɹ, ɚ ɜɟɥɢɱɢɧɨɣ, ɨɩɪɟɞɟɥɹɸɳɟɣ ɷɬɭ ɡɚɜɢɫɢɦɨɫɬɶ, ɹɜɥɹɟɬɫɹ ɪɚɡɧɨɫɬɶ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ 'Q.
ȼ ɢɬɨɝɟ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ. 1. ɋɦɟɳɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɫɬɨɪɨɧɭ ɪɚɫɯɨɞɨɜɚɧɢɹ ɜɟɳɟɫɬɜɚ ɩɪɢ ɟɝɨ ɜɜɟɞɟɧɢɢ ɜ ɫɢɫɬɟɦɭ (ɜ ɨɬɤɪɵɬɨɣ ɫɢɫɬɟɦɟ). 2. ɋɦɟɳɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɜ ɫɬɨɪɨɧɭ ɩɨɝɥɨɳɟɧɢɹ ɬɟɩɥɨɬɵ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ (ɜ ɡɚɤɪɵɬɨɣ ɫɢɫɬɟɦɟ). 3. ɋɦɟɳɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɜ ɫɬɨɪɨɧɭ ɭɦɟɧɶɲɟɧɢɹ ɨɛɴɟɦɚ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɞɚɜɥɟɧɢɹ (ɜ ɡɚɤɪɵɬɨɣ ɫɢɫɬɟɦɟ). Ⱥɧɚɥɢɡɢɪɭɹ ɩɨɞɨɛɧɵɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, Ʌɟ ɒɚɬɟɥɶɟ (H. L. Le Chatelier, 1884) ɫɮɨɪɦɭɥɢɪɨɜɚɥ ɨɛɳɢɣ ɩɪɢɧɰɢɩ: ɜɨɡɞɟɣɫɬɜɢɟ, ɜɵɜɨɞɹɳɟɟ ɫɢɫɬɟɦɭ ɢɡ ɪɚɜɧɨɜɟɫɢɹ, ɜɵɡɵɜɚɟɬ ɜ ɧɟɣ ɢɡɦɟɧɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɨɫɥɚɛɥɟɧɢɸ ɷɬɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ. ɉɪɢɧɰɢɩ ɛɵɥ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ ɨɛɨɫɧɨɜɚɧ Ȼɪɚɭɧɨɦ (C. Braun, 1887), ɩɨɷɬɨɦɭ ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɩɪɢɧɰɢɩɚ Ʌɟ ɒɚɬɟɥɶɟ – Ȼɪɚɭɧɚ. ȼ ɡɚɤɥɸɱɟɧɢɟ ɨɬɦɟɬɢɦ, ɱɬɨ ɩɪɢɫɭɬɫɬɜɢɟ ɤɚɬɚɥɢɡɚɬɨɪɚ ɧɟ ɨɤɚɡɵɜɚɟɬ ɜɥɢɹɧɢɹ ɧɚ ɤɨɧɫɬɚɧɬɭ ɪɚɜɧɨɜɟɫɢɹ, ɯɨɬɹ ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬ ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɟɣ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ. Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɤɚɬɚɥɢɡɚɬɨɪ ɜ ɪɚɜɧɨɣ ɫɬɟɩɟɧɢ ɭɫɤɨɪɹɟɬ (ɢɧɝɢɛɢɬɨɪ – ɡɚɦɟɞɥɹɟɬ) ɷɬɢ ɩɪɨɰɟɫɫɵ, ɬɚɤ ɱɬɨ ɟɝɨ ɧɚɥɢɱɢɟ ɜɥɢɹɟɬ ɥɢɲɶ ɧɚ ɫɤɨɪɨɫɬɶ ɭɫɬɚɧɨɜɥɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɚ ɧɟ ɧɚ ɟɝɨ ɩɨɥɨɠɟɧɢɟ.
B
25
26
II. ɋɉȿɄɌɊɈɎɈɌɈɆȿɌɊɂɑȿɋɄɂɃ ɂ ɄɈɅɈɊɂɆȿɌɊɂɑȿɋɄɂɃ ɆȿɌɈȾɕ
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɚɹ ɨɛɥɚɫɬɶ, ɢɫɫɥɟɞɭɸɳɚɹ ɩɨɝɥɨɳɟɧɢɟ ɜɟɳɟɫɬɜɨɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɜ ɨɩɬɢɱɟɫɤɨɦ ɞɢɚɩɚɡɨɧɟ (ɜɤɥɸɱɚɸɳɟɦ ɭɥɶɬɪɚɮɢɨɥɟɬɨɜɨɟ (ɍɎ), ɜɢɞɢɦɨɟ ɢ ɢɧɮɪɚɤɪɚɫɧɨɟ (ɂɄ) ɢɡɥɭɱɟɧɢɟ) ɧɚɡɵɜɚɟɬɫɹ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɫɩɟɤɬɪɨɮɨɬɨɦɟɬɪɢɟɣ. Ɇɟɬɨɞɵ ɫɩɟɤɬɪɨɮɨɬɨɦɟɬɪɢɢ ɩɪɢɦɟɧɹɸɬɫɹ ɜ ɯɢɦɢɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɣ ɜɟɳɟɫɬɜ, ɢɫɫɥɟɞɨɜɚɧɢɹ ɢɯ ɫɬɪɨɟɧɢɹ, ɪɟɚɤɰɢɣ ɢ ɞɪɭɝɢɯ ɰɟɥɟɣ. ȼ ɞɚɧɧɨɦ ɩɪɚɤɬɢɤɭɦɟ ɦɵ ɩɪɢɦɟɧɢɦ ɷɬɢ ɦɟɬɨɞɵ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɤɢɧɟɬɢɤɢ ɢ ɪɚɜɧɨɜɟɫɢɹ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ. 1. Ɉɛɳɢɟ ɫɜɟɞɟɧɢɹ ɉɭɫɬɶ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɨɟ ɢɡɥɭɱɟɧɢɟ ɫ ɞɥɢɧɨɣ ɜɨɥɧɵ O ɩɚɞɚɟɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɢɡ ɜɚɤɭɭɦɚ ɧɚ ɩɨɝɥɨɳɚɸɳɭɸ ɫɪɟɞɭ (ɪɢɫ. 5). ȼ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɨɬɪɚɠɟɧɢɟɦ ɢ ɪɚɫɫɟɹɧɢɟɦ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. Ɍɨɝɞɚ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɢɡɥɭɱɟɧɢɹ I(x) ɨɫɥɚɛɟɜɚɟɬ ɩɨ ɯɨɞɭ ɥɭɱɚ ɩɨ ɡɚɤɨɧɭ:
dI ( x) dx
DI ( x ) ,
(II.1)
ɝɞɟ D > 0 – ɤɨɷɮɮɢɰɢɟɧɬ, ɧɚɡɵɜɚɟɦɵɣ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɨɫɥɚɛɥɟɧɢɹ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɭɛɵɥɶ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɫɚɦɨɣ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɫɜɟɬɚ ɜ ɞɚɧɧɨɣ ɬɨɱɤɟ ɫɪɟɞɵ x. Ⱦɥɹ ɨ ɞ ɧ ɨ ɪ ɨ ɞ ɧ ɵ ɯ ɫɪɟɞ ɤɨɷɮɮɢɰɢɟɧɬ D ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɥɳɢɧɵ x ɫɥɨɹ, ɜ ɤɨɬɨɪɨɦ ɩɪɨɢɡɨɲɥɨ ɩɨɝɥɨɳɟɧɢɟ. ɉɪɢ ɷɬɨɦ ɭɫɥɨɊɢɫ. 5 ɜɢɢ ɭɪɚɜɧɟɧɢɟ (II.1) ɦɨɠɧɨ ɢɧɬɟɝɪɢɪɨɜɚɬɶ, ɫɨɜɦɟɳɚɹ ɧɚɱɚɥɨ ɨɬɫɱɟɬɚ (x = 0) ɫ ɝɪɚɧɢɰɟɣ ɩɨɝɥɨɳɚɸɳɟɣ ɫɪɟɞɵ: I ( x)
y I0
dI I
x
y
D dx . 0
Ɂɞɟɫɶ I0 – ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ, ɬɨ ɟɫɬɶ I0 = I|x = 0. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ I(x) = I0 e–Dx. (II.2) Ɏɨɪɦɭɥɚ (II.2) ɞɚɟɬ ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɫɜɟɬɨɩɨɝɥɨɳɟɧɢɹ, ɧɚɡɵɜɚɟɦɵɣ ɡɚɤɨɧɨɦ Ȼɭɝéɪɚ – Ʌáɦɛɟɪɬɚ (P. Bouguer, J. H. Lambert, 1760). Ɉɧɚ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɩɚɞɚɟɬ ɫ ɬɨɥɳɢɧɨɣ ɩɨɝɥɨɳɚɸɳɟɝɨ ɫɥɨɹ (ɪɢɫ. 5). ȼɜɨɞɹɬ ɫɥɟɞɭɸɳɢɟ ɮɨɬɨɦɟɬɪɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ: ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɩɪɨDx ɩɭɫɤɚɧɢɟ T I I 0 e , ɩɨɤɚɡɵɜɚɸɳɟɟ ɞɨɥɸ ɢɡɥɭɱɟɧɢɹ, ɩɪɨɲɟɞɲɟɝɨ ɤ ɬɨɱɤɟ x, ɜ ɫɪɚɜɧɟɧɢɢ ɫ ɩɚɞɚɸɳɢɦ; ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɩɨɝɥɨɳɟɧɢɟ A = 1 – T, ɩɨɤɚɡɵɜɚɸɳɟɟ ɞɨɥɸ ɡɚɞɟɪɠɚɧɧɨɝɨ ɢɡɥɭɱɟɧɢɹ; ɨɩɬɢɱɟɫɤɭɸ ɩɥɨɬɧɨɫɬɶ 27
D = – lg T = Dxlg e. ɉɨɫɥɟɞɧɹɹ ɜɟɥɢɱɢɧɚ ɬɚɤɠɟ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɬɟɩɟɧɶ ɩɨɝɥɨɳɟɧɢɹ, ɩɨɫɤɨɥɶɤɭ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɨɷɮɮɢɰɢɟɧɬɭ ɨɫɥɚɛɥɟɧɢɹ ɢ ɬɨɥɳɢɧɟ ɩɨɝɥɨɳɚɸɳɟɝɨ ɫɥɨɹ. ȿɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ D ɜɟɥɢɤ, ɬɨ ɞɚɠɟ ɬɨɧɤɢɣ ɫɥɨɣ ɜɟɳɟɫɬɜɚ ɧɟɩɪɨɡɪɚɱɟɧ ɞɥɹ ɞɚɧɧɨɣ ɞɥɢɧɵ ɜɨɥɧɵ (ɞɨɥɹ ɩɪɨɲɟɞɲɟɝɨ ɢɡɥɭɱɟɧɢɹ T ɦɚɥɚ, ɜɟɥɢɤɚ ɨɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ D). ȼɚɠɧɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɩɪɨɯɨɠɞɟɧɢɢ ɱɟɪɟɡ ɨɛɵɱɧɭɸ (ɧɟɚɤɬɢɜɧɭɸ) ɫɪɟɞɭ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɨɟ ɢɡɥɭɱɟɧɢɟ ɧɟ ɦɟɧɹɟɬ ɞɥɢɧɭ ɜɨɥɧɵ. ɇɚɩɪɢɦɟɪ, ɟɫɥɢ ɦɵ ɜɨɡɶɦɟɦ ɡɟɥɟɧɨɟ ɫɬɟɤɥɨ ɢ ɩɪɨɩɭɫɬɢɦ ɱɟɪɟɡ ɧɟɝɨ ɤɪɚɫɧɵɣ ɫɜɟɬ, ɬɨ ɧɚ ɜɵɯɨɞɟ ɦɵ ɭɜɢɞɢɦ ɫɢɥɶɧɨ ɨɫɥɚɛɥɟɧɧɵɣ, ɧɨ ɬɨɬ ɠɟ ɤɪɚɫɧɵɣ ɫɜɟɬ. ɍɪɚɜɧɟɧɢɹ (II.1), (II.2) ɡɚɩɢɫɚɧɵ ɞɥɹ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɨɣ ɜɨɥɧɵ. ȼɦɟɫɬɟ ɫ ɬɟɦ ɨɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ D ɡɚɜɢɫɢɬ ɨɬ ɞɥɢɧɵ ɜɨɥɧɵ. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɜɟɫɶɦɚ ɫɥɨɠɧɚ ɢ ɨɛɥɚɞɚɟɬ ɨɩɪɟɞɟɥɟɧɧɨɣ ɢɧɞɢɜɢɞɭɚɥɶɧɨɫɬɶɸ ɞɥɹ ɤɚɠɞɨɝɨ ɜɟɳɟɫɬɜɚ. Ɂɚɜɢɫɢɦɨɫɬɶ D(O) ɧɚɡɵɜɚɟɬɫɹ ɫɩɟɤɬɪɨɦ ɩɨɝɥɨɳɟɧɢɹ * ɢɥɢ ɚɛɫɨɪɛɰɢɨɧɧɵɦ ɫɩɟɤɬɪɨɦ ) . ɇɚ ɩɪɚɤɬɢɤɟ ɫɩɟɤɬɪɵ ɜɵɪɚɠɚɸɬ ɬɚɤɠɟ ɫ ɩɨɦɨɳɶɸ ɡɚɜɢɫɢɦɨɫɬɟɣ D(O) ɢɥɢ T(O) (ɜ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɫɩɟɤɬɪɟ ɩ ɪ ɨ ɩ ɭ ɫ ɤ ɚ ɧ ɢ ɹ). ɋɬɪɨɟɧɢɟ ɫɩɟɤɬɪɨɜ ɩɨɝɥɨɳɟɧɢɹ ɪɚɡɥɢɱɧɵɯ ɜɟɳɟɫɬɜ ɜ ɨɩɬɢɱɟɫɤɨɣ ɨɛɥɚɫɬɢ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɬɟɦ, ɱɬɨ ɨɧɢ ɫɨɫɬɨɹɬ ɢɡ ɧɚɛɨɪɚ ɦɚɤɫɢɦɭɦɨɜ, ɩɨɹɜɥɹɸɳɢɯɫɹ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɞɥɢɧ ɜɨɥɧ Om. ɋɭɳɟɫɬɜɨɜɚɧɢɟ ɦɚɤɫɢɦɭɦɚ D(Om) ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜɟɳɟɫɬɜɨ ɫɬɚɧɨɜɢɬɫɹ ɧɟɩɪɨɡɪɚɱɧɵɦ ɞɥɹ ɢɡɥɭɱɟɧɢɹ ɜ ɧɟɤɨɬɨɪɨɣ ɨɤɪɟɫɬɧɨɫɬɢ Om. ɉɨɷɬɨɦɭ ɤɚɠɞɵɣ ɬɚɤɨɣ ɦɚɤɫɢɦɭɦ ɧɚɡɵɜɚɸɬ ɩɨɥɨɫɨɣ ɩɨɝɥɨɳɟɧɢɹ. ȿɫɥɢ ɜɟɳɟɫɬɜɨ ɢɦɟɟɬ ɩɨɥɨɫɵ ɩɨɝɥɨɳɟɧɢɹ ɜ ɜɢɞɢɦɨɣ ɨɛɥɚɫɬɢ, ɬɨ ɨɧɢ ɨɛɭɫɥɨɜɥɢɜɚɸɬ ɨɤɪɚɫɤɭ ɷɬɨɝɨ ɜɟɳɟɫɬɜɚ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɧɚ ɪɢɫ. 6 ɩɪɢɜɟɞɟɧ ɫɩɟɤɬɪ T(O) ɜɨɞɧɨɝɨ ɪɚɫɬɜɨɪɚ ɫɢɧɟɣ ɤɪɚɫɤɢ, ɢɡɜɟɫɬɧɨɣ ɩɨɞ ɧɚɡɜɚɧɢɟɦ «ɛɪɨɦɬɢɦɨɥɨɜɵɣ ɫɢɧɢɣ». ȼ ɛɥɢɠɧɟɣ ɭɥɶɬɪɚɮɢɨɥɟɬɨɜɨɣ (O ɨɬ 200 ɞɨ 400 ɧɦ) ɢ ɜɢɞɢɦɨɣ (ɨɬ 400 ɞɨ 760 ɧɦ) ɨɛɥɚɫɬɢ ɧɚɛɥɸɞɚɸɬɫɹ ɱɟɬɵɪɟ ɩɨɥɨɫɵ ɩɨɝɥɨɳɟɧɢɹ (ɹɫɧɨ, ɱɬɨ ɦ ɚ ɤ ɫ ɢ ɦ ɭ ɦ ɩɨɝɥɨɳɟɧɢɹ D ɢɥɢ D ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦ ɢ ɧ ɢ ɦ ɭ ɦ ɭ ɩɪɨɩɭɫɤɚɧɢɹ T). ɒɢɪɨɤɚɹ ɢɧɬɟɧɫɢɜɧɚɹ ɩɨɥɨɫɚ ɜ ɜɢɞɢɦɨɣ ɨɛɥɚɫɬɢ ɢɦɟɟɬ ɦɚɤɫɢɦɭɦ ɩɪɢ 614 ɧɦ. Ɉɧɚ «ɜɵɪɟɡɚɟɬ» ɢɡ ɫɩɟɤɬɪɚ ɡɟɥɟɧɭɸ, ɠɟɥɬɭɸ ɢ ɨɪɚɧɠɟɜɨɤɪɚɫɧɭɸ ɱɚɫɬɢ. Ɂɞɟɫɶ ɜɟɳɟɫɬɜɨ ɧɟɩɪɨɡɪɚɱɧɨ. ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɭɥɶɬɪɚɮɢɨɥɟɬɨɜɚɹ ɩɨɥɨɫɚ 395 ɧɦ ɡɚɯɜɚɬɵɜɚɟɬ ɜɢɞɢɦɭɸ ɮɢɨɥɟɬɨɜɭɸ ɱɚɫɬɶ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭ ɧɚɲɟɝɨ ɜɟɳɟɫɬɜɚ ɨɛɪɚɡɭɟɬɫɹ «ɨɤɧɨ» ɩɪɨɩɭɫɤɚɧɢɹ ɜ ɨɛɥɚɫɬɢ ɩɪɢɦɟɪɧɨ ɨɬ 425 ɞɨ 525 ɧɦ. ɉɨɷɬɨɦɭ ɟɝɨ ɪɚɫɬɜɨɪ ɨɤɪɚɲɟɧ ɜ ɝɥɭɛɨɤɢɣ ɫɢɧɢɣ ɰɜɟɬ.
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Ɉɬ ɥɚɬ. absorbeo – ɩɨɝɥɨɳɚɸ. 28
ȿɫɥɢ ɬɟɩɟɪɶ ɢɦɟɟɬɫɹ ɫɦɟɫɶ ɜɟɳɟɫɬɜ, ɤɚɠɞɨɟ ɢɡ ɤɨɬɨɪɵɯ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɫɜɨɢɦ ɫɩɟɤɬɪɨɦ Hi(O), ɬɨ ɫɨɝɥɚɫɧɨ ɡɚɤɨɧɭ Ȼɟɪɚ ɤɨɷɮɮɢɰɢɟɧɬ ɨɫɥɚɛɥɟɧɢɹ D (O ) Hi (O )Ci .
6 i
Ɂɞɟɫɶ Ci – ɤɨɧɰɟɧɬɪɚɰɢɹ i-ɝɨ ɜɟɳɟɫɬɜɚ, ɚ ɫɭɦɦɚ ɛɟɪɟɬɫɹ ɩɨ ɜɫɟɦ ɜɟɳɟɫɬɜɚɦ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɢɧɞɢɜɢɞɭɚɥɶɧɵɟ ɫɩɟɤɬɪɵ ɤɨɦɩɨɧɟɧɬɨɜ ɫɤɥɚɞɵɜɚɸɬɫɹ ɫ ɭɱɟɬɨɦ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɣ, ɢ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɩɨɥɭɱɚɟɬɫɹ ɨɛɳɢɣ ɫɩɟɤɬɪ ɫɦɟɫɢ. 2. Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɣ
Ɋɢɫ. 6
Ɋɢɫ. 7
ɉɨɝɥɨɳɟɧɢɟ (ɧɚ ɤɚɠɞɨɣ ɞɥɢɧɟ ɜɨɥɧɵ) ɪɚɫɬɜɨɪɨɜ ɢ ɫɦɟɫɟɣ ɜɟɳɟɫɬɜ ɡɚɜɢɫɢɬ ɨɬ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ C. ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ Ȼɟɪɚ (A. Beer, 1852) ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɨɤɚɡɵɜɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ: D(O) = H(O)C. (II.3) ɉɨɫɬɨɹɧɧɚɹ H ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɤɫɬɢɧɤɰɢɢ *) . Ɉɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɩɪɨɩɭɫɤɚɧɢɟ T ɫɨɝɥɚɫɧɨ ɡɚɤɨɧɭ Ȼɭɝɟɪɚ – Ʌɚɦɛɟɪɬɚ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ: T = e–HCx. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɥɹ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ ɢɦɟɟɦ: D = HCxlg e. (II.4) Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪ ɜɨɞɧɵɯ ɪɚɫɬɜɨɪɨɜ ɯɪɨɦɚɬɚ ɤɚɥɢɹ K2CrO4. ɇɚ ɪɢɫ. 7 ɫɩɟɤɬɪɵ ɷɬɢɯ ɪɚɫɬɜɨɪɨɜ ɞɚɧɵ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɜ ɜɢɞɟ D(O) (ɩɨɥɨɫɟ ɩɨɝɥɨɳɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɚɤɫɢɦɭɦ). ɂɡ ɪɢɫɭɧɤɚ ɜɢɞɧɨ ɤɚɤ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɞɜɭɯ ɩɨɥɨɫ ɜɨɡɪɚɫɬɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɤɨɧɰɟɧɬɪɚɰɢɢ. ȿɫɥɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ, ɬɨ ɛɥɢɠɚɣɲɚɹ ɤ ɜɢɞɢɦɨɣ ɨɛɥɚɫɬɢ ɩɨɥɨɫɚ 376 ɧɦ ɩɟɪɟɤɪɵɜɚɟɬ ɫɢɧɸɸ ɢ ɡɟɥɟɧɭɸ ɨɛɥɚɫɬɢ, ɬɨɝɞɚ ɤɚɤ ɩɪɢ O > 550 ɧɦ ɪɚɫɬɜɨɪ ɩɪɨɡɪɚɱɟɧ (D 0). ɉɨɷɬɨɦɭ ɪɚɫɬɜɨɪ ɯɪɨɦɚɬɚ ɤɚɥɢɹ ɢɦɟɟɬ ɞɥɹ ɧɚɲɟɝɨ ɝɥɚɡɚ ɠɟɥɬɭɸ ɨɤɪɚɫɤɭ: ɦɵ ɜɢɞɢɦ ɤɪɚɣ ɭɥɶɬɪɚɮɢɨɥɟɬɨɜɨɣ ɩɨɥɨɫɵ ɩɨɝɥɨɳɟɧɢɹ.
*)
Ɂɚɤɨɧ Ȼɟɪɚ ɜ ɮɨɪɦɟ (II.4) ɩɨɡɜɨɥɹɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɡɦɟɪɟɧɢɹ ɫɜɟɬɨɩɨɝɥɨɳɟɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɣ. ɗɬɚ ɡɚɞɚɱɚ ɫɨɫɬɚɜɥɹɟɬ ɩɪɟɞɦɟɬ * ɤɨɥɨɪɢɦɟɬɪɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ) . ɉɪɟɞɫɬɚɜɢɦ ɫɟɛɟ, ɱɬɨ ɦɵ ɪɚɛɨɬɚɟɦ ɫ ɨɛɪɚɡɰɚɦɢ ɜɟɳɟɫɬɜɚ ɮɢɤɫɢɪɨɜɚɧɧɨɣ ɬɨɥɳɢɧɵ x. Ɍɨɝɞɚ ɩɪɨɢɡɜɟɞɟɧɢɟ ɷɤɫɬɢɧɤɰɢɢ H ɧɚ ɬɨɥɳɢɧɭ ɨɛɪɚɡɰɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɜɟɥɢɱɢɧɭ ɩɨɫɬɨɹɧɧɭɸ. Ɉɛɨɡɧɚɱɚɹ E = Hx lg e (lg e | 0,434), ɩɨɥɭɱɢɦ: D = EC. (II.5) Ɏɨɪɦɭɥɭ (II.5) ɱɚɳɟ ɜɫɟɝɨ ɩɪɢɦɟɧɹɸɬ ɫ ɩɨɦɨɳɶɸ ɬɚɤɨɝɨ ɩɪɢɟɦɚ. ɉɪɟɠɞɟ ɜɫɟɝɨ ɫɬɚɧɞɚɪɬɢɡɢɪɭɸɬ ɬɨɥɳɢɧɭ ɢɡɦɟɪɹɟɦɵɯ ɨɛɪɚɡɰɨɜ. ȿɫɥɢ ɪɚɛɨɬɚɸɬ ɫ ɠɢɞɤɢɦɢ ɜɟɳɟɫɬɜɚɦɢ, ɧɚɩɪɢɦɟɪ, ɠɢɞɤɢɦɢ ɪɚɫɬɜɨɪɚɦɢ, ɬɨ ɢɯ ɩɨɦɟɳɚɸɬ ɜ ɫɩɟɰɢɚɥɶɧɵɟ ɩɪɨɡɪɚɱɧɵɟ ɤɸɜɟɬɵ, ɢɦɟɸɳɢɟ ɨɩɪɟɞɟɥɟɧɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɥɨɫɤɢɦɢ ɩɚɪɚɥɥɟɥɶɧɵɦɢ ɫɬɟɧɤɚɦɢ. Ƚɨɬɨɜɹɬ ɪɹɞ ɪɚɫɬɜɨɪɨɜ ɢɫɫɥɟɞɭɟɦɨɝɨ ɜɟɳɟɫɬɜɚ ɫ ɡɚɞɚɧɧɵɦɢ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ (C1, C2, …, CN) ɢ ɢɡɦɟɪɹɸɬ ɢɯ ɨɩɬɢɱɟɫɤɢɟ ɩɥɨɬɧɨɫɬɢ (D1, D2, …, DN). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɫɬɪɨɹɬ ɝɪɚɞɭɢɪɨɜɨɱɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ D(C) ɢɥɢ ɜɵɱɢɫɥɹɸɬ ɫɪɟɞɧɢɣ ɦɟɠɞɭ ɜɫɟɦɢ ɢɡɦɟɪɟɧɢɹɦɢ ɤɨɷɮɮɢɰɢɟɧɬ N
E
29
n
n 1
n
2 n
.
n 1
ɍɫɪɟɞɧɟɧɢɟ E ɩɨ ɤɨɧɰɟɧɬɪɚɰɢɹɦ ɩɨɡɜɨɥɹɟɬ ɫɧɢɡɢɬɶ ɩɨɝɪɟɲɧɨɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ. Ɍɟɩɟɪɶ, ɢɦɟɹ ɝɪɚɞɭɢɪɨɜɤɭ, ɦɨɠɧɨ ɧɚɣɬɢ ɤɨɧɰɟɧɬɪɚɰɢɸ ɥɸɛɨɝɨ ɪɚɫɬɜɨɪɚ ɞɚɧɧɨɝɨ ɜɟɳɟɫɬɜɚ, ɫɬɨɢɬ ɬɨɥɶɤɨ ɢɡɦɟɪɢɬɶ ɟɝɨ ɨɩɬɢɱɟɫɤɭɸ ɩɥɨɬɧɨɫɬɶ: C D E. əɫɧɨ, ɱɬɨ ɜɫɟ ɢɡɦɟɪɟɧɢɹ ɧɭɠɧɨ ɩɪɨɜɨɞɢɬɶ ɧɚ ɩɨɫɬɨɹɧɧɨɣ ɞɥɢɧɟ ɜɨɥɧɵ. Ⱦɥɹ ɷɬɨɣ ɰɟɥɢ ɜɵɛɢɪɚɸɬ ɞɥɢɧɭ ɜɨɥɧɵ, ɨɬɜɟɱɚɸɳɭɸ ɦɚɤɫɢɦɭɦɭ ɧɚɢɛɨɥɟɟ ɢɧɬɟɧɫɢɜɧɨɣ ɢ ɱɟɬɤɨ ɨɩɪɟɞɟɥɹɟɦɨɣ ɩɨɥɨɫɵ ɩɨɝɥɨɳɟɧɢɹ. Ɍɟɦ ɫɚɦɵɦ ɩɨɜɵɲɚɟɬɫɹ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ ɦɟɬɨɞɚ. *)
Ɉɬ ɥɚɬ. exstinctio – ɩɨɬɭɯɚɧɢɟ.
N
6C D 6C
Ɉɬ ɥɚɬ. color – ɰɜɟɬ, ɨɤɪɚɫɤɚ. ɇɟ ɩɭɬɚɬɶ ɫ ɤɚɥɨɪɢɦɟɬɪɢɟɣ (ɥɚɬ. calor – ɬɟɩɥɨ, ɠɚɪ). 30
ɉɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɜɟɳɟɫɬɜ ɜ ɪɚɫɬɜɨɪɚɯ ɧɟɨɛɯɨɞɢɦɨ ɢɡ ɨɛɳɟɝɨ ɩɨɝɥɨɳɟɧɢɹ ɪɚɫɬɜɨɪɚ ɢɫɤɥɸɱɢɬɶ ɩɨɝɥɨɳɟɧɢɟ ɪɚɫɬɜɨɪɢɬɟɥɹ. Ⱦɥɹ ɷɬɨɝɨ ɢɡɦɟɪɹɸɬ ɬɚɤ ɧɚɡɵɜɚɟɦɭɸ «ɯɨɥɨɫɬɭɸ ɩɪɨɛɭ» – ɫɬɚɧɞɚɪɬɧɭɸ ɤɸɜɟɬɭ, ɡɚɩɨɥɧɟɧɧɭɸ ɱɢɫɬɵɦ ɪɚɫɬɜɨɪɢɬɟɥɟɦ. Ⱦɚɥɟɟ ɢɡ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ ɪɚɫɬɜɨɪɚ ɜɵɱɢɬɚɸɬ ɩɥɨɬɧɨɫɬɶ «ɯɨɥɨɫɬɨɣ ɩɪɨɛɵ» ɬɟɦ ɫɚɦɵɦ ɜɨɫɫɬɚɧɚɜɥɢɜɚɹ ɡɧɚɱɟɧɢɟ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɜɟɳɟɫɬɜɚ. ɗɬɨɬ ɩɪɢɟɦ ɩɨɡɜɨɥɹɟɬ ɬɚɤɠɟ ɫɧɢɡɢɬɶ ɜɥɢɹɧɢɟ ɨɬɪɚɠɟɧɢɹ ɧɚ ɝɪɚɧɢɰɚɯ ɜɨɡɞɭɯ / ɦɚɬɟɪɢɚɥ ɤɸɜɟɬɵ, ɦɚɬɟɪɢɚɥ ɤɸɜɟɬɵ / ɪɚɫɬɜɨɪ. III. ɉɊȺɄɌɂɑȿɋɄɂȿ ɊȺȻɈɌɕ
Ⱥɧɚɥɢɡ ɩɨ ɫɜɟɬɨɩɨɝɥɨɳɟɧɢɸ ɩɪɢɦɟɧɹɟɬɫɹ ɤɚɤ ɨɞɢɧ ɢɡ ɦɟɬɨɞɨɜ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜ ɮɢɡɢɱɟɫɤɨɣ ɯɢɦɢɢ. ɐɟɥɶ ɦɟɬɨɞɚ ɫɨɫɬɨɢɬ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɤɨɧɰɟɧɬɪɚɰɢɣ ɤɨɦɩɨɧɟɧɬɨɜ ɪɟɚɝɢɪɭɸɳɟɣ ɢɥɢ ɪɚɜɧɨɜɟɫɧɨɣ ɫɢɫɬɟɦɵ ɜ ɭɫɥɨɜɢɹɯ, ɧɟ ɧɚɪɭɲɚɸɳɢɯ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ ɢ ɯɨɞɚ ɩɪɨɰɟɫɫɚ. ɉɭɫɬɶ, ɧɚɩɪɢɦɟɪ, ɢɦɟɟɬɫɹ ɪɟɚɤɰɢɹ A + B ĺ X + Y. ȿɫɥɢ ɨɞɧɨ ɢɡ ɜɟɳɟɫɬɜ, ɫɤɚɠɟɦ, A, ɢɦɟɟɬ ɩɨɥɨɫɭ ɩɨɝɥɨɳɟɧɢɹ OA ɜ ɬɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɞɪɭɝɢɟ ɜɟɳɟɫɬɜɚ ɩɪɨɡɪɚɱɧɵ, ɬɨ ɡɚ ɤɢɧɟɬɢɤɨɣ ɩɪɟɜɪɚɳɟɧɢɹ ɦɨɠɧɨ ɧɚɛɥɸɞɚɬɶ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ, ɢɡɦɟɪɹɹ ɨɩɬɢɱɟɫɤɭɸ ɩɥɨɬɧɨɫɬɶ ɫɢɫɬɟɦɵ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɨ ɡɚɤɨɧɭ Ȼɟɪɚ (II.5) ɨɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɨɧɰɟɧɬɪɚɰɢɢ CA. Ɂɧɚɱɢɬ, ɜɪɟɦɟɧɧáɹ ɡɚɜɢɫɢɦɨɫɬɶ DOA(W) ɜɨɫɩɪɨɢɡɜɨɞɢɬ ɤɢɧɟɬɢɱɟɫɤɭɸ ɡɚɜɢɫɢɦɨɫɬɶ CA(W), ɚ ɩɪɨɢɡɜɨɞɧɚɹ ɩɨ ɜɪɟɦɟɧɢ dDO A dC
E
dW dW ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ. Ⱥɧɚɥɨɝɢɱɧɨ ɩɪɢ ɯɢɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ ɨɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɪɚɜɧɨɜɟɫɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ [A] ɜɟɳɟɫɬɜɚ. ɗɬɢɦ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɤɚɤ ɞɥɹ ɤɚɱɟɫɬɜɟɧɧɨɝɨ ɧɚɛɥɸɞɟɧɢɹ ɡɚ ɫɦɟɳɟɧɢɟɦ ɪɚɜɧɨɜɟɫɢɹ, ɬɚɤ ɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɧɫɬɚɧɬ ɪɚɜɧɨɜɟɫɢɹ. 1. ɂɫɫɥɟɞɨɜɚɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɜ ɫɢɫɬɟɦɟ «ɯɪɨɦɚɬ–ɛɢɯɪɨɦɚɬ»
ɋɨɥɢ ɯɪɨɦɨɜɨɣ ɤɢɫɥɨɬɵ H2CrO4 – ɯɪɨɦɚɬɵ – ɜ ɜɨɞɧɵɯ ɪɚɫɬɜɨɪɚɯ ɱɚɫɬɢɱɧɨ ɩɟɪɟɯɨɞɹɬ ɜ ɫɨɥɢ ɞɜɭɯɪɨɦɨɜɨɣ ɤɢɫɥɨɬɵ H2Cr2O7 – ɛɢɯɪɨɦɚɬɵ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɪɚɫɬɜɨɪɟ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɪɚɜɧɨɜɟɫɢɟ 2– (III.1) 2CrO42– + 2H+ ĺ ĸ Cr2O7 + H2O. + ɉɨɫɤɨɥɶɤɭ ɜ ɪɚɜɧɨɜɟɫɢɢ ɭɱɚɫɬɜɭɸɬ ɢɨɧɵ H , ɟɝɨ ɦɨɠɧɨ ɫɦɟɳɚɬɶ, ɢɡɦɟɧɹɹ pH ɪɚɫɬɜɨɪɚ. ɏɪɨɦɚɬɵ ɢ ɛɢɯɪɨɦɚɬɵ ɢɦɟɸɬ ɪɚɡɥɢɱɧɵɟ ɫɩɟɤɬɪɵ, ɩɨɷɬɨɦɭ ɡɚ ɫɦɟɳɟɧɢɟɦ ɪɚɜɧɨɜɟɫɢɹ ɭɞɨɛɧɨ ɫɥɟɞɢɬɶ, ɢɡɦɟɪɹɹ ɫɩɟɤɬɪ ɩɨɝɥɨɳɟɧɢɹ (ɩɪɨɩɭɫɤɚɧɢɹ) ɪɚɫɬɜɨɪɚ. ȼ ɨɛɥɚɫɬɢ O > 400 ɧɦ ɮɢɤɫɢɪɭɟɬɫɹ ɤɪɚɣ ɛɥɢɠɧɟɣ ɭɥɶɬɪɚ31
ɮɢɨɥɟɬɨɜɨɣ ɩɨɥɨɫɵ ɩɨɝɥɨɳɟɧɢɹ ɯɪɨɦɚɬɚ ɤɚɥɢɹ (ɪɢɫ. 7). ɇɚɩɪɨɬɢɜ, ɛɢɯɪɨɦɚɬ ɤɚɥɢɹ ɢɦɟɟɬ ɢɧɬɟɧɫɢɜɧɭɸ ɩɨɥɨɫɭ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ 440 ɧɦ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɜɨɞɨɪɨɞɧɵɣ ɩɨɤɚɡɚɬɟɥɶ (potentio Hydrogenii) ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɥɨɝɚɪɢɮɦ ɨɛɪɚɬɧɨɣ ɪɚɜɧɨɜɟɫɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢɨɧɨɜ ɜɨɞɨɪɨɞɚ: pH = – lg [H+]. ȼ ɧɟɣɬɪɚɥɶɧɨɣ ɫɪɟɞɟ (ɩɪɢ 25 qC) pH = 7, ɜ ɤɢɫɥɨɣ pH < 7, ɜ ɳɺɥɨɱɧɨɣ pH > 7.
ɐɟɥɶ ɪɚɛɨɬɵ. ɇɚɛɥɸɞɚɬɶ ɫɦɟɳɟɧɢɟ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɨɞɧɨɝɨ ɢɡ ɤɨɦɩɨɧɟɧɬɨɜ (ɢɨɧɨɜ H+). ɍɫɬɚɧɨɜɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɫɦɟɳɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ. Ɉɛɨɪɭɞɨɜɚɧɢɟ ɢ ɪɟɚɤɬɢɜɵ. Ɏɨɬɨɦɟɬɪ ɄɎɄ-5Ɇ ɫ ɧɚɛɨɪɨɦ ɫɜɟɬɨɮɢɥɶɬɪɨɜ 400–670 ɧɦ, 3 ɤɸɜɟɬɵ ɫ ɬɨɥɳɢɧɨɣ ɩɨɝɥɨɳɚɸɳɟɝɨ ɫɥɨɹ 10,00 ɦɦ. pH-ɦɟɬɪ ɫɨ ɫɬɟɤɥɹɧɧɵɦ ɷɥɟɤɬɪɨɞɨɦ. Ɇɚɝɧɢɬɧɚɹ ɦɟɲɚɥɤɚ ɫ ɹɤɨɪɟɦ. Ɋɚɫɬɜɨɪ 0,005 ɦɨɥɶ/ɥ ɯɪɨɦɚɬɚ ɤɚɥɢɹ. ɋɟɪɧɚɹ ɤɢɫɥɨɬɚ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɚɹ, ɫɟɪɧɚɹ ɤɢɫɥɨɬɚ 1 ɦɨɥɶ/ɥ. Ɋɚɫɬɜɨɪ KOH 1 ɦɨɥɶ/ɥ. ȼɨɞɚ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɚɹ. 3 ɫɬɚɤɚɧɚ ɟɦɤɨɫɬɶɸ 100 ɦɥ, 2 ɤɚɩɟɥɶɧɵɟ ɩɢɩɟɬɤɢ. Ȼɭɦɚɠɧɵɟ ɮɢɥɶɬɪɵ.
ȼɵɩɨɥɧɟɧɢɟ ɪɚɛɨɬɵ. ȼ ɫɬɚɤɚɧ ɜɧɟɫɢɬɟ 20–30 ɦɥ ɪɚɫɬɜɨɪɚ ɯɪɨɦɚɬɚ ɤɚɥɢɹ. Ɉɩɭɫɬɢɬɟ ɹɤɨɪɶ ɦɚɝɧɢɬɧɨɣ ɦɟɲɚɥɤɢ ɢ ɩɨɫɬɚɜɶɬɟ ɫɬɚɤɚɧ ɧɚ ɩɨɞɫɬɚɜɤɭ ɦɟɲɚɥɤɢ. Ɋɟɝɭɥɢɪɭɹ ɱɚɫɬɨɬɭ ɜɪɚɳɟɧɢɹ, ɞɨɛɟɣɬɟɫɶ ɯɨɪɨɲɟɝɨ ɩɟɪɟɦɟɲɢɜɚɧɢɹ ɪɚɫɬɜɨɪɚ. ȼɧɟɫɢɬɟ ɜ ɪɚɫɬɜɨɪ ɷɥɟɤɬɪɨɞ pH-ɦɟɬɪɚ. ɇɚɛɥɸɞɚɹ ɡɚ ɩɨɤɚɡɚɧɢɹɦɢ ɩɪɢɛɨɪɚ ɞɨɠɞɢɬɟɫɶ ɭɫɬɚɧɨɜɥɟɧɢɹ ɩɨɫɬɨɹɧɧɨɝɨ ɡɧɚɱɟɧɢɹ. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɞɥɹ ɩɪɚɜɢɥɶɧɵɯ ɩɨɤɚɡɚɧɢɣ pH ɬɪɟɛɭɟɬɫɹ ɜɪɟɦɹ, ɱɬɨɛɵ ɧɚ ɷɥɟɤɬɪɨɞɟ ɭɫɬɚɧɨɜɢɥɨɫɶ ɦɟɦɛɪɚɧɧɨɟ ɪɚɜɧɨɜɟɫɢɟ. ȼɇɂɆȺɇɂȿ! ɋɬɟɤɥɹɧɧɵɣ ɷɥɟɤɬɪɨɞ ɯɪɭɩɨɤ ɢ ɬɪɟɛɭɟɬ ɨɫɬɨɪɨɠɧɨɝɨ ɨɛɪɚɳɟɧɢɹ. ɇɟ ɞɨɩɭɫɤɚɟɬɫɹ ɫɢɥɶɧɨ ɜɫɬɪɹɯɢɜɚɬɶ ɷɥɟɤɬɪɨɞ ɢ ɩɪɢɤɚɫɚɬɶɫɹ ɪɚɛɨɱɟɣ ɱɚɫɬɶɸ ɤ ɩɨɫɬɨɪɨɧɧɢɦ ɩɪɟɞɦɟɬɚɦ. ȿɫɥɢ ɷɥɟɤɬɪɨɞ ɧɟ ɢɫɩɨɥɶɡɭɟɬɫɹ, ɨɧ ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɜ ɨɬɞɟɥɶɧɨɦ ɫɬɚɤɚɧɟ ɫ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɨɣ ɜɨɞɨɣ. ɂɡɜɥɟɤɚɹ ɷɥɟɤɬɪɨɞ, ɩɪɨɦɨɤɧɢɬɟ ɤɚɩɥɢ ɜɨɞɵ ɢɥɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɪɚɫɬɜɨɪɚ ɛɭɦɚɠɧɵɦ ɮɢɥɶɬɪɨɦ.
ɇɟɫɤɨɥɶɤɢɦɢ ɤɚɩɥɹɦɢ ɳɟɥɨɱɢ ɞɨɜɟɞɢɬɟ pH ɪɚɫɬɜɨɪɚ ɞɨ ɡɧɚɱɟɧɢɹ ɜ ɢɧɬɟɪɜɚɥɟ 9–11. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ ɧɚ ɰɜɟɬ ɪɚɫɬɜɨɪɚ. ȼɧɟɫɢɬɟ ɩɪɢɝɨɬɨɜɥɟɧɧɵɣ ɳɺɥɨɱɧɵɣ ɪɚɫɬɜɨɪ ɜ ɤɸɜɟɬɭ, ɞɪɭɝɭɸ ɤɸɜɟɬɭ ɡɚɩɨɥɧɢɬɟ ɞɢɫɬɢɥɥɢɪɨ32
ɜɚɧɧɨɣ ɜɨɞɨɣ. ɋɧɢɦɢɬɟ ɫɩɟɤɬɪ ɩɪɨɩɭɫɤɚɧɢɹ ɪɚɫɬɜɨɪɚ T(O) ɜ ɨɛɥɚɫɬɢ ɞɥɢɧ ɜɨɥɧ 400–670 ɧɦ, ɢɫɩɨɥɶɡɭɹ ɜ ɤɚɱɟɫɬɜɟ «ɯɨɥɨɫɬɨɣ ɩɪɨɛɵ» ɤɸɜɟɬɭ ɫ ɜɨɞɨɣ. Ɋɟɡɭɥɶɬɚɬɵ ɢɡɦɟɪɟɧɢɣ ɪɟɤɨɦɟɧɞɭɟɦ ɜɧɟɫɬɢ ɜ ɬɚɛɥɢɰɭ: O, ɧɦ
ɉɪɨɩɭɫɤɚɧɢɟ T, % pH = … pH = …
ȼ ɞɪɭɝɨɦ ɫɬɚɤɚɧɟ ɚɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɩɪɢɝɨɬɨɜɶɬɟ ɪɚɫɬɜɨɪ ɯɪɨɦɚɬɚ ɤɚɥɢɹ, ɩɨɞɤɢɫɥɟɧɧɵɣ ɫɟɪɧɨɣ ɤɢɫɥɨɬɨɣ. Ⱦɥɹ ɷɬɨɝɨ ɜ ɯɨɪɨɲɨ ɩɟɪɟɦɟɲɢɜɚɟɦɵɣ ɪɚɫɬɜɨɪ ɜɧɨɫɢɬɟ ɩɢɩɟɬɤɨɣ ɤɢɫɥɨɬɭ (ɨɫɬɨɪɨɠɧɨ, ɩɨ ɤɚɩɥɹɦ!), ɧɚɛɥɸɞɚɹ ɡɚ ɡɧɚɱɟɧɢɹɦɢ pH ɩɨ ɩɨɤɚɡɚɧɢɹɦ pH-ɦɟɬɪɚ. Ⱦɨɜɟɞɢɬɟ pH ɪɚɫɬɜɨɪɚ ɞɨ ɡɧɚɱɟɧɢɹ 1–3. Ɂɚɦɟɬɶɬɟ ɰɜɟɬ ɪɚɫɬɜɨɪɚ. ɋɧɢɦɢɬɟ ɫɩɟɤɬɪ ɩɪɨɩɭɫɤɚɧɢɹ ɜ ɨɛɥɚɫɬɢ 400–670 ɧɦ. Ɂɚɞɚɧɢɹ. ɉɨɫɬɪɨɣɬɟ ɫɩɟɤɬɪɵ ɩɪɨɩɭɫɤɚɧɢɹ ɢɫɫɥɟɞɨɜɚɧɧɵɯ ɪɚɫɬɜɨɪɨɜ ɜ ɤɨɨɪɞɢɧɚɬɚɯ T(O). Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɫɪɚɜɧɟɧɢɹ ɨɛɚ ɫɩɟɤɬɪɚ ɪɟɤɨɦɟɧɞɭɟɦ ɩɨɫɬɪɨɢɬɶ ɧɚ ɨɞɧɨɦ ɪɢɫɭɧɤɟ. Ɉɛɴɹɫɧɢɬɟ ɪɚɡɥɢɱɢɟ ɫɩɟɤɬɪɨɜ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɫɦɟɳɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ (III.1). ɋɨɝɥɚɫɭɣɬɟ ɜɚɲɟ ɧɚɛɥɸɞɟɧɢɟ ɫ ɡɚɤɨɧɨɦ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɢ ɩɪɢɧɰɢɩɨɦ Ʌɟ ɒɚɬɟɥɶɟ. Ɉɛɴɹɫɧɢɬɟ ɜɢɞɢɦɵɟ ɰɜɟɬɚ ɪɚɫɬɜɨɪɨɜ ɩɨɫɥɟ ɩɨɞɤɢɫɥɟɧɢɹ ɢ ɩɨɞɳɟɥɚɱɢɜɚɧɢɹ. 2. ɂɫɫɥɟɞɨɜɚɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɞɢɫɫɨɰɢɚɰɢɢ. Ɉɩɪɟɞɟɥɟɧɢɟ pKa ɫɥɚɛɨɣ ɤɢɫɥɨɬɵ
ȼ ɪɚɫɬɜɨɪɟ ɫɥɚɛɨɣ ɤɢɫɥɨɬɵ HA ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɪɚɜɧɨɜɟɫɢɟ + – HA ĺ (III.2) ĸH +A ɞɢɫɫɨɰɢɚɰɢɢ (ɢɨɧɢɡɚɰɢɢ). Ʉɨɧɫɬɚɧɬɚ ɷɬɨɝɨ ɪɚɜɧɨɜɟɫɢɹ Ka ɧɚɡɵɜɚɟɬɫɹ ɤɨɧɫɬɚɧɬɨɣ ɤɢɫɥɨɬɧɨɣ ɞɢɫɫɨɰɢɚɰɢɢ ɢ ɢɦɟɟɬ ɜɢɞ:
Ka
[H ][ A ] [HA]
ɢɥɢ
pK a
lg
[ A ] pH , [HA]
(III.3)
ɟɫɥɢ ɩɟɪɟɣɬɢ ɤ ɥɨɝɚɪɢɮɦɭ. Ɂɞɟɫɶ ɜɜɟɞɟɧɚ ɮɭɧɤɰɢɹ pKa = – lg Ka, ɧɚɡɵɜɚɟɦɚɹ ɩɨɤɚɡɚɬɟɥɟɦ ɤɨɧɫɬɚɧɬɵ. Ɂɧɚɱɟɧɢɟ ɤɨɧɫɬɚɧɬɵ ɪɚɜɧɨɜɟɫɢɹ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɪɚɜɧɨɜɟɫɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ [H+], [A–], [HA] ɱɚɫɬɢɰ H+, A– ɢ HA. ɇɚɩɪɨɬɢɜ, ɤɚɤɨɜɵ ɛɵ ɧɢ ɛɵɥɢ ɷɬɢ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɢɯ ɨɬɧɨɲɟɧɢɟ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ ɩɪɢ ɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ. Ɉɬɫɸɞɚ ɹɫɧɨ, ɱɬɨ ɨɩɪɟɞɟɥɢɬɶ ɜɟɥɢɱɢɧɭ pKa ɦɨɠɧɨ, ɩɨɞɛɢɪɚɹ ɬɚɤɨɟ ɡɧɚɱɟɧɢɟ pH0, ɩɪɢ ɤɨɬɨɪɨɦ [A–] = [HA]. ɂɡ ɭɪɚɜɧɟɧɢɹ (III.3) ɫɥɟɞɭɟɬ, ɱɬɨ pKa = pH0.
(III.4)
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚɞɚɱɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɧɫɬɚɧɬɵ ɞɢɫɫɨ33
ɰɢɚɰɢɢ ɫɜɨɞɢɬɫɹ ɤ ɜɵɪɚɜɧɢɜɚɧɢɸ ɤɨɧɰɟɧɬɪɚɰɢɣ ɞɢɫɫɨɰɢɢɪɨɜɚɧɧɨɣ A– ɢ ɧɟɞɢɫɫɨɰɢɢɪɨɜɚɧɧɨɣ HA ɮɨɪɦ. ɗɬɭ ɡɚɞɚɱɭ ɦɨɠɧɨ ɪɟɲɢɬɶ ɫ ɩɨɦɨɳɶɸ ɫɩɟɤɬɪɨɮɨɬɨɦɟɬɪɢɢ, ɟɫɥɢ ɮɨɪɦɵ HA ɢ A– ɢɦɟɸɬ ɪɟɡɤɨ ɪɚɡɥɢɱɧɵɟ ɫɩɟɤɬɪɵ ɩɨɝɥɨɳɟɧɢɹ. Ɍɚɤɢɦ ɫɜɨɣɫɬɜɨɦ ɨɛɥɚɞɚɸɬ ɧɟɤɨɬɨɪɵɟ ɫɥɚɛɵɟ ɨɪɝɚɧɢɱɟɫɤɢɟ ɤɢɫɥɨɬɵ. ɂɯ ɢɨɧɵ A– ɢ ɧɟɞɢɫɫɨɰɢɢɪɨɜɚɧɧɵɟ ɦɨɥɟɤɭɥɵ HA ɱɚɫɬɨ ɛɵɜɚɸɬ ɨɤɪɚɲɟɧɵ ɜ ɪɚɡɧɵɟ ɰɜɟɬɚ, ɬɨ ɟɫɬɶ ɢɦɟɸɬ ɩɨɥɨɫɵ ɩɨɝɥɨɳɟɧɢɹ ɜ ɜɢɞɢɦɨɣ ɨɛɥɚɫɬɢ. ɉɨɫɤɨɥɶɤɭ ɪɚɜɧɨɜɟɫɢɟ (III.2) ɡɚɜɢɫɢɬ ɨɬ pH, ɷɬɢ ɜɟɳɟɫɬɜɚ ɩɪɢɦɟɧɹɸɬ ɜ ɤɚɱɟɫɬɜɟ ɤɢɫɥɨɬɧɨɨɫɧóɜɧɵɯ ɢɧɞɢɤɚɬɨɪɨɜ. Ɍɚɤɨɜɵ, ɧɚɩɪɢɦɟɪ, ɮɟɧɨɥɮɬɚɥɟɢɧ, ɦɟɬɢɥɨɜɵɣ ɨɪɚɧɠɟɜɵɣ ɢ ɦɧɨɝɢɟ ɞɪɭɝɢɟ. ȼ ɷɬɨɣ ɪɚɛɨɬɟ ɦɵ ɢɫɩɨɥɶɡɭɟɦ ɨɞɢɧ ɢɡ ɢɧɞɢɤɚɬɨɪɨɜ – ɛɪɨɦɬɢɦɨɥɨɜɵɣ ɫɢɧɢɣ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɫɥɚɛɭɸ ɨɞɧɨɨɫɧóɜɧɭɸ ɤɢɫɥɨɬɭ HA. ɐɟɥɶ ɪɚɛɨɬɵ. Ɉɩɪɟɞɟɥɢɬɶ ɤɨɧɫɬɚɧɬɭ ɞɢɫɫɨɰɢɚɰɢɢ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɨɝɨ ɢɧɞɢɤɚɬɨɪɚ ɜ ɜɨɞɧɨɦ ɪɚɫɬɜɨɪɟ. Ɉɛɨɪɭɞɨɜɚɧɢɟ ɢ ɪɟɚɤɬɢɜɵ. Ɏɨɬɨɦɟɬɪ ɄɎɄ-5Ɇ ɫ ɧɚɛɨɪɨɦ ɫɜɟɬɨɮɢɥɶɬɪɨɜ 400–670 ɧɦ, 4 ɤɸɜɟɬɵ ɫ ɬɨɥɳɢɧɨɣ ɩɨɝɥɨɳɚɸɳɟɝɨ ɫɥɨɹ 10,00 ɦɦ. pH-ɦɟɬɪ ɫɨ ɫɬɟɤɥɹɧɧɵɦ ɷɥɟɤɬɪɨɞɨɦ. Ɇɚɝɧɢɬɧɚɹ ɦɟɲɚɥɤɚ ɫ ɹɤɨɪɟɦ. Ɋɚɫɬɜɨɪ 0,02–0,04 ɝ/ɥ ɛɪɨɦɬɢɦɨɥɨɜɨɝɨ ɫɢɧɟɝɨ. Ɋɚɫɬɜɨɪ ɫɟɪɧɨɣ ɤɢɫɥɨɬɵ 1 ɦɨɥɶ/ɥ. Ɋɚɫɬɜɨɪ KOH 1 ɦɨɥɶ/ɥ. ȼɨɞɚ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɚɹ. 4 ɫɬɚɤɚɧɚ ɟɦɤɨɫɬɶɸ 100 ɦɥ, 3 ɤɚɩɟɥɶɧɵɟ ɩɢɩɟɬɤɢ. Ȼɭɦɚɠɧɵɟ ɮɢɥɶɬɪɵ.
ȼɵɩɨɥɧɟɧɢɟ ɪɚɛɨɬɵ. ȼ ɫɬɚɤɚɧ ɟɦɤɨɫɬɶɸ 100 ɦɥ ɜɧɟɫɢɬɟ ɨɤɨɥɨ 50 ɦɥ ɪɚɫɬɜɨɪɚ ɛɪɨɦɬɢɦɨɥɨɜɨɝɨ ɫɢɧɟɝɨ. ɂɫɩɨɥɶɡɭɹ ɦɚɝɧɢɬɧɭɸ ɦɟɲɚɥɤɭ, ɞɨɛɟɣɬɟɫɶ ɯɨɪɨɲɟɝɨ ɩɟɪɟɦɟɲɢɜɚɧɢɹ ɪɚɫɬɜɨɪɚ. ȼɧɟɫɢɬɟ ɜ ɪɚɫɬɜɨɪ ɷɥɟɤɬɪɨɞ pH-ɦɟɬɪɚ ɢ, ɞɨɛɚɜɥɹɹ ɩɨ ɤɚɩɥɹɦ ɫɟɪɧɭɸ ɤɢɫɥɨɬɭ, ɞɨɜɟɞɢɬɟ pH ɞɨ ɡɧɚɱɟɧɢɹ 4–5. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɜɚɦɢ ɛɭɞɟɬ ɩɨɥɭɱɟɧ ɪɚɫɬɜɨɪ ʋ 1 (ɡɚɦɟɬɶɬɟ ɟɝɨ ɰɜɟɬ). ȼ ɞɪɭɝɨɦ ɫɬɚɤɚɧɟ ɩɪɢɝɨɬɨɜɶɬɟ ɳɺɥɨɱɧɵɣ ɪɚɫɬɜɨɪ ɫ pH ɜ ɢɧɬɟɪɜɚɥɟ 9–10. Ⱦɥɹ ɷɬɨɝɨ ɜ 50 ɦɥ ɛɪɨɦɬɢɦɨɥɨɜɨɝɨ ɫɢɧɟɝɨ ɜɧɨɫɢɬɟ ɧɟɫɤɨɥɶɤɨ ɤɚɩɟɥɶ KOH, ɧɟɩɪɟɪɵɜɧɨ ɩɟɪɟɦɟɲɢɜɚɹ ɪɚɫɬɜɨɪ ɢ ɢɡɦɟɪɹɹ ɜɨɞɨɪɨɞɧɵɣ ɩɨɤɚɡɚɬɟɥɶ ɫ ɩɨɦɨɳɶɸ pH-ɦɟɬɪɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɛɭɞɟɬ ɩɨɥɭɱɟɧ ɪɚɫɬɜɨɪ ʋ 2 (ɡɚɦɟɬɶɬɟ ɟɝɨ ɰɜɟɬ). ɂɫɩɨɥɶɡɭɹ ɤɢɫɥɵɣ (ʋ 1) ɢ ɳɺɥɨɱɧɵɣ (ʋ 2) ɪɚɫɬɜɨɪɵ, ɩɪɢɝɨɬɨɜɶɬɟ ɪɹɞ ɪɚɫɬɜɨɪɨɜ ɫɨ ɫɪɟɞɧɢɦɢ ɡɧɚɱɟɧɢɹɦɢ pH. Ⱦɥɹ ɷɬɨɝɨ ɜ ɨɬɞɟɥɶɧɨɦ ɫɬɚɤɚɧɟ ɜɨɡɶɦɢɬɟ ɨɤɨɥɨ 30 ɦɥ ɪɚɫɬɜɨɪɚ ʋ 1. ɉɪɢɛɚɜɥɹɹ ɤ ɧɟɦɭ ɩɨ ɤɚɩɥɹɦ ɪɚɫɬɜɨɪ ʋ 2 ɞɨɜɟɞɢɬɟ ɡɧɚɱɟɧɢɟ pH ɞɨ 6,0–6,5 (ɬɳɚɬɟɥɶɧɨ ɩɟɪɟɦɟɲɢɜɚɣɬɟ ɫ ɩɨɦɨɳɶɸ ɦɚɝɧɢɬɧɨɣ ɦɟɲɚɥɤɢ). Ʉɨɝɞɚ ɧɭɠɧɨɟ ɡɧɚɱɟɧɢɟ pH ɛɭɞɟɬ ɞɨɫɬɢɝɧɭɬɨ, ɨɬɥɟɣɬɟ ɧɟɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɩɪɢɝɨɬɨɜɥɟɧɧɨɝɨ ɪɚɫɬɜɨɪɚ ɜ ɤɸɜɟɬɭ. Ʉɸɜɟɬɚ ɞɨɥɠɧɚ ɛɵɬɶ ɡɚɩɨɥɧɟɧɚ ɧɚ 2/3. Ɍɚɤɢɦ ɠɟ ɦɟɬɨɞɨɦ, ɩɪɢɛɚɜɥɹɹ ɤ ɭɠɟ ɢɦɟɸɳɟɦɭɫɹ ɪɚɫɬɜɨɪɭ ɳɺɥɨɱɧɵɣ 34
ʋ 2, ɩɪɢɝɨɬɨɜɶɬɟ ɪɚɫɬɜɨɪɵ ɫ pH = 6,5–7,0 ɢ 7,0–7,5. Ɂɞɟɫɶ ɭɤɚɡɚɧɵ ɬɨɥɶɤɨ ɢɧɬɟɪɜɚɥɵ, ɜ ɤɨɬɨɪɵɯ ɞɨɥɠɟɧ ɥɟɠɚɬɶ ɜɨɞɨɪɨɞɧɵɣ ɩɨɤɚɡɚɬɟɥɶ. ɇɟɨɛɯɨɞɢɦɨ ɢɡɦɟɪɢɬɶ ɢ ɡɚɩɢɫɚɬɶ ɡɧɚɱɟɧɢɹ pH ɤɚɠɞɨɝɨ ɪɚɫɬɜɨɪɚ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɜɬɨɪɨɝɨ ɡɧɚɤɚ. ɉɨ ɬɪɟɛɨɜɚɧɢɸ ɩɪɟɩɨɞɚɜɚɬɟɥɹ ɱɢɫɥɨ ɩɪɨɛ ɦɨɠɟɬ ɛɵɬɶ ɭɜɟɥɢɱɟɧɨ ɞɨ 5. Ɇɨɠɧɨ ɢɡɦɟɧɹɬɶ pH ɢɫɫɥɟɞɭɟɦɵɯ ɪɚɫɬɜɨɪɨɜ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 6,0 ɞɨ 7,5.
ɂɡɦɟɪɶɬɟ ɨɩɬɢɱɟɫɤɭɸ ɩɥɨɬɧɨɫɬɶ ɬɪɟɯ ɪɚɫɬɜɨɪɨɜ ɫɨ ɫɪɟɞɧɢɦɢ ɡɧɚɱɟɧɢɹɦɢ pH, ɢɫɩɨɥɶɡɭɹ ɜ ɤɚɱɟɫɬɜɟ «ɯɨɥɨɫɬɨɣ ɩɪɨɛɵ» ɤɸɜɟɬɭ ɫ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɨɣ ɜɨɞɨɣ. ɂɡɦɟɪɟɧɢɹ ɩɪɨɜɟɞɢɬɟ ɧɚ ɞɜɭɯ ɞɥɢɧɚɯ ɜɨɥɧ ɫɨ ɫɜɟɬɨɮɢɥɶɬɪɚɦɢ 440 ɢ 590 ɧɦ. Ɋɟɡɭɥɶɬɚɬɵ ɦɨɠɧɨ ɡɚɧɟɫɬɢ ɜ ɩɟɪɜɵɟ ɬɪɢ ɤɨɥɨɧɤɢ ɬɚɛɥɢɰɵ: pH
Ɉɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ D 440 ɧɦ 590 ɧɦ
Ɋɚɜɧɨɜɟɫɧ. ɤɨɧɰ-ɹ, ɝ/ɥ HA A–
pKa
Ɉɛɪɚɛɨɬɤɚ ɪɟɡɭɥɶɬɚɬɨɜ. ɋɨɝɥɚɫɧɨ ɩɪɢɧɰɢɩɭ Ʌɟ ɒɚɬɟɥɶɟ ɜ ɳɺɥɨɱɧɨɦ ɪɚɫɬɜɨɪɟ (ɩɪɢ pH > 9) ɞɨɦɢɧɢɪɭɟɬ ɞɢɫɫɨɰɢɢɪɨɜɚɧɧɚɹ ɮɨɪɦɚ A– ɛɪɨɦɬɢɦɨɥɨɜɨɝɨ ɫɢɧɟɝɨ. Ʉɨɧɰɟɧɬɪɚɰɢɟɣ ɧɟɞɢɫɫɨɰɢɢɪɨɜɚɧɧɵɯ ɦɨɥɟɤɭɥ HA ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. ɂɨɧɵ A– ɢɦɟɸɬ ɩɨɥɨɫɭ ɩɨɝɥɨɳɟɧɢɹ ɜ ɤɪɚɫɧɨɣ ɨɛɥɚɫɬɢ (ɫɦ. ɪɢɫ. 6) ɢ ɨɤɪɚɲɟɧɵ ɜ ɫ ɢ ɧ ɢ ɣ ɰɜɟɬ. ȼ ɤɢɫɥɨɦ ɪɚɫɬɜɨɪɟ (ɩɪɢ pH < 5), ɧɚɨɛɨɪɨɬ, ɩɪɢɫɭɬɫɬɜɭɸɬ ɦɨɥɟɤɭɥɵ HA, ɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ A– ɱɪɟɡɜɵɱɚɣɧɨ ɦɚɥɚ. Ɉɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɩɪɢ ɩɪɢɫɨɟɞɢɧɟɧɢɢ ɩɪɨɬɨɧɚ (A– + H+ ĺ HA) ɫɩɟɤɬɪ ɜɟɳɟɫɬɜɚ ɫɢɥɶɧɨ ɢɡɦɟɧɹɟɬɫɹ: ɢɫɱɟɡɚɟɬ ɤɪɚɫɧɚɹ ɩɨɥɨɫɚ ɩɨɝɥɨɳɟɧɢɹ ɢ ɩɨɹɜɥɹɟɬɫɹ ɫɢɧɹɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɢɫɥɚɹ ɮɨɪɦɚ ɨɤɪɚɲɟɧɚ ɜ ɨ ɪ ɚ ɧ ɠ ɟ ɜ ɨɤ ɪ ɚ ɫ ɧ ɵ ɣ ɰɜɟɬ. ɉɪɢ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɹɯ pH ɜ ɪɚɜɧɨɜɟɫɢɢ (III.4) ɩɪɢɫɭɬɫɬɜɭɸɬ ɨɛɟ ɮɨɪɦɵ – HA ɢ A–. ɂɡɦɟɪɹɹ ɨɩɬɢɱɟɫɤɭɸ ɩɥɨɬɧɨɫɬɶ ɧɚ ɞɥɢɧɟ ɜɨɥɧɵ 440, ɦɵ ɨɛɧɚɪɭɠɢɜɚɟɦ ɩɟɪɜɭɸ ɢɡ ɷɬɢɯ ɮɨɪɦ; ɧɚ ɞɥɢɧɟ ɜɨɥɧɵ 590 ɧɦ – ɜɬɨɪɭɸ. ɉɨ ɡɚɤɨɧɭ Ȼɟɪɚ (II.5) D440 = E440 [HA], D590 = E590 [A–]. (III.5)
Ɉɬɫɸɞɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ. ɉɪɟɞɜɚɪɢɬɟɥɶɧɵɟ (ɝɪɚɞɭɢɪɨɜɨɱɧɵɟ) ɢɡɦɟɪɟɧɢɹ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ E440 = 20,46 ɥ/ɝ,
E590 = 41,74 ɥ/ɝ.
Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɧɫɬɚɧɬɵ pKa (ɩɟɪɜɵɣ ɫɩɨɫɨɛ). ɉɨ ɮɨɪɦɭɥɚɦ (III.5) ɜɵɱɢɫɥɢɬɟ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ [HA] ɢ [A–] ɞɥɹ ɤɚɠɞɨɝɨ ɢɡ ɢɫɫɥɟɞɨɜɚɧɧɵɯ ɡɧɚɱɟɧɢɣ pH. Ɋɟɡɭɥɶɬɚɬɵ ɡɚɧɟɫɢɬɟ ɜ ɬɚɛɥɢɰɭ. ɉɨ ɭɪɚɜɧɟɧɢɸ (III.3) ɜɵɱɢɫɥɢɬɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ pKa, ɧɚɣɞɢɬɟ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ, ɚɛɫɨɥɸɬɧɭɸ ɢ ɨɬɧɨɫɢɬɟɥɶɧɭɸ ɩɨɝɪɟɲɧɨɫɬɢ. ȼɬɨɪɨɣ ɫɩɨɫɨɛ. ɉɨɫɬɪɨɣɬɟ ɝɪɚɮɢɤɢ ɡɚɜɢɫɢɦɨɫɬɟɣ ɪɚɜɧɨɜɟɫɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ [HA] ɢ [A–] ɨɬ pH ɜ ɨɞɧɨɣ ɤɨɨɪɞɢɧɚɬɧɨɣ ɫɟɬɤɟ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ 35
ɬɨɱɤɢ ɫɨɟɞɢɧɢɬɟ ɩɥɚɜɧɵɦɢ ɤɪɢɜɵɦɢ, ɩɪɨɞɨɥɠɚɹ ɢɯ ɞɨ ɜɡɚɢɦɧɨɝɨ ɩɟɪɟɫɟɱɟɧɢɹ. Ɍɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ pH0, ɬɨ ɟɫɬɶ ɬɨɱɤɚ ɪɚɜɟɧɫɬɜɚ ɤɨɧɰɟɧɬɪɚɰɢɣ [HA] = [A–], ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɟɥɢɱɢɧɟ pKa. 3. ɂɫɫɥɟɞɨɜɚɧɢɟ ɤɢɧɟɬɢɤɢ ɪɟɚɤɰɢɢ ɪɚɡɥɨɠɟɧɢɹ ɬɢɨɫɟɪɧɨɣ ɤɢɫɥɨɬɵ
Ɍɢɨɫɟɪɧɚɹ ɤɢɫɥɨɬɚ H2S2O3 ɜ ɜɨɞɧɵɯ ɪɚɫɬɜɨɪɚɯ ɧɟɭɫɬɨɣɱɢɜɚ ɢ ɪɚɡɥɚɝɚɟɬɫɹ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ H2S2O3(ɪ.) ĺ SO2(ɪ.) + H2O + S(ɬɜ.).
(III.6)
ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɟɚɤɰɢɢ ɜɵɞɟɥɹɟɬɫɹ ɨɤɫɢɞ ɫɟɪɵ SO2, ɤɨɬɨɪɵɣ ɨɫɬɚɟɬɫɹ ɜ ɪɚɫɬɜɨɪɟ (ɪ.), ɢ ɧɟɪɚɫɬɜɨɪɢɦɚɹ ɜ ɜɨɞɟ ɫɟɪɚ. ɉɨɫɥɟɞɧɹɹ ɜɵɞɟɥɹɟɬɫɹ ɜ ɜɢɞɟ ɨɱɟɧɶ ɦɟɥɤɢɯ ɬɜɟɪɞɵɯ ɱɚɫɬɢɰ, ɨɛɪɚɡɭɸɳɢɯ ɤɨɥɥɨɢɞɧɵɣ ɪɚɫɬɜɨɪ (ɡɨɥɶ). Ʉɨɥɥɨɢɞɧɵɟ ɱɚɫɬɢɰɵ ɪɚɫɫɟɢɜɚɸɬ ɫɜɟɬ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ ɤɨɥɥɨɢɞɧɨɝɨ ɪɚɫɬɜɨɪɚ ɩɨɧɢɠɚɟɬɫɹ, ɞɚɠɟ ɟɫɥɢ ɜɟɳɟɫɬɜɨ ɧɟ ɢɦɟɟɬ ɫɨɛɫɬɜɟɧɧɨɣ ɨɤɪɚɫɤɢ. ȼ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɨɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɢɫɥɭ ɪɚɫɫɟɢɜɚɸɳɢɯ n ɱɚɫɬɢɰ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ: D n. ɗɬɢɦ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɤɢɧɟɬɢɤɢ ɪɟɚɤɰɢɢ (III.6), ɩɨɫɤɨɥɶɤɭ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɜɪɟɦɟɧɢ D(W) ɩɨɤɚɡɵɜɚɟɬ ɤɢɧɟɬɢɤɭ ɧɚɤɨɩɥɟɧɢɹ ɨɞɧɨɝɨ ɢɡ ɩɪɨɞɭɤɬɨɜ ɪɟɚɤɰɢɢ. Ⱦɪɭɝɢɟ ɜɟɳɟɫɬɜɚ, ɭɱɚɫɬɜɭɸɳɢɟ ɜ ɪɟɚɤɰɢɢ, ɧɟ ɩɨɝɥɨɳɚɸɬ ɢ ɧɟ ɪɚɫɫɟɢɜɚɸɬ ɫɜɟɬ ɜ ɜɢɞɢɦɨɣ ɨɛɥɚɫɬɢ. ɐɟɥɶ ɪɚɛɨɬɵ. ɂɫɫɥɟɞɨɜɚɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɟɜɪɚɳɚɸɳɟɝɨɫɹ ɜɟɳɟɫɬɜɚ. Ɉɩɪɟɞɟɥɢɬɶ ɷɧɟɪɝɢɸ ɚɤɬɢɜɚɰɢɢ ɪɟɚɤɰɢɢ ɪɚɡɥɨɠɟɧɢɹ ɬɢɨɫɟɪɧɨɣ ɤɢɫɥɨɬɵ. Ɉɛɨɪɭɞɨɜɚɧɢɟ ɢ ɪɟɚɤɬɢɜɵ. Ɏɨɬɨɦɟɬɪ ɄɎɄ-5Ɇ ɫɨ ɫɜɟɬɨɮɢɥɶɬɪɨɦ 400 ɧɦ, 4 ɩɪɨɛɢɪɤɢ ɞɥɹ ɮɨɬɨɦɟɬɪɢɪɨɜɚɧɢɹ (ɢɡ ɤɨɦɩɥɟɤɬɚ ɩɪɢɛɨɪɚ). ɋɟɤɭɧɞɨɦɟɪ. Ɍɟɪɦɨɦɟɬɪ ɥɚɛɨɪɚɬɨɪɧɵɣ. Ɋɚɫɬɜɨɪ ɬɢɨɫɭɥɶɮɚɬɚ ɧɚɬɪɢɹ 0,1 ɦɨɥɶ/ɥ. Ɋɚɫɬɜɨɪ ɫɟɪɧɨɣ ɤɢɫɥɨɬɵ 0,1 ɦɨɥɶ/ɥ. ȼɨɞɚ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɚɹ. 4 ɫɬɚɤɚɧɚ ɟɦɤɨɫɬɶɸ 100 ɦɥ, 3 ɦɟɪɧɵɯ ɰɢɥɢɧɞɪɚ ɧɚ 50 ɦɥ. 2 ɛɨɥɶɲɢɟ ɩɪɨɛɢɪɤɢ. Ɍɟɪɦɨɫɬɚɬ ɢɥɢ ɜɨɞɹɧɚɹ ɛɚɧɹ. Ȼɭɦɚɠɧɵɟ ɮɢɥɶɬɪɵ.
ȼɵɩɨɥɧɟɧɢɟ ɪɚɛɨɬɵ. 1. ɉɨɞɝɨɬɨɜɶɬɟ ɮɨɬɨɦɟɬɪ ɤ ɢɡɦɟɪɟɧɢɹɦ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ. ɍɫɬɚɧɨɜɢɬɟ ɫɜɟɬɨɮɢɥɶɬɪ ɧɚ 400 ɧɦ. ȼ ɩɪɨɛɢɪɤɟ ɞɥɹ ɮɨɬɨɦɟɬɪɢɪɨɜɚɧɢɹ (ɧɚɯɨɞɢɬɫɹ ɜ ɤɨɦɩɥɟɤɬɟ ɩɪɢɛɨɪɚ) ɜ ɤɚɱɟɫɬɜɟ «ɯɨɥɨɫɬɨɣ ɩɪɨɛɵ» ɢɡɦɟɪɶɬɟ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɭɸ ɜɨɞɭ. 36
ɉɪɢɝɨɬɨɜɶɬɟ ɢ ɢɡɦɟɪɶɬɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɱɟɬɵɪɟ ɪɚɫɬɜɨɪɚ ɫɨ ɫɥɟɞɭɸɳɢɦɢ ɤɨɥɢɱɟɫɬɜɚɦɢ ɪɟɚɝɟɧɬɨɜ: ʋ 1 2 3 4
Na2S2O3, ɦɥ 15,0 10,0 7,5 5,0
H2O, ɦɥ 0 5,0 7,5 10,0
H2SO4, ɦɥ 15,0 15,0 15,0 15,0
Ⱦɥɹ ɷɬɨɝɨ ɦɟɪɧɵɦ ɰɢɥɢɧɞɪɨɦ ɨɬɛɟɪɢɬɟ 15,0 ɦɥ ɪɚɫɬɜɨɪɚ ɬɢɨɫɭɥɶɮɚɬɚ ɧɚɬɪɢɹ Na2S2O3 ɢ ɩɟɪɟɧɟɫɢɬɟ ɪɚɫɬɜɨɪ ɜ ɫɬɚɤɚɧ. ȼ ɞɪɭɝɨɦ ɰɢɥɢɧɞɪɟ ɜɨɡɶɦɢɬɟ 15,0 ɦɥ ɪɚɫɬɜɨɪɚ ɫɟɪɧɨɣ ɤɢɫɥɨɬɵ. ɉɪɢɥɟɣɬɟ ɤɢɫɥɨɬɭ ɤ ɫɨɞɟɪɠɢɦɨɦɭ ɫɬɚɤɚɧɚ, ɨ ɞ ɧ ɨ ɜ ɪ ɟ ɦ ɟ ɧ ɧ ɨ ɩɭɫɬɢɜ ɨɬɫɱɟɬ ɜɪɟɦɟɧɢ ɩɨ ɫɟɤɭɧɞɨɦɟɪɭ. Ɋɟɚɤɰɢɹ ɧɚɱɢɧɚɟɬɫɹ ɜ ɦɨɦɟɧɬ ɫɥɢɜɚɧɢɹ. ɉɟɪɟɦɟɲɚɣɬɟ ɪɟɚɝɢɪɭɸɳɢɣ ɪɚɫɬɜɨɪ, ɫɥɟɝɤɚ ɜɡɛɚɥɬɵɜɚɹ ɫɬɚɤɚɧ. ɇɚɥɟɣɬɟ ɩɨɥɭɱɟɧɧɵɣ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɪɚɫɬɜɨɪ ʋ 1 ɜ ɱɢɫɬɭɸ ɩɪɨɛɢɪɤɭ ɞɥɹ ɮɨɬɨɦɟɬɪɢɪɨɜɚɧɢɹ (ɧɚ 2/3 ɟɟ ɨɛɴɟɦɚ). ɍɫɬɚɧɨɜɢɬɟ ɩɪɨɛɢɪɤɭ ɜ ɮɨɬɨɦɟɬɪ ɢ ɫɥɟɞɢɬɟ ɡɚ ɩɨɤɚɡɚɧɢɹɦɢ ɩɪɢɛɨɪɚ. ɋɧɢɦɚɣɬɟ ɩɨɤɚɡɚɧɢɹ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ ɱɟɪɟɡ ɤɚɠɞɵɟ 15 (ɠɟɥɚɬɟɥɶɧɨ) ɢɥɢ 30 ɫ ɜ ɬɟɱɟɧɢɟ 5–6 ɦɢɧ, ɡɚɩɢɫɵɜɚɹ ɢɯ ɜ ɬɚɛɥɢɰɭ: ɇɚɱɚɥɶɧɚɹ ɤɨɧɰ. H2S2O3, ɦɨɥɶ/ɥ
ɦɟɬɪɚ: ɪɟɤɨɦɟɧɞɭɟɬɫɹ, ɱɬɨɛɵ ɨɬɤɥɨɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɨɬ ɡɚɞɚɧɧɨɣ ɧɟ ɩɪɟɜɵɲɚɥɨ 2 qC. ɉɪɢ ɩɨɹɜɥɟɧɢɢ ɨɩɚɥɟɫɰɟɧɰɢɢ ɛ ɵ ɫ ɬ ɪ ɨ ɢɡɜɥɟɤɢɬɟ ɩɪɨɛɢɪɤɢ, ɢɡɜɥɟɤɢɬɟ ɬɟɪɦɨɦɟɬɪ ɢ ɨɬɥɟɣɬɟ ɧɟɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɪɚɫɬɜɨɪɚ ɜ ɩɪɨɛɢɪɤɭ ɞɥɹ ɮɨɬɨɦɟɬɪɢɪɨɜɚɧɢɹ. ɍɫɬɚɧɨɜɢɬɟ ɩɪɨɛɭ ɜ ɮɨɬɨɦɟɬɪ ɢ ɫɥɟɞɢɬɟ ɡɚ ɩɨɤɚɡɚɧɢɹɦɢ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ. Ʉɨɝɞɚ ɨɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ ɞɨɫɬɢɝɧɟɬ ɡɧɚɱɟɧɢɹ 1,50 0,05, ɨɫɬɚɧɨɜɢɬɟ ɫɟɤɭɧɞɨɦɟɪ. Ɂɚɧɟɫɢɬɟ ɢɡɦɟɪɟɧɢɟ ɜ ɬɚɛɥɢɰɭ: t, qC
ɉɪɢɝɨɬɨɜɶɬɟ ɢ ɢɡɦɟɪɶɬɟ ɤɚɤ ɭɤɚɡɚɧɨ ɪɚɫɬɜɨɪ ʋ 2, ɡɚɬɟɦ, ɩɨ ɨɱɟɪɟɞɢ, ʋ 3 ɢ 4. Ⱦɥɹ ɤɚɠɞɨɝɨ ɪɟɚɝɟɧɬɚ – ɜɨɞɵ, ɤɢɫɥɨɬɵ ɢ ɬɢɨɫɭɥɶɮɚɬɚ ɧɚɬɪɢɹ – ɢɫɩɨɥɶɡɭɣɬɟ ɨɬɞɟɥɶɧɵɟ ɦɟɪɧɵɟ ɰɢɥɢɧɞɪɵ. ȼɧɚɱɚɥɟ ɫɦɟɲɢɜɚɣɬɟ ɜ ɫɬɚɤɚɧɟ ɪɚɫɬɜɨɪ ɬɢɨɫɭɥɶɮɚɬɚ ɢ ɜɨɞɭ, ɩɨɫɥɟ ɱɟɝɨ ɞɨɛɚɜɥɹɣɬɟ ɨɬɦɟɪɟɧɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɢɫɥɨɬɵ. Ɂɚɩɭɫɤɚɣɬɟ ɫɟɤɭɧɞɨɦɟɪ ɬɨɥɶɤɨ ɜ ɦɨɦɟɧɬ ɩɪɢɥɢɜɚɧɢɹ ɤɢɫɥɨɬɵ. 2. ȼ ɞɜɟ ɛɨɥɶɲɢɟ ɩɪɨɛɢɪɤɢ ɜɨɡɶɦɢɬɟ: ɜ ɨɞɧɭ – 5,0 ɦɥ ɪɚɫɬɜɨɪɚ ɬɢɨɫɭɥɶɮɚɬɚ ɧɚɬɪɢɹ, ɜ ɞɪɭɝɭɸ – 5,0 ɦɥ ɪɚɫɬɜɨɪɚ ɫɟɪɧɨɣ ɤɢɫɥɨɬɵ. ȼ ɩɪɨɛɢɪɤɭ ɫ Na2S2O3 ɜɧɟɫɢɬɟ ɬɟɪɦɨɦɟɬɪ ɢ ɩɨɦɟɫɬɢɬɟ ɨ ɛ ɟ ɩɪɨɛɢɪɤɢ ɜ ɬɟɪɦɨɫɬɚɬ, ɧɚɝɪɟɬɵɣ ɞɨ 30 qC, ɢɥɢ ɧɚ ɜɨɞɹɧɭɸ ɛɚɧɸ. ɇɚɝɪɟɜ ɪɚɫɬɜɨɪɵ ɞɨ ɡɚɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ, ɩɪɢɥɟɣɬɟ ɫɟɪɧɭɸ ɤɢɫɥɨɬɭ ɤ ɬɢɨɫɭɥɶɮɚɬɭ, ɨɞɧɨɜɪɟɦɟɧɧɨ ɡɚɩɭɫɬɢɜ ɫɟɤɭɧɞɨɦɟɪ. Ɉɫɬɚɜɥɹɣɬɟ ɪɟɚɝɢɪɭɸɳɢɣ ɪɚɫɬɜɨɪ ɫ ɬɟɪɦɨɦɟɬɪɨɦ ɜ ɬɟɪɦɨ* ɫɬɚɬɟ ɞɨ ɧɚɱɚɥɚ ɨɩɚɥɟɫɰɟɧɰɢɢ ) . ɉɪɢ ɷɬɨɦ ɫɥɟɞɢɬɟ ɡɚ ɩɨɤɚɡɚɧɢɹɦɢ ɬɟɪɦɨ-
v¯, ɫ–1
ɉɨɜɬɨɪɢɬɟ ɷɤɫɩɟɪɢɦɟɧɬ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ 10q, 20q ɢ 40 qC. Ⱦɥɹ ɨɯɥɚɠɞɟɧɢɹ ɞɨ 10 qC ɜɨɫɩɨɥɶɡɭɣɬɟɫɶ ɥɢɛɨ ɬɟɪɦɨɫɬɚɬɨɦ, ɥɢɛɨ ɫɬɪɭɟɣ ɜɨɞɨɩɪɨɜɨɞɧɨɣ ɜɨɞɵ. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɩɨɫɥɟ ɤɚɠɞɨɝɨ ɢɡɦɟɪɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɨɩɨɥɨɫɧɭɬɶ ɩɪɨɛɢɪɤɭ, ɜ ɤɨɬɨɪɨɣ ɛɵɥ ɢɫɫɥɟɞɭɟɦɵɣ ɪɚɫɬɜɨɪ, ɢ ɬɟɪɦɨɦɟɬɪ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɨɣ ɜɨɞɨɣ. ɉɨ ɭɤɚɡɚɧɢɸ ɩɪɟɩɨɞɚɜɚɬɟɥɹ ɷɬɚ ɪɚɛɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɞɟɥɟɧɚ ɧɚ ɞɜɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɱɚɫɬɢ: 1) ɢɫɫɥɟɞɨɜɚɧɢɟ ɤɢɧɟɬɢɤɢ ɪɟɚɤɰɢɢ ɢ 2) ɨɩɪɟɞɟɥɟɧɢɟ ɷɧɟɪɝɢɢ ɚɤɬɢɜɚɰɢɢ.
Ɉɛɪɚɛɨɬɤɚ ɪɟɡɭɥɶɬɚɬɨɜ. ɉɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɬɢɨɫɭɥɶɮɚɬɚ ɧɚɬɪɢɹ ɢ ɫɟɪɧɨɣ ɤɢɫɥɨɬɵ ɜɵɞɟɥɹɟɬɫɹ ɫɥɚɛɚɹ ɬɢɨɫɟɪɧɚɹ ɤɢɫɥɨɬɚ:
W, ɫ Ɉɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ D
W, ɫ
Na2S2O3 + H2SO4 ĺ H2S2O3 + Na2SO4 ɢɥɢ ɢɨɧɧɨɣ ɮɨɪɦɟ:
S2O32– + 2H+ ĺ H2S2O3.
ɗɬɚ ɫɬɚɞɢɹ ɩɪɨɰɟɫɫɚ ɩɪɨɢɫɯɨɞɢɬ ɨɱɟɧɶ ɛɵɫɬɪɨ, ɫɨ ɫɤɨɪɨɫɬɶɸ ɧɚ ɧɟɫɤɨɥɶɤɨ ɩɨɪɹɞɤɨɜ ɩɪɟɜɵɲɚɸɳɟɣ ɫɤɨɪɨɫɬɶ ɪɚɫɩɚɞɚ (III.6) ɬɢɨɫɟɪɧɨɣ ɤɢɫɥɨɬɵ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɨɦɟɧɬ ɫɥɢɜɚɧɢɹ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɚɱɚɥɨɦ ɢɫɫɥɟɞɭɟɦɨɣ ɪɟɚɤɰɢɢ. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɜ 1-ɦ ɷɤɫɩɟɪɢɦɟɧɬɟ ɦɵ ɢɡɦɟɧɹɟɦ ɧɚɱɚɥɶɧɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ ɬɢɨɫɟɪɧɨɣ ɤɢɫɥɨɬɵ C 0 ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ (ɤɨɦɧɚɬɧɨɣ) ɬɟɦɩɟɪɚɬɭɪɟ, ɬɨɝɞɚ ɤɚɤ ɜɨ 2-ɦ – ɢɡɦɟɧɹɟɦ ɬɟɦɩɟɪɚɬɭɪɭ ɩɪɢ ɧɟɢɡɦɟɧɧɨɣ ɧɚɱɚɥɶɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ. ȼɵɱɢɫɥɢɬɟ ɧɚɱɚɥɶɧɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ C 0 (ɦɨɥɶ/ɥ), ɜɡɹɬɭɸ ɜ ɤɚɠɞɨɦ ɢɡɦɟɪɟɧɢɢ. 1. ɉɨɫɬɪɨɣɬɟ ɝɪɚɮɢɤɢ ɡɚɜɢɫɢɦɨɫɬɢ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ D ɨɬ ɜɪɟɦɟɧɢ W ɩɪɢ ɱɟɬɵɪɟɯ ɡɧɚɱɟɧɢɹɯ C 0 (ɜ ɨɞɧɨɣ ɤɨɨɪɞɢɧɚɬɧɨɣ ɫɟɬɤɟ). Ʉɪɢɜɵɟ ɢɦɟɸɬ
Ɉɩɚɥɟɫɰɟɧɰɢɹ (ɨɬ ɥɚɬ. opalus) – ɪɟɡɤɨɟ ɭɜɟɥɢɱɟɧɢɟ ɫɜɟɬɨɪɚɫɫɟɹɧɢɹ ɩɪɢ ɨɛɪɚɡɨɜɚɧɢɢ ɡɨɥɹ. ɗɬɨ ɹɜɥɟɧɢɟ ɡɚɦɟɱɚɟɬɫɹ ɜ ɜɢɞɟ ɩɟɪɟɥɢɜɱɚɬɨɝɨ ɝɨɥɭɛɨɜɚɬɨɝɨ ɩɨɦɭɬɧɟɧɢɹ.
ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ Ɋɟɥɟɹ – ɨɫɧɨɜɧɨɦɭ ɡɚɤɨɧɭ ɫɜɟɬɨɪɚɫɫɟɹɧɢɹ – ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɫɜɟɬɚ, ɪɚɫɫɟɹɧɧɨɝɨ ɦɭɬɧɨɣ ɫɪɟɞɨɣ, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɟɬɜɟɪɬɨɣ ɫɬɟɩɟɧɢ ɞɥɢɧɵ ɜɨɥɧɵ: Id ~ O–4. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɨɪɨɬɤɢɟ ɜɨɥɧɵ ɪɚɫɫɟɢɜɚɸɬɫɹ ɫɢɥɶɧɟɟ. ɗɬɢɦ ɨɛɴɹɫɧɹɟɬɫɹ ɝɨɥɭɛɨɜɚɬɵɣ ɰɜɟɬ ɡɨɥɟɣ ɜ ɪɚɫɫɟɹɧɧɨɦ ɫɜɟɬɟ ɢ ɤɪɚɫɧɨɜɚɬɵɣ ɜ ɩɪɨɯɨɞɹɳɟɦ. ɗɬɢɦ ɠɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɛɨɪ ɤɨɪɨɬɤɨɜɨɥɧɨɜɨɝɨ ɫɜɟɬɨɮɢɥɶɬɪɚ (400 ɧɦ) ɜ ɧɚɲɟɦ ɷɤɫɩɟɪɢɦɟɧɬɟ.
37
38
*)
S-ɨɛɪɚɡɧɭɸ ɮɨɪɦɭ ɫ ɦɟɞɥɟɧɧɵɦ ɧɚɱɚɥɶɧɵɦ ɭɱɚɫɬɤɨɦ, ɛɵɫɬɪɵɦ ɫɪɟɞɧɢɦ ɢ * ɜɧɨɜɶ ɡɚɦɟɞɥɹɸɳɢɦɫɹ ɮɢɧɚɥɶɧɵɦ ) . ȼɵɞɟɥɢɬɟ ɧɚ ɤɚɠɞɨɣ ɤɪɢɜɨɣ ɫɪɟɞɧɢɣ ɥɢɧɟɣɧɵɣ ɭɱɚɫɬɨɤ ɢ ɷɤɫɬɪɚɩɨɥɢɪɭɣɬɟ ɟɝɨ ɞɨ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɨɫɶɸ ɚɛɫɰɢɫɫ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 8. Ɉɩɪɟɞɟɥɢɬɟ ɜɪɟɦɹ W*, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɷɬɨɦɭ ɩɟɪɟɫɟɱɟɧɢɸ. ɋɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɤɚɤ ɨɛɪɚɬɧɨɟ ɜɪɟɦɹ:
v (C ) 0 n
1 . Wn*
(III.7)
ɉɨɥɶɡɭɹɫɶ ɷɬɨɣ ɮɨɪɦɭɥɨɣ, ɪɚɫɫɱɢɬɚɣɬɟ ɫɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ ɢ ɩɨɫɬɪɨɣɬɟ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɫɤɨɪɨɫɬɢ ɨɬ ɧɚɱɚɥɶɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ v (C 0 ) . Ɉɛɴɹɫɧɢɬɟ ɜɢɞ ɩɨɥɭɱɟɧɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɡɚɤɨɧɚ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ. Ɋɢɫ. 8 2. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɢ ɩɪɨɱɢɯ ɪɚɜɧɵɯ ɭɫɥɨɜɢɹɯ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɟɦ Ⱥɪɪɟɧɢɭɫɚ (I.12):
v v0 e Ea
RT
ȿɫɥɢ ɜɵ ɜɥɚɞɟɟɬɟ ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ ɢɥɢ ɩɪɨɝɪɚɦɦɧɵɦ ɨɛɟɫɩɟɱɟɧɢɟɦ, ɪɟɚɥɢɡɭɸɳɢɦ ɷɬɨɬ ɦɟɬɨɞ, ɪɟɤɨɦɟɧɞɭɟɦ ɜɵɩɨɥɧɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɵɱɢɫɥɟɧɢɹ. Ɉɛɪɚɬɢɬɟɫɶ ɡɚ ɤɨɧɫɭɥɶɬɚɰɢɟɣ ɤ ɩɪɟɩɨɞɚɜɚɬɟɥɸ.
Ɂɚɜɟɪɲɚɸɳɢɣ ɭɱɚɫɬɨɤ ɤɪɢɜɨɣ ɦɨɠɟɬ ɛɵɬɶ ɧɢɫɩɚɞɚɸɳɢɦ. ɗɬɨ ɜɵɡɜɚɧɨ ɬɟɦ, ɱɬɨ ɤɨɥɥɨɢɞɧɵɟ ɱɚɫɬɢɰɵ ɫɟɪɵ ɧɚɱɢɧɚɸɬ ɫɥɢɩɚɬɶɫɹ (ɤɨɚɥɟɫɰɢɪɨɜɚɬɶ), ɚ ɤɪɭɩɧɵɟ ɚɝɪɟɝɚɬɵ ɩɨɫɬɟɩɟɧɧɨ ɨɛɪɚɡɭɸɬ ɨɫɚɞɨɤ. Ɋɚɫɫɟɹɧɢɟ ɫɜɟɬɚ ɩɪɢ ɷɬɨɦ ɭɦɟɧɶɲɚɟɬɫɹ. 39
Ɉɤɢɫɥɟɧɢɟ ɢɨɞɢɞ-ɢɨɧɨɜ ɞɨ ɫɜɨɛɨɞɧɨɝɨ ɢɨɞɚ ɩɪɨɢɫɯɨɞɢɬ ɜ ɤɢɫɥɨɣ ɫɪɟɞɟ ɩɟɪɟɤɢɫɶɸ ɜɨɞɨɪɨɞɚ ɩɨ ɭɪɚɜɧɟɧɢɸ 2I– + H2O2 + 2H+ ĺ I2 + 2H2O. Ɋɟɚɤɰɢɹ ɤɚɬɚɥɢɡɢɪɭɟɬɫɹ ɫɨɟɞɢɧɟɧɢɹɦɢ ɩɟɪɟɯɨɞɧɵɯ ɦɟɬɚɥɥɨɜ – ɫɨɥɹɦɢ ɜɨɥɶɮɪɚɦɨɜɨɣ H2WO4, ɦɨɥɢɛɞɟɧɨɜɨɣ H2MoO2 ɤɢɫɥɨɬ, ɫɨɟɞɢɧɟɧɢɹɦɢ ɠɟɥɟɡɚ, ɰɢɪɤɨɧɢɹ ɢ ɪɹɞɨɦ ɞɪɭɝɢɯ. ɉɨɫɤɨɥɶɤɭ ɜɨɞɧɵɟ ɪɚɫɬɜɨɪɵ ɢɨɞɚ ɨɤɪɚɲɟɧɵ, ɚ ɢɨɞɢɞɨɜ ɛɟɫɰɜɟɬɧɵ, ɡɚ ɤɢɧɟɬɢɤɨɣ ɩɪɨɰɟɫɫɚ ɦɨɠɧɨ ɫɥɟɞɢɬɶ ɩɨ ɢɡɦɟɧɟɧɢɸ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ ɜ ɜɢɞɢɦɨɣ ɨɛɥɚɫɬɢ. Ɇɚɤɫɢɦɭɦ ɩɨɝɥɨɳɟɧɢɹ ɧɚɛɥɸɞɚɟɬɫɹ ɩɪɢ 460 ɧɦ. Ʉɪɨɦɟ ɬɨɝɨ, ɢɨɞ ɞɚɟɬ ɨɤɪɚɲɟɧɧɵɣ ɤɨɦɩɥɟɤɫ ɫ ɤɪɚɯɦɚɥɨɦ, ɢɦɟɸɳɢɣ ɢɧɬɟɧɫɢɜɧɭɸ ɪɚɡɦɵɬɭɸ ɩɨɥɨɫɭ ɜ ɨɛɥɚɫɬɢ ɨɬ 600 ɞɨ 750 ɧɦ. ɉɨɷɬɨɦɭ ɪɚɫɬɜɨɪɵ ɤɪɚɯɦɚɥɚ ɩɪɢɦɟɧɹɸɬ ɤɚɤ ɱɭɜɫɬɜɢɬɟɥɶɧɵɟ ɢɧɞɢɤɚɬɨɪɵ ɢɨɞɚ. ɐɟɥɶ ɪɚɛɨɬɵ. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɨɪɹɞɤɚ ɪɟɚɤɰɢɢ ɩɨ ɪɟɚɝɟɧɬɭ. ɋɪɚɜɧɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɤɚɬɚɥɢɬɢɱɟɫɤɨɝɨ ɢ ɧɟɤɚɬɚɥɢɬɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɨɜ. Ɉɛɨɪɭɞɨɜɚɧɢɟ ɢ ɪɟɚɤɬɢɜɵ.
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Ɂɞɟɫɶ v0 – ɜɟɥɢɱɢɧɚ, ɫɨɞɟɪɠɚɳɚɹ ɤɨɧɫɬɚɧɬɭ ɫɤɨɪɨɫɬɢ ɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɪɟɚɝɢɪɭɸɳɢɯ ɜɟɳɟɫɬɜ ɩɨ ɡɚɤɨɧɭ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ. ɉɨɫɤɨɥɶɤɭ ln v ɥɢɧɟɣɧɨ ɡɚɜɢɫɢɬ ɨɬ 1/T, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɷɧɟɪɝɢɸ ɚɤɬɢɜɚɰɢɢ ɱɟɪɟɡ ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɹɦɨɣ ɜ ɤɨɨɪɞɢɧɚɬɚɯ «ɥɨɝɚɪɢɮɦ ɫɤɨɪɨɫɬɢ – ɨɛɪɚɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ». ɉɨ ɮɨɪɦɭɥɟ (III.7) ɜɵɱɢɫɥɢɬɟ ɫɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɩɪɢ ɤɚɠɞɨɣ ɬɟɦɩɟɪɚɬɭɪɟ. ɉɨɫɬɪɨɣɬɟ ɝɪɚɮɢɤ, ɨɬɤɥɚɞɵɜɚɹ ɩɨ ɨɫɹɦ ɡɧɚɱɟɧɢɹ ln v ɢ 1/T. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɬɨɱɤɢ ɞɨɥɠɧɵ ɩɪɢɦɟɪɧɨ ɭɤɥɚɞɵɜɚɬɶɫɹ ɧɚ ɩɪɹɦɭɸ. ɇɟ ɫɥɟɞɭɟɬ ɨɠɢɞɚɬɶ, ɱɬɨ ɬɨɱɤɢ «ɜ ɫɨɜɟɪɲɟɧɫɬɜɟ» ɜɵɫɬɪɨɹɬɫɹ ɜ ɩɪɹɦɭɸ. Ɉɧɢ ɛɭɞɭɬ ɨɬɤɥɨɧɹɬɶɫɹ ɨɬ ɧɟɤɨɬɨɪɨɣ ɨɩɬɢɦɚɥɶɧɨɣ ɩɪɹɦɨɣ ɜ ɜɢɞɭ ɩɨɝɪɟɲɧɨɫɬɟɣ ɷɤɫɩɟɪɢɦɟɧɬɚ. ɉɪɨɜɟɞɢɬɟ ɭɫɪɟɞɧɟɧɧɭɸ ɩɪɹɦɭɸ, ɤɨɬɨɪɚɹ ɩɪɨɯɨɞɢɥɚ ɛɵ ɤɚɤ ɦɨɠɧɨ ɛɥɢɠɟ ɤ ɤɚɠɞɨɣ ɢɡ ɬɨɱɟɤ. Ɉɩɪɟɞɟɥɢɬɟ ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɢ ɧɚɣɞɢɬɟ ɷɧɟɪɝɢɸ ɚɤɬɢɜɚɰɢɢ.
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4. Ʉɚɬɚɥɢɬɢɱɟɫɤɨɟ ɨɤɢɫɥɟɧɢɟ ɢɨɞɢɞɚ ɤɚɥɢɹ
Ɏɨɬɨɦɟɬɪ ɄɎɄ-5Ɇ ɫɨ ɫɜɟɬɨɮɢɥɶɬɪɨɦ 400 ɧɦ, 4 ɤɸɜɟɬɵ ɫ ɬɨɥɳɢɧɨɣ ɩɨɝɥɨɳɚɸɳɟɝɨ ɫɥɨɹ 10,00 ɦɦ. ɋɟɤɭɧɞɨɦɟɪ. Ɋɚɫɬɜɨɪ ɢɨɞɢɞɚ ɤɚɥɢɹ 0,005 ɦɨɥɶ/ɥ. Ɋɚɫɬɜɨɪ ɩɟɪɟɤɢɫɢ ɜɨɞɨɪɨɞɚ 0,01 ɦɨɥɶ/ɥ. ɋɨɥɹɧɚɹ ɤɢɫɥɨɬɚ 1 ɦɨɥɶ/ɥ. Ɋɚɫɬɜɨɪ ɜɨɥɶɮɪɚɦɚɬɚ ɧɚɬɪɢɹ ɢɥɢ ɦɨɥɢɛɞɚɬɚ ɚɦɦɨɧɢɹ ɨɤ. 110–5 ɦɨɥɶ/ɥ. Ɋɚɫɬɜɨɪ ɤɪɚɯɦɚɥɚ 0,2 %. ȼɨɞɚ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɚɹ. 4 ɦɟɪɧɵɯ ɰɢɥɢɧɞɪɚ (ɢɥɢ ɫɬɚɤɚɧɚ) ɧɚ 100 ɦɥ. 4 ɦɟɪɧɵɯ ɰɢɥɢɧɞɪɚ ɧɚ 50 ɦɥ. Ȼɭɦɚɠɧɵɟ ɮɢɥɶɬɪɵ.
ȼɵɩɨɥɧɟɧɢɟ ɪɚɛɨɬɵ. ɉɨɞɝɨɬɨɜɶɬɟ ɮɨɬɨɦɟɬɪ ɞɥɹ ɢɡɦɟɪɟɧɢɣ ɨɩɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ. 1. ȼ ɦɟɪɧɵɣ ɫɬɚɤɚɧ ɢɥɢ ɰɢɥɢɧɞɪ ɧɚ 100 ɦɥ ɜɧɟɫɢɬɟ 5 ɦɥ ɫɨɥɹɧɨɣ ɤɢɫɥɨɬɵ, 5 ɦɥ ɪɚɫɬɜɨɪɚ ɢɨɞɢɞɚ ɤɚɥɢɹ, 2–3 ɤɚɩɥɢ ɤɪɚɯɦɚɥɚ ɢ 5 ɦɥ ɪɚɫɬɜɨɪɚ ɜɨɥɶɮɪɚɦɚɬɚ ɧɚɬɪɢɹ ɢɥɢ ɦɨɥɢɛɞɚɬɚ ɚɦɦɨɧɢɹ ɤɚɤ ɤɚɬɚɥɢɡɚɬɨɪɨɜ. ɗɬɭ ɫɦɟɫɶ ɧɟɨɛɯɨɞɢɦɨ ɪɚɡɛɚɜɢɬɶ ɜɨɞɨɣ ɩɪɢɦɟɪɧɨ ɞɨ 30–40 ɦɥ. ɉɨɫɥɟ ɩɟɪɟɦɟɲɢɜɚɧɢɹ ɞɨɛɚɜɶɬɟ 5 ɦɥ ɪɚɫɬɜɨɪɚ ɩɟɪɟɤɢɫɢ ɜɨɞɨɪɨɞɚ, ɨɞɧɨɜɪɟɦɟɧɧɨ ɩɭɫɬɢɜ ɫɟɤɭɧɞɨɦɟɪ. ɇɟ ɬɟɪɹɹ ɜɪɟɦɟɧɢ, ɞɨɥɟɣɬɟ ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɭɸ ɜɨɞɭ ɬɚɤ, ɱɬɨɛɵ ɨɛɴɟɦ ɪɟɚɝɢɪɭɸɳɟɝɨ ɪɚɫɬɜɨɪɚ ɩɨɥɭɱɢɥɫɹ ɪɚɜɧɵɦ 50 ɦɥ. ɂɫɩɨɥɶɡɭɹ ɫɜɟɬɨɮɢɥɶɬɪ 590 ɢɥɢ 670 ɧɦ, ɢɡɦɟɪɶɬɟ «ɯɨɥɨɫɬɭɸ ɩɪɨɛɭ» ɞɢɫɬɢɥɥɢɪɨɜɚɧɧɨɣ ɜɨɞɵ. Ɂɚɬɟɦ, ɨɬɥɢɜ ɩɨɪɰɢɸ ɪɟɚɝɢɪɭɸɳɟɝɨ ɪɚɫɬɜɨɪɚ ɜ ɤɸɜɟɬɭ, 40
ɢɡɦɟɪɹɣɬɟ ɟɝɨ ɨɩɬɢɱɟɫɤɭɸ ɩɥɨɬɧɨɫɬɶ ɜ ɬɟɱɟɧɢɟ 10–15 ɦɢɧ, ɡɚɩɢɫɵɜɚɹ ɩɨɤɚɡɚɧɢɹ ɩɪɢɛɨɪɚ ɤɚɠɞɭɸ ɦɢɧɭɬɭ: CKI, ɦɨɥɶ/ɥ W, ɦɢɧ D
ɉɨɜɬɨɪɢɬɟ ɢɡɦɟɪɟɧɢɹ, ɦɟɧɹɹ ɤɨɥɢɱɟɫɬɜɨ ɢɨɞɢɞɚ ɤɚɥɢɹ. Ⱦɥɹ ɷɬɨɝɨ ɜ ɪɚɫɬɜɨɪ ɜɧɨɫɢɬɟ 10, 15 ɢ 20 ɦɥ ɢɨɞɢɞɚ ɤɚɥɢɹ, ɧ ɟ ɢ ɡ ɦ ɟ ɧ ɹ ɹ ɤɨɥɢɱɟɫɬɜ ɨɫɬɚɥɶɧɵɯ ɪɟɚɝɟɧɬɨɜ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɛɭɞɭɬ ɩɨɥɭɱɟɧɵ ɱɟɬɵɪɟ ɤɢɧɟɬɢɱɟɫɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɢɨɞɢɞɚ. 2. ɉɨɜɬɨɪɢɬɟ ɷɤɫɩɟɪɢɦɟɧɬ ɫ ɨɞɧɨɣ ɢɡ ɤɨɧɰɟɧɬɪɚɰɢɣ ɢɨɞɢɞɚ (ɧɚɩɪɢɦɟɪ, ɧɚɢɛɨɥɶɲɟɣ), ɧɨ ɧɟ ɜɧɨɫɹ ɜ ɪɟɚɤɰɢɨɧɧɭɸ ɫɦɟɫɶ ɤɚɬɚɥɢɡɚɬɨɪ. Ɉɛɪɚɛɨɬɤɚ ɪɟɡɭɥɶɬɚɬɨɜ. ɉɨɫɬɪɨɣɬɟ ɤɢɧɟɬɢɱɟɫɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɜ ɤɨɨɪɞɢɧɚɬɚɯ «ɨɩɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ – ɜɪɟɦɹ». ɉɨɫɤɨɥɶɤɭ ɦɟɞɥɟɧɧɚɹ ɪɟɚɤɰɢɹ ɧɚɛɥɸɞɚɥɚɫɶ ɜ ɬɟɱɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɨɝɨ ɧɚɱɚɥɶɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜɪɟɦɟɧɢ, ɷɬɢ ɡɚɜɢɫɢɦɨɫɬɢ ɛɥɢɡɤɢ ɤ ɥɢɧɟɣɧɵɦ. ɉɨ ɧɚɤɥɨɧɭ ɥɢɧɟɣɧɵɯ ɭɱɚɫɬɤɨɜ ɨɩɪɟɞɟɥɢɬɟ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɩɪɢ ɤɚɠɞɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢɨɞɢɞɚ ɤɚɥɢɹ. p ȿɫɥɢ ɫɤɨɪɨɫɬɶ ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ v kcCI , ɬɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨɪɹɞɨɤ ɪɟɚɤɰɢɢ ɩɨ ɢɨɞɢɞɭ p ɦɨɠɧɨ, ɩɨɫɬɪɨɢɜ ɡɚɜɢɫɢɦɨɫɬɶ v(CI–) ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ: ln v = ln kc + p ln CI–. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɪɹɞɨɤ ɪɟɚɤɰɢɢ ɧɚɯɨɞɢɬɫɹ ɤɚɤ ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɹɦɨɣ ln v = f (ln CI–). ɋɪɚɜɧɢɬɟ ɫɤɨɪɨɫɬɢ ɨɤɢɫɥɟɧɢɹ ɢɨɞɢɞ-ɢɨɧɨɜ ɜ ɩɪɢɫɭɬɫɬɜɢɢ ɤɚɬɚɥɢɡɚɬɨɪɚ ɢ ɛɟɡ ɧɟɝɨ.
ȾɈɉɈɅɇȿɇɂȿ Ʉ ɪɚɛɨɬɟ 2 «ɂɫɫɥɟɞɨɜɚɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɞɢɫɫɨɰɢɚɰɢɢ. Ɉɩɪɟɞɟɥɟɧɢɟ pKa ɫɥɚɛɨɣ ɤɢɫɥɨɬɵ» (ɢɧɮɨɪɦɚɰɢɹ ɞɥɹ ɩɪɟɩɨɞɚɜɚɬɟɥɟɣ)
ȼɵɛɨɪ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɨɝɨ ɢɧɞɢɤɚɬɨɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɟɝɨ ɫɩɟɤɬɪɚɥɶɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ: ɧɚɥɢɱɢɟɦ ɞɜɭɯ ɩɨɥɨɫ ɩɨɝɥɨɳɟɧɢɹ ɜ ɜɢɞɢɦɨɣ ɨɛɥɚɫɬɢ, ɪɚɡɥɢɱɚɸɳɢɯɫɹ ɞɥɹ ɩɪɨɬɨɧɢɪɨɜɚɧɧɨɣ ɢ ɞɟɩɪɨɬɨɧɢɪɨɜɚɧɧɨɣ ɮɨɪɦ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɩɪɢɦɟɧɢɬɶ ɫɩɟɤɬɪɨɮɨɬɨɦɟɬɪɢɱɟɫɤɢɣ ɦɟɬɨɞ (ɜ ɜɚɪɢɚɧɬɟ ɤɨɥɨɪɢɦɟɬɪɢɢ) ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɜɧɨɜɟɫɧɵɯ ɮɨɪɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɪɚɛɨɬɟ ɦɨɠɟɬ ɛɵɬɶ ɞɨɫɬɢɝɧɭɬɚ ɰɟɥɶ ɩɪɹɦɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɧɫɬɚɧɬɵ ɢɨɧɢɡɚɰɢɢ, ɭɫɬɚɧɨɜɥɟɧɢɹ ɟɟ ɩɨɫɬɨɹɧɫɬɜɚ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ. ɉɨ ɫɬɪɨɟɧɢɸ ɢ ɯɪɨɦɨɮɨɪɧɵɦ ɮɭɧɤɰɢɹɦ ɛɪɨɦɬɢɦɨɥɨɜɵɣ ɫɢɧɢɣ (ɞɢɛɪɨɦɬɢɦɨɥɫɭɥɶɮɨɮɬɚɥɟɢɧ, ȻɌɋ) ɨɬɧɨɫɢɬɫɹ ɤ ɤɪɚɫɢɬɟɥɹɦ ɬɪɢɮɟɧɢɥɦɟɬɚɧɨɜɨɣ ɝɪɭɩɩɵ (ɧɚɪɹɞɭ ɫ ɮɟɧɨɥɮɬɚɥɟɢɧɨɦ, ɪɨɡɨɥɨɜɨɣ ɤɢɫɥɨɬɨɣ ɢ ɞɪ.). ɉɪɨɬɨɝɟɧɧɨɣ ɹɜɥɹɟɬɫɹ ɫɭɥɶɮɨɝɪɭɩɩɚ SO3–H+. ɂɧɬɟɪɜɚɥ pH ɩɟɪɟɯɨɞɚ ɨɤɪɚɫɤɢ ɨɬ 6,0 ɞɨ 7,6.
Ɋɢɫ. 9 41
Ɋɢɫ. 10 42
ɋɩɟɤɬɪɵ ɩɨɝɥɨɳɟɧɢɹ ɪɚɫɬɜɨɪɨɜ ȻɌɋ ɜ ɢɧɬɟɪɜɚɥɟ pH ɨɬ 5,6 ɞɨ 7,3 ɫɦ. ɧɚ ɪɢɫ. 9 (ɤɨɧɰɟɧɬɪɚɰɢɹ > 0,02 ɝ/ɥ, ɬɨɥɳɢɧɚ ɩɨɝɥɨɳɚɸɳɟɝɨ ɫɥɨɹ 10 ɦɦ, ɫɩɟɤɬɪɵ ɩɨɥɭɱɟɧɵ ɧɚ ɫɩɟɤɬɪɨɮɨɬɨɦɟɬɪɟ ɋɎ-2000). Ɉɩɪɟɞɟɥɟɧɢɸ ɩɪɨɬɨɧɢɪɨɜɚɧɧɨɣ ɮɨɪɦɵ HȻɌɋ ɨɬɱɚɫɬɢ ɦɟɲɚɟɬ ɮɢɨɥɟɬɨɜɚɹ ɩɨɥɨɫɚ 395 ɧɦ ɮɨɪɦɵ ȻɌɋ– (ɫɦɟɳɟɧɢɟ ɦɚɤɫɢɦɭɦɚ 433 ɧɦ). Ʉɪɚɫɧɚɹ ɩɨɥɨɫɚ 614 ɧɦ ɢɧɬɟɧɫɢɜɧɟɟ ɫɢɧɟɣ 433 ɧɦ, ɩɨɷɬɨɦɭ ɢɧɬɟɪɜɚɥ ɜɢɞɢɦɨɝɨ ɩɟɪɟɯɨɞɚ ɨɤɪɚɫɤɢ ɫɦɟɳɟɧ ɜ ɤɢɫɥɭɸ ɫɬɨɪɨɧɭ. ɂɡɦɟɪɟɧɢɹ ɜ ɪɚɛɨɬɟ ɫɥɟɞɭɟɬ ɩɪɨɜɨɞɢɬɶ ɧɚ ɞɥɢɧɚɯ ɜɨɥɧ 440 ɢ 590 ɧɦ, ɧɚɢɛɨɥɟɟ ɛɥɢɡɤɢɯ ɤ ɦɚɤɫɢɦɭɦɚɦ ɩɨɥɨɫ ɩɨɝɥɨɳɟɧɢɹ. ɇɚɣɞɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɜɧɨɜɟɫɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɨɬ pH ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 10. Ɍɨɱɤɟ ɪɚɜɟɧɫɬɜɚ ɨɬɜɟɱɚɟɬ ɡɧɚɱɟɧɢɟ pKa = 7,4. ȼɵɱɢɫɥɟɧɢɟ pKa ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɞɚɟɬ ɡɚɧɢɠɟɧɧɵɟ ɡɧɚɱɟɧɢɹ, ɨɫɨɛɟɧɧɨ, ɩɪɢ pH < 6,0. Ɍɟɦ ɧɟ ɦɟɧɟɟ, ɦɨɠɧɨ ɪɟɤɨɦɟɧɞɨɜɚɬɶ ɬɚɤɨɟ ɜɵɱɢɫɥɟɧɢɟ ɤɚɤ ɩɪɨɜɟɪɤɭ ɡɚɤɨɧɚ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ. ɉɨɫɤɨɥɶɤɭ ɦɨɥɹɪɧɵɟ ɦɚɫɫɵ ɞɟɩɪɨɬɨɧɢɪɨɜɚɧɧɨɣ ɢ ɩɪɨɬɨɧɢɪɨɜɚɧɧɨɣ ɮɨɪɦ ɨɬɥɢɱɚɸɬɫɹ ɬɨɥɶɤɨ ɧɚ ɟɞɢɧɢɰɭ (ɩɪɢ ɦɨɥ. ɦɚɫɫɟ ȻɌɋ 624 ɝ/ɦɨɥɶ), ɦɨɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɦɚɫɫɨɜɨɣ ɨɛɴɟɦɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɟɣ.
ɅɂɌȿɊȺɌɍɊȺ Ɉɛɳɢɟ ɪɭɤɨɜɨɞɫɬɜɚ ɫ ɢɡɥɨɠɟɧɢɟɦ ɨɫɧɨɜ ɤɢɧɟɬɢɤɢ 1. Ɏɪɨɥɨɜ ɘ.Ƚ. Ɏɢɡɢɱɟɫɤɚɹ ɯɢɦɢɹ / ɘ.Ƚ. Ɏɪɨɥɨɜ, ȼ. ȼ. Ȼɟɥɢɤ. – Ɇ. : ɏɢɦɢɹ, 1993. – 464 ɫ. 2. Ɏɢɡɢɱɟɫɤɚɹ ɯɢɦɢɹ. ȼ 2 ɤɧ. Ʉɧ. 2. ɗɥɟɤɬɪɨɯɢɦɢɹ. ɏɢɦɢɱɟɫɤɚɹ ɤɢɧɟɬɢɤɚ ɢ ɤɚɬɚɥɢɡ / Ʉ.ɋ. Ʉɪɚɫɧɨɜ [ɢ ɞɪ.] ; ɩɨɞ ɪɟɞ. Ʉ.ɋ. Ʉɪɚɫɧɨɜɚ. – Ɇ. : ȼɵɫɲ. ɲɤ., 2001. – 319 ɫ. 3. ɍɝɚɣ ə.Ⱥ. Ɉɛɳɚɹ ɯɢɦɢɹ / ə.Ⱥ. ɍɝɚɣ. – Ɇ. : ȼɵɫɲ. ɲɤ., 1984. – 440 ɫ. ɋɩɟɰɢɚɥɶɧɵɟ ɩɨɫɨɛɢɹ 4. ɗɦɚɧɭɷɥɶ ɇ.Ɇ. Ʉɭɪɫ ɯɢɦɢɱɟɫɤɨɣ ɤɢɧɟɬɢɤɢ / ɇ.Ɇ. ɗɦɚɧɭɷɥɶ, Ⱦ.Ƚ. Ʉɧɨɪɪɟ. – Ɇ. : ȼɵɫɲ. ɲɤ., 1984. – 463 ɫ. 5. Ⱦɟɧɢɫɨɜ ȿ.Ɍ. ɏɢɦɢɱɟɫɤɚɹ ɤɢɧɟɬɢɤɚ / ȿ.Ɍ. Ⱦɟɧɢɫɨɜ, Ɉ.Ɇ. ɋɚɪɤɢɫɨɜ, Ƚ.ɂ. Ʌɢɯɬɟɧɲɬɟɣɧ. – Ɇ. : ɏɢɦɢɹ, 2000. – 565 ɫ. ɋɩɟɤɬɪɨɮɨɬɨɦɟɬɪɢɹ 6. ȼɢɥɤɨɜ Ʌ.ȼ. Ɏɢɡɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜ ɯɢɦɢɢ / Ʌ.ȼ. ȼɢɥɤɨɜ, ɘ.Ⱥ. ɉɟɧɬɢɧ. – Ɇ. : ȼɵɫɲ. ɲɤ., 1987. – 366 ɫ. 7. Ȼɭɥɚɬɨɜ Ɇ.ɂ. ɉɪɚɤɬɢɱɟɫɤɨɟ ɪɭɤɨɜɨɞɫɬɜɨ ɩɨ ɮɨɬɨɦɟɬɪɢɱɟɫɤɢɦ ɦɟɬɨɞɚɦ ɚɧɚɥɢɡɚ / Ɇ.ɂ. Ȼɭɥɚɬɨɜ, ɂ.ɉ. Ʉɚɥɢɧɤɢɧ. – Ʌ. : ɏɢɦɢɹ, 1986. – 431 ɫ.
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ɋɈȾȿɊɀȺɇɂȿ ɉɪɟɞɢɫɥɨɜɢɟ......................................................................................................... 3 I. ɗɥɟɦɟɧɬɵ ɝɨɦɨɝɟɧɧɨɣ ɤɢɧɟɬɢɤɢ 1. Ɉɫɧɨɜɧɨɣ ɡɚɤɨɧ ɫɬɟɯɢɨɦɟɬɪɢɢ................................................................. 4 2. ɋɤɨɪɨɫɬɶ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ................................................................ 6 3. Ɂɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ......................................................................... 8 4. ɉɨɪɹɞɨɤ ɢ ɦɨɥɟɤɭɥɹɪɧɨɫɬɶ .................................................................... 10 5. Ʉɢɧɟɬɢɤɚ ɧɟɤɨɬɨɪɵɯ ɩɪɨɫɬɵɯ ɪɟɚɤɰɢɣ................................................. 11 6. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɪɟɚɤɰɢɢ.................................................................... 14 7. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ................................................. 16 8. Ɉ ɬɟɨɪɢɢ ɚɤɬɢɜɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ......................................................... 18 9. Ɉɛɪɚɬɢɦɵɟ ɪɟɚɤɰɢɢ ................................................................................ 20 10. ɏɢɦɢɱɟɫɤɨɟ ɪɚɜɧɨɜɟɫɢɟ.......................................................................... 22 11. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɧɫɬɚɧɬɵ ɪɚɜɧɨɜɟɫɢɹ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ. ɉɪɢɧɰɢɩ Ʌɟ ɒɚɬɟɥɶɟ.............................................................................. 25 II. ɋɩɟɤɬɪɨɮɨɬɨɦɟɬɪɢɱɟɫɤɢɣ ɢ ɤɨɥɨɪɢɦɟɬɪɢɱɟɫɤɢɣ ɦɟɬɨɞɵ 1. Ɉɛɳɢɟ ɫɜɟɞɟɧɢɹ....................................................................................... 27 2. Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɣ ................................................................... 30 III. ɉɪɚɤɬɢɱɟɫɤɢɟ ɪɚɛɨɬɵ 1. ɂɫɫɥɟɞɨɜɚɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɜ ɫɢɫɬɟɦɟ «ɯɪɨɦɚɬ–ɛɢɯɪɨɦɚɬ».................. 31 2. ɂɫɫɥɟɞɨɜɚɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɞɢɫɫɨɰɢɚɰɢɢ. Ɉɩɪɟɞɟɥɟɧɢɟ pKa ɫɥɚɛɨɣ ɤɢɫɥɨɬɵ ......................................................... 33 3. ɂɫɫɥɟɞɨɜɚɧɢɟ ɤɢɧɟɬɢɤɢ ɪɟɚɤɰɢɢ ɪɚɡɥɨɠɟɧɢɹ ɬɢɨɫɟɪɧɨɣ ɤɢɫɥɨɬɵ.................................................................................. 36 4. Ʉɚɬɚɥɢɬɢɱɟɫɤɨɟ ɨɤɢɫɥɟɧɢɟ ɢɨɞɢɞɚ ɤɚɥɢɹ............................................. 40 Ⱦɨɩɨɥɧɟɧɢɟ ........................................................................................................ 42 Ʌɢɬɟɪɚɬɭɪɚ ......................................................................................................... 44
ɍɱɟɛɧɨɟ ɢɡɞɚɧɢɟ
ɏɂɆɂɑȿɋɄȺə ɄɂɇȿɌɂɄȺ ɍɱɟɛɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ
ɋɨɫɬɚɜɢɬɟɥɶ ɇɚɭɦɨɜ Ⱥɥɟɤɫɚɧɞɪ ȼɥɚɞɢɦɢɪɨɜɢɱ Ɋɟɞɚɤɬɨɪ ɂ.Ƚ. ȼɚɥɵɧɤɢɧɚ
ɉɨɞɩɢɫɚɧɨ ɜ ɩɟɱɚɬɶ 28.12.2007. Ɏɨɪɦɚɬ 60×84/16. ɍɫɥ. ɩɟɱ. ɥ. 2,7. Ɍɢɪɚɠ 150 ɷɤɡ. Ɂɚɤɚɡ 2092. ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. 394000, ɝ. ȼɨɪɨɧɟɠ, ɩɥ. ɢɦ. Ʌɟɧɢɧɚ, 10. Ɍɟɥ. 208-298, 598-026 (ɮɚɤɫ) http://www.ppc.vsu.ru; e-mail:
[email protected] Ɉɬɩɟɱɚɬɚɧɨ ɜ ɬɢɩɨɝɪɚɮɢɢ ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɨɝɨ ɰɟɧɬɪɚ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. 394000, ɝ. ȼɨɪɨɧɟɠ, ɭɥ. ɉɭɲɤɢɧɫɤɚɹ, 3. Ɍɟɥ. 204-133. 45
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