1 курс / Химия / ANALITIChESKAYa_KhIMIYa_V_TABLITsAKh

Ɋɚɫɫɱɢɬɵɜɚɟɦ ɤɨɧɰɟɧɬɪɚɰɢɸ ɫɨɥɢ ɜ ɦɨɥɶ·ɥ-1:

	Cɫɨɥɢ	m		0,9814		0,1 ɦɨɥɶ ɥ 1 ,
		M V	98,143 0,1

ɝɞɟ: m – ɦɚɫɫɚ ɫɨɥɢ, ɝ;

V – ɨɛɴɟɦ ɪɚɫɬɜɨɪɚ, ɥ;

Ɇ – ɦɨɥɹɪɧɚɹ ɦɚɫɫɚ ɫɨɥɢ, ɝ·ɦɨɥɶ-1.

ɇɚɯɨɞɢɦ ɡɧɚɱɟɧɢɟ K CH 3COOH 1,74 10-5 . ɉɨɞɫɬɚɜɢɦ ɩɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɜ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɫɬɟɩɟɧɢ ɝɢɞɪɨɥɢɡɚ:

h	1 10-14		7,58 10 5 § 7,6·10– 5.
	1,74 10
		5	0,1

ɂɡ ɩɪɢɜɟɞɟɧɧɨɝɨ ɜɵɲɟ ɭɪɚɜɧɟɧɢɹ ɝɢɞɪɨɥɢɡɚ ɚɰɟɬɚɬ-ɢɨɧɨɜ ɫɥɟɞɭɟɬ, ɱɬɨ ɤɨɧɰɟɧɬɪɚɰɢɹ ɨɛɪɚɡɭɸɳɢɯɫɹ ɝɢɞɪɨɤɫɢɞ-ɢɨɧɨɜ ɪɚɜɧɚ ɤɨɧɰɟɧɬɪɚɰɢɢ ɚɰɟɬɚɬ-

ɢɨɧɨɜ. Ɍɨɝɞɚ, [Oɇ– ] = [CH3COO – ] = h·ɋɫɨɥɢ = 7,6·10 – 5·0,1 = 7,6·10 – 6 ɦɨɥɶ·ɥ-1. Ɉɬɫɸɞɚ, ɪɈɇ = –lg 7,6·10 – 6 = 5,12 ɢ ɪɇ = 14 – 5,12 = 8,88.

Ɂɚɞɚɱɚ 2 . ȼɵɱɢɫɥɢɬɶ ɤɨɧɫɬɚɧɬɭ ɝɢɞɪɨɥɢɡɚ ɚɦɦɨɧɢɹ ɯɥɨɪɢɞɚ ɢ ɪɇ ɟɝɨ 0,1 ɦɨɥɶ·ɥ-1 ɪɚɫɬɜɨɪɚ.

ɉɪɢɦɟɪ ɪɟɲɟɧɢɹ. Ⱥɦɦɨɧɢɹ ɯɥɨɪɢɞ ɢɨɧɢɡɢɪɭɟɬ ɩɨ ɭɪɚɜɧɟɧɢɸ:

NH4Cl	NH4+ + Cl–.
Ɍɚɤ ɤɚɤ ɞɚɧɧɚɹ ɫɨɥɶ ɨɛɪɚɡɨɜɚɧɚ ɫɥɚɛɵɦ ɨɫɧɨɜɚɧɢɟɦ ɢ ɫɢɥɶɧɨɣ ɤɢɫɥɨɬɨɣ,
ɝɢɞɪɨɥɢɡ ɢɞɟɬ ɩɨ ɤɚɬɢɨɧɭ:
NH4+ + ɇ2Ɉ		NH4OH + H+.

Ⱦɥɹ ɪɚɫɱɟɬɚ ɤɨɧɫɬɚɧɬɵ ɝɢɞɪɨɥɢɡɚ ɫɨɥɢ ɩɨɞɨɛɧɨɝɨ ɬɢɩɚ ɫɥɟɞɭɟɬ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɮɨɪɦɭɥɨɣ:

K ɝ	K w				10 14		5,68 10 10 .
	K	NH 4OH		1,76 10 5
Ɂɧɚɱɟɧɢɟ ɜɟɥɢɱɢɧɵ [ɇ+] ɜ ɪɚɫɬɜɨɪɟ ɚɦɦɨɧɢɹ ɯɥɨɪɢɞɚ ɧɚɣɞɟɦ ɩɨ ɮɨɪɦɭ-
ɥɟ:
[H ] Ʉɝ ɋɫɨɥɢ			5,68 10 10 0,1				7,63 10 6 ɦɨɥɶ ɥ 1 .

Ɍɨɝɞɚ, ɪɇ = –lg 7,53·10 – 6 = 5,12.

Ɂɚɞɚɱɚ 3 . ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɭɜɟɥɢɱɢɬɫɹ ɫɬɟɩɟɧɶ ɝɢɞɪɨɥɢɡɚ ɚɦɦɨɧɢɹ ɚɰɟɬɚɬɚ, ɟɫɥɢ ɟɝɨ ɪɚɫɬɜɨɪ ɧɚɝɪɟɬɶ ɫ 25° ɞɨ 60°ɋ? (Ʉw = 10 – 13 ɩɪɢ 60°ɋ. Ʉɨɧɫɬɚɧɬɵ ɢɨɧɢɡɚɰɢɢ ɭɤɫɭɫɧɨɣ ɤɢɫɥɨɬɵ ɢ ɚɦɦɨɧɢɹ ɝɢɞɪɨɤɫɢɞɚ ɫɱɢɬɚɬɶ ɧɟ ɢɡɦɟɧɹɸɳɢɦɢɫɹ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ).

ɉɪɢɦɟɪ ɪɟɲɟɧɢɹ. Ⱥɰɟɬɚɬ ɚɦɦɨɧɢɹ ɢɨɧɢɡɢɪɭɟɬ ɩɨ ɭɪɚɜɧɟɧɢɸ:

CH3COONH4	CH3COO – + NH4+.
Ɍɚɤ ɤɚɤ ɞɚɧɧɚɹ ɫɨɥɶ ɨɛɪɚɡɨɜɚɧɚ ɫɥɚɛɵɦ ɨɫɧɨɜɚɧɢɟɦ ɢ ɫɥɚɛɨɣ ɤɢɫɥɨɬɨɣ,
ɬɨ ɝɢɞɪɨɥɢɡ ɢɞɟɬ ɩɨ ɤɚɬɢɨɧɭ ɢ ɚɧɢɨɧɭ:
CH3COO – + NH4+ + ɇ2Ɉ		CH3COOH + NH3·H2Ɉ.

61

ɂɡ ɬɚɛɥɢɰɵ ɫɥɟɞɭɟɬ, ɱɬɨ ɞɥɹ ɪɚɫɱɟɬɚ ɫɬɟɩɟɧɢ ɝɢɞɪɨɥɢɡɚ ɬɚɤɢɯ ɫɨɥɟɣ ɫɥɟɞɭɟɬ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɮɨɪɦɭɥɨɣ:

									K w
							h	K a K b .
			1						K w
									K a		K b
Ɋɚɫɫɱɢɬɚɟɦ ɫɬɟɩɟɧɶ ɝɢɞɪɨɥɢɡɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ:
					10-14
25°ɋ	h	25qC	1,74 10-5 1,76 10 5															5,74 10 3
			10-14																	;
			1
			1,74 10-5 1,76 10 5
				10-13
60°ɋ	h60qC		1,74 10-5 1,76 10 5												1,82 10 2 .
			10-13
			1
			1,74 10-5 1,76 10							5
																h		60qC		1,82 10 2			3,17 ɪɚɡɚ	.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɫɬɟɩɟɧɶɝɢɞɪɨɥɢɡɚɜɨɡɪɨɫɥɚɜ
		,														h				5,74 10 3
																		25qC
Ɋɟɲɢɬɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɫɥɟɞɭɸɳɢɟ ɡɚɞɚɱɢ.
Ɂɚɞɚɱɚ 4 . ȼɵɱɢɫɥɢɬɶ ɪɇ 0, 01 Ɇ ɪɚɫɬɜɨɪɚ ɚɦɦɨɧɢɹ ɯɥɨɪɢɞɚ.
Ɂɚɞɚɱɚ	5 . ɉɪɢ 60°ɋ ɢɨɧɧɨɟ ɩɪɨɢɡɜɟɞɟɧɢɟ ɜɨɞɵ ɪɚɜɧɨ 10– 13. ɋɱɢɬɚɹ,

ɱɬɨ ɤɨɧɫɬɚɧɬɚ ɢɨɧɢɡɚɰɢɢ ɯɥɨɪɧɨɜɚɬɢɫɬɨɣ ɤɢɫɥɨɬɵ ɧɟ ɢɡɦɟɧɹɟɬɫɹ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ, ɜɵɱɢɫɥɢɬɶ ɪɇ 0,001Ɇ ɪɚɫɬɜɨɪɚ KOCl ɩɪɢ 25° ɢ 60°ɋ ɢ ɪɚɫɫɱɢɬɚɬɶ, ɜɨ ɫɤɨɥɶɤɨ ɪɚɡ ɜɨɡɪɨɫɥɚ ɫɬɟɩɟɧɶ ɝɢɞɪɨɥɢɡɚ ɫɨɥɢ.

Ɂɚɞɚɱɚ 6 . ɋɤɨɥɶɤɨ ɝɪɚɦɦɨɜ ɚɦɦɨɧɢɹ ɯɥɨɪɢɞɚ ɧɭɠɧɨ ɜɡɹɬɶ, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ 100 ɦɥ ɪɚɫɬɜɨɪɚ, ɢɦɟɸɳɟɝɨ ɜɟɥɢɱɢɧɭ ɪɇ = 5,12?

Ɋɚɜɧɨɜɟɫɢɹ ɜ ɛɭɮɟɪɧɵɯ ɪɚɫɬɜɨɪɚɯ

ȼ ɫɚɦɨɦ ɲɢɪɨɤɨɦ ɫɦɵɫɥɟ ɛɭɮɟɪɧɵɦɢ ɧɚɡɵɜɚɸɬ ɫɢɫɬɟɦɵ, ɩɨɞɞɟɪɠɢɜɚɸɳɢɟ ɨɩɪɟɞɟɥɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɤɚɤɨɝɨ-ɥɢɛɨ ɩɚɪɚɦɟɬɪɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɨɫɬɚɜɚ. Ȼɭɮɟɪɧɵɟ ɪɚɫɬɜɨɪɵ ɦɨɝɭɬ ɛɵɬɶ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɦɢ – ɩɨɞɞɟɪɠɢɜɚɸɬ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ ɪɇ ɩɪɢ ɜɜɟɞɟɧɢɢ ɤɢɫɥɨɬ ɢɥɢ ɨɫɧɨɜɚɧɢɣ; ɨɤɢɫɥɢɬɟɥɶɧɨɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɦɢ – ɫɨɯɪɚɧɹɸɬ ɩɨɫɬɨɹɧɧɵɦ ɩɨɬɟɧɰɢɚɥ ɫɢɫɬɟɦ ɩɪɢ ɜɜɟɞɟɧɢɢ ɨɤɢɫɥɢɬɟɥɟɣ ɢɥɢ ɜɨɫɫɬɚɧɨɜɢɬɟɥɟɣ; ɢɡɜɟɫɬɧɵ ɦɟɬɚɥɥɨɛɭɮɟɪɧɵɟ ɪɚɫɬɜɨɪɵ, ɜ ɤɨ-

62

ɋɫɨɥɢ

ɋɫɨɥɢ

ɬɨɪɵɯ ɩɨɞɞɟɪɠɢɜɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ ɪɆɟ. Ȼɭɮɟɪɧɵɣ ɪɚɫɬɜɨɪ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɩɪɹɠɟɧɧɭɸ ɩɚɪɭ; ɜ ɱɚɫɬɧɨɫɬɢ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɟ – ɫɨɩɪɹɠɟɧɧɭɸ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɭɸ ɩɚɪɭ. ɇɚɩɪɢɦɟɪ, ɚɰɟɬɚɬɧɵɣ ɛɭɮɟɪɧɵɣ ɪɚɫɬɜɨɪ ɫɨɫɬɨɢɬ ɢɡ ɋɇ3ɋɈɈɇ ɢ CH3COONa, ɚɦɦɨɧɢɣɧɵɣ – ɢɡ NH3·H2O ɢ NH4Cl, ɮɨɫɮɚɬɧɵɣ – ɢɡ

NaH2PO4 ɢ Na2HPO4.

ɪɇ ɛɭɮɟɪɧɵɯ ɪɚɫɬɜɨɪɨɜ, ɫɨɫɬɨɹɳɢɯ ɢɡ ɫɥɚɛɨɣ ɤɢɫɥɨɬɵ ɢ ɟɟ ɫɨɥɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɭɪɚɜɧɟɧɢɸ:

pH pKa lg Cɤɢɫɥɨɬɵ .

pH ɛɭɮɟɪɧɵɯ ɪɚɫɬɜɨɪɨɜ, ɫɨɫɬɨɹɳɢɯ ɢɡ ɫɥɚɛɨɝɨ ɨɫɧɨɜɚɧɢɹ ɢ ɟɝɨ ɫɨɥɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɭɪɚɜɧɟɧɢɸ:

pH 14 pKɜ lg ɋɨɫɧɨɜɚɧɢɹ .

Ɂɚɞɚɱɚ. ȼɵɱɢɫɥɢɬɶ ɪɇ ɚɰɟɬɚɬɧɨɣ ɛɭɮɟɪɧɨɣ ɫɦɟɫɢ, ɫɨɞɟɪɠɚɳɟɣ ɜ 1 ɥ ɪɚɫɬɜɨɪɚ ɩɨ 0,2 ɦɨɥɶ ɤɚɠɞɨɝɨ ɤɨɦɩɨɧɟɧɬɚ. Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɪɇ ɩɪɢ ɞɨɛɚɜɥɟɧɢɢ ɤ 1 ɥ ɫɦɟɫɢ:

ɚ) 0,01 ɦɨɥɶ HCl; ɛ) 0,01 ɦɨɥɶ NaOH.

ɉɪɢɦɟɪ ɪɟɲɟɧɢɹ. ȼ ɫɨɫɬɚɜ ɚɰɟɬɚɬɧɨɣ ɛɭɮɟɪɧɨɣ ɫɦɟɫɢ ɜɯɨɞɹɬ

CH3COOH ɢ CH3COONa.

CH3COOɇ CH3COO – + H+ (ɫɥɚɛɵɣ ɷɥɟɤɬɪɨɥɢɬ: ɢɨɧɢɡɢɪɭɟɬ ɨɛɪɚ-

ɬɢɦɨ)

CH3COONa CH3COO – + Na+ (ɫɢɥɶɧɵɣ ɷɥɟɤɬɪɨɥɢɬ: ɞɢɫɫɨɰɢɢɪɭɟɬ ɧɚ-

ɰɟɥɨ)

ȼ ɩɪɢɫɭɬɫɬɜɢɢ ɨɞɧɨɢɦɟɧɧɵɯ ɢɨɧɨɜ (ɋɇ3ɋɈɈ– ) ɢɨɧɢɡɚɰɢɹ ɋɇ3ɋɈɈɇ ɝɥɭɛɨɤɨ ɩɨɞɚɜɥɟɧɚ. ɉɨɷɬɨɦɭ ɤɨɧɰɟɧɬɪɚɰɢɸ ɧɟɢɨɧɢɡɢɪɨɜɚɧɧɨɣ ɱɚɫɬɢ ɤɢɫɥɨɬɵ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɪɚɜɧɨɣ ɟɟ ɧɚɱɚɥɶɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɬ.ɟ.

[ɋɇ3ɋɈɈɇ] = ɋɤɢɫɥɨɬɵ.

ɉɪɚɤɬɢɱɟɫɤɢ ɜɫɟ ɚɰɟɬɚɬ-ɢɨɧɵ ɨɛɪɚɡɭɸɬɫɹ ɜɫɥɟɞɫɬɜɢɟ ɞɢɫɫɨɰɢɚɰɢɢ ɫɨɥɢ, ɬ.ɟ. [ɋɇ3ɋɈɈ– ] = ɋɫɨɥɢ.

pH pKɚ	lg	Cɤɢɫɥɨɬɵ	; pH	4,76 lg	0,2	4,76
		ɋɫɨɥɢ		0,2

ɚ) ɟɫɥɢ ɩɪɢɛɚɜɢɬɶ 0,01 ɦɨɥɶ HCl, ɬɨ ɩɪɨɢɡɨɣɞɟɬ ɪɟɚɤɰɢɹ ɦɟɠɞɭ HCl ɢ CH3COONa:

CH3COO – + H+ CH3COOH,

ɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɭɤɫɭɫɧɨɣ ɤɢɫɥɨɬɵ ɜɨɡɪɚɫɬɟɬ ɢ ɫɬɚɧɟɬ ɪɚɜɧɨɣ 0,2 + 0,01 = 0,21 ɦɨɥɶ·ɥ– 1, ɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɫɨɥɢ ɩɨɧɢɡɢɬɫɹ ɞɨ: 0,2 – 0,01 = 0,19 ɦɨɥɶ·ɥ– 1.

pH 4,76 lg 0,21 4,72 0,19

63

ɛ) ɟɫɥɢ ɩɪɢɛɚɜɢɬɶ 0,01 ɦɨɥɶ NaOH, ɬɨ ɩɪɨɢɡɨɣɞɟɬ ɪɟɚɤɰɢɹ ɦɟɠɞɭ NaOH

ɢ CH3COOH:
CH3COOH – + Oɇ–	CH3COO – + H2O,

ɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɭɤɫɭɫɧɨɣ ɤɢɫɥɨɬɵ ɫɬɚɧɟɬ ɪɚɜɧɨɣ 0,2 – 0,01 = 0,19 ɦɨɥɶ·ɥ– 1, ɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɫɨɥɢ ɭɜɟɥɢɱɢɬɫɹ: 0,2 + 0,01 = 0,21 ɦɨɥɶ·ɥ– 1.

pH 4,76 lg 0,19 4,80 0,21

Ɉɬɜɟɬ.pH = 4,76; ɚ) ɪɇ = 4,72; ɛ) pH = 4,80.

Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɨɛɚɜɥɹɬɶ ɫɢɥɶɧɭɸ ɤɢɫɥɨɬɭ ɢɥɢ ɫɢɥɶɧɨɟ ɨɫɧɨɜɚɧɢɟ ɤ ɛɭɮɟɪɧɨɦɭ ɪɚɫɬɜɨɪɭ ɢ ɧɚɞɟɹɬɶɫɹ ɧɚ ɧɟɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɪɇ ɦɨɠɧɨ ɥɢɲɶ ɜ ɨɩɪɟɞɟɥɟɧɧɵɯ ɩɪɟɞɟɥɚɯ. Ʉɚɠɞɵɣ ɛɭɮɟɪɧɵɣ ɪɚɫɬɜɨɪ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɫɨɩɪɨɬɢɜɥɹɟɦɨɫɬɶɸ ɤ ɢɡɦɟɧɟɧɢɹɦ. Ʉɨɥɢɱɟɫɬɜɟɧɧɨ ɟɟ ɜɵɪɚɠɚɸɬ ɛɭɮɟɪɧɨɣ ɟɦɤɨɫɬɶɸ ʌ. Ɉɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɢɫɥɨɦ ɦɨɥɟɣ ɷɤɜɢɜɚɥɟɧɬɨɜ ɫɢɥɶɧɨɣ ɤɢɫɥɨɬɵ ɢɥɢ ɨɫɧɨɜɚɧɢɹ, ɤɨɬɨɪɵɟ ɧɭɠɧɨ ɞɨɛɚɜɢɬɶ ɤ 1 ɥɪɚɫɬɜɨɪɚ, ɱɬɨɛɵ ɢɡɦɟɧɢɬɶ ɪɇɪɚɫɬɜɨɪɚɧɚ ɟɞɢɧɢɰɭ:

S dcɤɢɫɥ. ɢ S dcɨɫɧ. ,

dpH dpH

ɝɞɟ dc – ɩɪɢɪɨɫɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɫɢɥɶɧɨɣ ɤɢɫɥɨɬɵ (dcɤɢɫɥ) ɢɥɢ ɨɫɧɨɜɚɧɢɹ (dcɨɫɧ), ɜɵɡɜɚɜɲɢɣ ɢɡɦɟɧɟɧɢɟ dɪɇ (ɡɧɚɤ ɦɢɧɭɫ ɭɤɚɡɵɜɚɟɬ ɧɚ ɭɦɟɧɶɲɟɧɢɟ ɪɇ ɩɪɢ ɞɨɛɚɜɥɟɧɢɢ ɫɢɥɶɧɨɣ ɤɢɫɥɨɬɵ ɇȺ). Ȼɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɩɪɢɪɨɫɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɫɢɥɶɧɨɣ ɤɢɫɥɨɬɵ (dcɤɢɫɥ) ɩɪɢɜɨɞɢɬ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɬɚɤɨɝɨ ɠɟ ɤɨɥɢɱɟɫɬɜɚ ɫɥɚɛɨɣ ɤɢɫɥɨɬɵ d[ɇȺ], ɚ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɩɪɢɪɨɫɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɫɢɥɶɧɨɝɨ ɨɫɧɨɜɚɧɢɹ (dcɨɫɧ) ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɬɚɤɨɝɨ ɠɟ ɤɨɥɢɱɟɫɬɜɚ ɫɥɚɛɨɝɨ ɨɫɧɨɜɚɧɢɹ d[A–], ɬɨɥɶɤɨ ɜ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɪɇ ɧɟɦɧɨɝɨ ɭɦɟɧɶɲɚɟɬɫɹ, ɚ ɜɨ ɜɬɨɪɨɦ ɭɜɟɥɢɱɢɜɚɟɬɫɹ. ɋɭɦɦɚɪɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɤɨɦɩɨɧɟɧɬɨɜ ɫɦɟɫɢ ɫɛɭɮ ɧɟ ɦɟɧɹɟɬɫɹ.

Ȼɭɮɟɪɧɭɸ ɟɦɤɨɫɬɶ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɮɨɪɦɭɥɚɦ:

ʌ 2,3 [H ]		K1i	Cɛɭɮ			, ɢɥɢ
	(K1 [H ])2
		i
ʌ 2,3		cHA cA			,
		cHA	c
			A

ɝɞɟ: ɋɇȺ ɢ ɋȺ- — ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɨɦɩɨɧɟɧɬɨɜ ɫɨɩɪɹɠɟɧɧɨɣ ɤɢɫɥɨɬɧɨɨɫɧɨɜɧɨɣ ɩɚɪɵ;

ɋɛɭɮ. = ɋɫɨɥɢ + ɋɤ-ɬɵ( ɨɫɧ.).

Ʉi1 = Ka (ɞɥɹ ɫɥɚɛɵɯ ɤɢɫɥɨɬ),

	K	1	K a	(ɞɥɹ ɫɥɚɛɵɯ ɨɫɧɨɜɚɧɢɣ).
		i	K b

Ɂɧɚɹ ɛɭɮɟɪɧɭɸ ɟɦɤɨɫɬɶ, ɦɨɠɧɨ ɧɚɣɬɢ ɢɡɦɟɧɟɧɢɟ ɪɇ ɪɚɫɬɜɨɪɚ ɩɪɢ ɞɨɛɚɜɥɟɧɢɢ ɫɢɥɶɧɨɣ ɤɢɫɥɨɬɵ ɢɥɢ ɨɫɧɨɜɚɧɢɹ, ɨɩɪɟɞɟɥɢɬɶ ɫɨɫɬɚɜ ɛɭɮɟɪɧɨɣ ɫɦɟɫɢ ɢ ɪɟɲɚɬɶ ɞɪɭɝɢɟ ɜɨɩɪɨɫɵ.

64

Ɂɚɞɚɱɚ. Ɋɚɫɫɱɢɬɚɬɶ ɛɭɮɟɪɧɭɸ ɟɦɤɨɫɬɶ ɚɦɦɨɧɢɣɧɨɣ ɛɭɮɟɪɧɨɣ ɫɦɟɫɢ, ɫɨɞɟɪɠɚɳɟɣ 0,10Ɇ NH3 ɢ 0,20Ɇ NH4Cl (ɪɇ = 8,96). Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɪɇ ɩɪɢ ɞɨɛɚɜɥɟɧɢɢ ɤ 1 ɥ ɛɭɮɟɪɧɨɣ ɫɦɟɫɢ 1·10-2 ɦɨɥɶ HCl?

ɉɪɢɦɟɪ ɪɟɲɟɧɢɹ.

ɪɇ = 8,96 ɫɨɨɬɜɟɬɫɬɜɭɟɬ [H+] =1,1·10-9 ɦɨɥɶ·ɥ– 1 Ɋɚɫɫɱɢɬɵɜɚɟɦ ɛɭɮɟɪɧɭɸ ɟɦɤɨɫɬɶ ɪɚɫɬɜɨɪɚ:

	ʌ 2,3 1,1 10 9				5,7 10 10 0,30								0,15ɦɨɥɶ ɥ 1
				(5,7 10 10				1,1 10 9 )2
		2,3			0,10 0,20					0,15 ɦɨɥɶ ɥ 1 .
	ɢɥɢ ʌ				0,10 0,20
	ɉɪɢ ɞɨɛɚɜɥɟɧɢɢ ɤ 1 ɥ ɷɬɨɝɨ ɪɚɫɬɜɨɪɚ 1,0·10–2 ɦɨɥɶ HCl:
	ǻpH			ǻc	HCl	1,0 10				2		6,7 10 2 .
				ʌ				0,15

ɪɇ ɪɚɫɬɜɨɪɚ ɩɨɫɥɟ ɜɜɟɞɟɧɢɹ HCl ɫɬɚɥ 8,96 – 6,7·10–2 = 8,89.

Ɉɬɜɟɬ. ʌ = 0,15 ɦɨɥɶ·ɥ– 1; ɪɇ = 8,89.

Ɋɟɲɢɬɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɫɥɟɞɭɸɳɢɟ ɡɚɞɚɱɢ.

Ɂɚɞɚɱɚ 1. ȼɵɱɢɫɥɢɬɶ ɪɇ ɚɰɟɬɚɬɧɨɣ ɛɭɮɟɪɧɨɣ ɫɦɟɫɢ, ɫɨɞɟɪɠɚɳɟɣ ɜ 1 ɥ ɪɚɫɬɜɨɪɚ 0,2Ɇ CH3COOONa, 0,2Ɇ CH3COOH. Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɪɇ ɷɬɨɝɨ ɪɚɫɬɜɨɪɚ ɩɪɢ ɞɨɛɚɜɥɟɧɢɢ 0,01Ɇ Hɋl?

Ɂɚɞɚɱɚ 2 . Ȼɟɧɡɨɚɬɧɚɹ ɛɭɮɟɪɧɚɹ ɫɦɟɫɶ ɫɨɞɟɪɠɢɬ 0,35 ɦɨɥɶ C6H5COOH ɢ 0,35 ɦɨɥɶ C6H5COONa ɜ 1 ɥ ɪɚɫɬɜɨɪɚ. ȼɵɱɢɫɥɢɬɶ ɪɇ ɛɭɮɟɪɧɨɝɨ ɪɚɫɬɜɨɪɚ.

Ɂɚɞɚɱɚ 3 . Ʉ 25 ɦɥ 0,1Ɇ ɪɚɫɬɜɨɪɚ CH3COOH ɩɪɢɛɚɜɢɥɢ 25 ɦɥ 0,1Ɇ ɪɚɫɬɜɨɪɚ CH3COONa. ȼɵɱɢɫɥɢɬɶ ɪɇ ɩɨɥɭɱɟɧɧɨɝɨ ɪɚɫɬɜɨɪɚ. Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɪɇ ɷɬɨɝɨ ɪɚɫɬɜɨɪɚ ɩɪɢ ɞɨɛɚɜɥɟɧɢɢ 0,01Ɇ NaOH?

Ɂɚɞɚɱɚ 4. ȼɵɱɢɫɥɢɬɶ ɪɇ ɚɦɦɢɚɱɧɨɣ ɛɭɮɟɪɧɨɣ ɫɦɟɫɢ, ɫɨɞɟɪɠɚɳɟɣ ɩɨ 0,5 ɦɨɥɶ NH3 ɇ2Ɉ ɢ NH4Cl ɜ 1 ɥ ɪɚɫɬɜɨɪɚ. Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɪɇ ɷɬɨɝɨ ɪɚɫɬɜɨɪɚ ɩɪɢ ɞɨɛɚɜɥɟɧɢɢ 0,2Ɇ NaOH?

Ɂɚɞɚɱɚ 5. ȼɵɱɢɫɥɢɬɶ ɪɇ ɪɚɫɬɜɨɪɚ, ɫɨɞɟɪɠɚɳɟɝɨ 0,5 ɦɨɥɶ ɦɭɪɚɜɶɢɧɨɣ ɤɢɫɥɨɬɵ ɢ 0,5 ɦɨɥɶ ɧɚɬɪɢɹ ɮɨɪɦɢɚɬɚ ɜ 1 ɥ.

Ɂɚɞɚɱɚ 6. Ʉɚɤɢɦ ɞɨɥɠɧɨ ɛɵɬɶ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɤɨɦɩɨɧɟɧɬɚɦɢ ɜ ɚɰɟɬɚɬɧɨɦ ɛɭɮɟɪɧɨɦ ɪɚɫɬɜɨɪɟ, ɪɇ ɤɨɬɨɪɨɝɨ ɪɚɜɧɨ 5,0?

Ɋɚɜɧɨɜɟɫɢɹ ɜ ɪɚɫɬɜɨɪɚɯ ɤɨɦɩɥɟɤɫɧɵɯ ɫɨɟɞɢɧɟɧɢɣ

Ʉɨɦɩɥɟɤɫɵ – ɯɢɦɢɱɟɫɤɢɟ ɫɨɟɞɢɧɟɧɢɹ ɫɨɫɬɨɹɳɢɟ ɢɡ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ (ɤɨɦɩɥɟɤɫɨɨɛɪɚɡɨɜɚɬɟɥɶ), ɤɨɬɨɪɚɹ ɫɜɹɡɚɧɚ ɫ ɨɞɧɢɦ ɢɥɢ ɧɟɫɤɨɥɶɤɢɦɢ ɢɨɧɚɦɢ (ɦɨɥɟɤɭɥɚɦɢ), ɧɚɡɵɜɚɟɦɵɦɢ ɥɢɝɚɧɞɚɦɢ.

65

ɉɪɢ ɨɩɢɫɚɧɢɢ ɪɚɜɧɨɜɟɫɢɣ ɤɨɦɩɥɟɤɫɨɨɛɪɚɡɨɜɚɧɢɹ ɫɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɢɨɧɵ ɜ ɪɚɫɬɜɨɪɟ ɜɫɟɝɞɚ ɫɨɥɶɜɚɬɢɪɨɜɚɧɵ. ɉɨɷɬɨɦɭ ɨɛɪɚɡɨɜɚɧɢɟ ɤɨɦɩɥɟɤɫɨɜ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɡɚɦɟɳɟɧɢɟ ɦɨɥɟɤɭɥ ɪɚɫɬɜɨɪɢɬɟɥɹ (S) ɧɚ ɦɨɥɟɤɭɥɵ ɢɥɢ ɢɨɧɵ ɥɢɝɚɧɞɚ (L):

MSn+ L = MSn-1L+S MSn-1L + L = MSn-2L2 + S MSLn-1 + L = MLn + S

ɇɟɨɛɯɨɞɢɦɵɦ ɭɫɥɨɜɢɟɦ ɜɨɡɦɨɠɧɨɫɬɢ ɬɚɤɢɯ ɩɪɨɰɟɫɫɨɜ ɹɜɥɹɟɬɫɹ ɛɨɥɟɟ ɜɵɫɨɤɚɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɪɚɫɬɜɨɪɢɬɟɥɟɦ ɞɨɧɨɪɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɥɢɝɚɧɞɚ ɢ ɫɬɟɪɢɱɟɫɤɚɹ ɞɨɫɬɭɩɧɨɫɬɶ.

ɉɨɫɤɨɥɶɤɭ ɜ ɪɚɡɛɚɜɥɟɧɧɵɯ ɪɚɫɬɜɨɪɚɯ ɚɤɬɢɜɧɨɫɬɶ ɪɚɫɬɜɨɪɢɬɟɥɹ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɫɬɨɹɧɧɚ, ɚ ɬɨɱɧɨɟ ɱɢɫɥɨ ɦɨɥɟɤɭɥ ɪɚɫɬɜɨɪɢɬɟɥɹ, ɫɨɥɶɜɚɬɢɪɭɸɳɟɝɨ ɢɨɧ, ɧɟ ɜɫɟɝɞɚ ɢɡɜɟɫɬɧɨ, ɬɨ ɪɚɜɧɨɜɟɫɢɹ ɤɨɦɥɟɤɫɨɨɛɪɚɡɨɜɚɧɢɹ ɨɛɵɱɧɨ ɩɪɟɞɫɬɚɜɥɹɸɬ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ:

ɋɬɭɩɟɧɱɚɬɵɟ	ɋɭɦɦɚɪɧɵɟ
M + L = ML	M + L = ML
ML + L = ML2	M + 2L = ML2
MLn-1 + L = MLn	M+ nL = MLn

ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɤɨɧɨɦ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɫɬɭɩɟɧɱɚɬɨɟ ɨɛɪɚɡɨɜɚɧɢɟ ɤɨɦɩɥɟɤɫɨɜ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɧɚɛɨɪɨɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɬɭɩɟɧɱɚɬɵɯ ɤɨɧɫɬɚɧɬ ɭɫɬɨɣɱɢɜɨɫɬɢ:

K0				ɚ ML
		1		ɚ M	ɚ L
K		0		ɚ ML2
		2		ɚ ML	ɚ L
K	0			ɚ MLn
	n
				ɚ MLn 1	ɚ L

Ʉɨɧɫɬɚɧɬɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɭɦɦɚɪɧɵɯ ɪɚɜɧɨɜɟɫɢɣ ɧɚɡɵɜɚɸɬ ɨɛɳɢɦɢ (ɫɭɦɦɚɪɧɵɦɢ) ɤɨɧɫɬɚɧɬɚɦɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɢ ɨɛɨɡɧɚɱɚɸɬ ɫɢɦɜɨɥɨɦ ȕ:

			ȕ0		K			0				ɚ ML
			1					1
												ɚ M ɚ L
			0		0				0				ɚ ML2
		ȕ		K			K
			2		1				2			ɚ M ɚ L2
	0			0		0					0		ɚ MLn
ȕ			K		K			...K
	n			1		2					n		ɚ M ɚ Ln

66

Ɂɚɞɚɱɚ. ȼɵɱɢɫɥɢɬɶ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢɨɧɨɜ ɫɟɪɟɛɪɚ (I) ɢ ɦɨɥɟɤɭɥ ɚɦɦɢɚɤɚ ɜ 0,05 Ɇ ɪɚɫɬɜɨɪɟ [Ag(NH3)2]Cl.

ɉɪɢɦɟɪ ɪɟɲɟɧɢɹ. Ⱦɢɫɫɨɰɢɚɰɢɹ ɫɨɥɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɭɪɚɜɧɟɧɢɹɦɢ:

[Ag(NH3)2]Cl	[Ag(NH3)2]+ +Cl–										(1)
[Ag(NH3)2]+		Ag+ + 2NH3									(2)
Ⱦɥɹ ɜɬɨɪɨɝɨ ɨɛɪɚɬɢɦɨɝɨ ɩɪɨɰɟɫɫɚ ɡɚɩɢɲɟɦ ɜɵɪɚɠɟɧɢɟ ɤɨɧɫɬɚɧɬɵ ɪɚɜɧɨ-
ɜɟɫɢɹ (ɤɨɧɫɬɚɧɬɵ ɧɟɫɬɨɣɤɨɫɬɢ):
			[Ag ] [NH	3		]2	.
		Ʉɧɟɫɬ	[[Ag(NH 3 )2
					] ]
lg ȕ = 7,23, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ȕ = 107,23 = 1,7·107, K						1			5,9	10	8 .
						ɧɟɫɬ E
Ɉɛɨɡɧɚɱɢɦ [Ag+] = ɯ ɦɨɥɶ·ɥ– 1, ɬɨɝɞɚ ɢɡ						ɭɪɚɜɧɟɧɢɹ				(2)	[NH 3 ] = 2ɯ

ɦɨɥɶ·ɥ– 1, ɚ [[Ag(NH3)2]+] = C – ɯ ɦɨɥɶ·ɥ– 1. ɉɨɞɫɬɚɜɢɦ ɷɬɢ ɨɛɨɡɧɚɱɟɧɢɹ ɜ ɜɵɪɚɠɟɧɢɟ:

				x (2x)2		|	4x3	.
	Ʉɧɟɫɬ			C - x
							C
	C
x 3 Ʉɧɟɫɬ		3	5,9 10 8			0,05			0,9 10 3 ;
4		4
[Ag+] = x = 0,9·10 – 3						ɦɨɥɶ·ɥ– 1;
[NH3 ] = 2x = 1,8·10– 3 ɦɨɥɶ·ɥ– 1.
Ɉɬɜɟɬ. [Ag+] =0,9·10– 3	ɦɨɥɶ·ɥ– 1

[NH3 ] = 1,8·10– 3 ɦɨɥɶ·ɥ– 1

Ɋɟɲɢɬɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɫɥɟɞɭɸɳɢɟ ɡɚɞɚɱɢ.

Ɂɚɞɚɱɚ 1 . ȼɵɱɢɫɥɢɬɟ [Cu2+] ɢ [NH3] ɜ 0,1Ɇ ɪɚɫɬɜɨɪɟ [Cu(NH3)4] SO4. Ɂɚɞɚɱɚ 2 . ȼɵɱɢɫɥɢɬɟ [Co2+] ɢ [NH3] ɜ 0,1Ɇ ɪɚɫɬɜɨɪɟ [Co(NH3)6] SO4. Ɂɚɞɚɱɚ 3 . ȼɵɱɢɫɥɢɬɟ [Hg2+], [I-], [K+] ɜ 0,2Ɇ ɪɚɫɬɜɨɪɟ K2[HgI4].

Ɂɚɞɚɱɚ 4 . ȼɵɱɢɫɥɢɬɟ [Fe3+], [CN-], [K+] ɜ 0,05Ɇ ɪɚɫɬɜɨɪɟ K3[Fe(CN)6].

Ɂɚɞɚɱɚ 5 . ȼɵɱɢɫɥɢɬɟ [Bi3+], [I-], [K+] ɜ 0,25Ɇ ɪɚɫɬɜɨɪɟ K[BiI4].

Ɉɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɟ ɩɪɨɰɟɫɫɵ

Ɉɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɟ ɪɟɚɤɰɢɢ – ɪɟɚɤɰɢɢ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɫ ɭɱɚɫɬɢɟɦ ɷɥɟɤɬɪɨɧɨɜ ɢ ɩɪɢɜɨɞɹɳɢɟ ɤ ɢɡɦɟɧɟɧɢɸ ɫɬɟɩɟɧɢ ɨɤɢɫɥɟɧɢɹ ɷɥɟɦɟɧɬɨɜ ɪɟɚɝɢɪɭɸɳɢɯ ɫɢɫɬɟɦ.

Ox1 + nƝ Red1

Red2 - nƝ Ox2

Ox1 + Red2 = Red1 + Ox2

67

ɋɩɨɫɨɛɧɨɫɬɶ ɨɬɞɚɜɚɬɶ ɢ ɩɪɢɧɢɦɚɬɶ ɷɥɟɤɬɪɨɧɵ ɭ ɪɚɡɧɵɯ ɜɟɳɟɫɬɜ ɪɚɡɥɢɱɧɚ. Ⱦɥɹ ɨɰɟɧɤɢ ɷɬɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɪɟɚɤɰɢɢ, ɜɵɪɚɠɟɧɧɚɹ ɱɟɪɟɡ ɚɤɬɢɜɧɨɫɬɢ:

		ɚ		ɚ
K			Ɉɯ2	Re d1	.
	Ɋ ɚ			ɚ
			Ɉɯ1	Re d 2

Ⱦɥɹ ɨɰɟɧɤɢ ɨɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɛɨɥɟɟ ɭɞɨɛɧɨɣ ɨɤɚɡɚɥɚɫɶ ɞɪɭɝɚɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ – ɩɨɬɟɧɰɢɚɥ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɭɧɢɤɚɥɶɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɞɚɧɧɨɝɨ ɬɢɩɚ ɪɟɚɤɰɢɣ: ɩɨɥɭɪɟɚɤɰɢɢ ɨɤɢɫɥɟɧɢɹ ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɩɨɫɤɨɥɶɤɭ ɩɪɢ ɩɟɪɟɧɨɫɟ ɷɥɟɤɬɪɨɧɨɜ ɜɨɡɧɢɤɚɟɬ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɧɟɪɝɢɸ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɦɨɠɧɨ ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ. ɉɪɚɤɬɢɱɟɫɤɢ ɬɚɤɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɝɚɥɶɜɚɧɢɱɟɫɤɨɦ ɷɥɟɦɟɧɬɟ. ɉɨɷɬɨɦɭ ɦɨɠɧɨ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɨɩɢɫɵɜɚɬɶ ɨɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɟ ɪɟɚɤɰɢɢ ɧɟ ɤɨɧɫɬɚɧɬɨɣ ɪɚɜɧɨɜɟɫɢɹ, ɚ ɷɥɟɤɬɪɨɞɜɢɠɭɳɟɣ ɫɢɥɨɣ ɝɚɥɶɜɚɧɢɱɟɫɤɨɝɨ ɷɥɟɦɟɧɬɚ – ɩɨɬɟɧɰɢɚɥɨɦ.

Ɂɚɜɢɫɢɦɨɫɬɶ ɨɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɭɪɚɜɧɟɧɢɸ ɇɟɪɧɫɬɚ:

	0		RT		aA
E = E		+		ln	ox	,
			nF		aB
					red

ɝɞɟ: E – ɪɟɚɥɶɧɵɣ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥ ɫɢɫɬɟɦɵ, ȼ;

E0 ɫɬɚɧɞɚɪɬɧɵɣ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥ ɫɢɫɬɟɦɵ*, ȼ; T – ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ, Ʉ;

n – ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɬɨɪɵɟ ɭɱɚɫɬɜɭɸɬ ɜ ɨɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨ- ɜɢɬɟɥɶɧɨɦ ɩɪɨɰɟɫɫɟ;

R – ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ, ɪɚɜɧɚɹ 8,312 Ⱦɠ/(ɦɨɥɶ Ʉ); F – ɩɨɫɬɨɹɧɧɚɹ Ɏɚɪɚɞɟɹ, ɪɚɜɧɚɹ 96 500 Ʉɥ;

aoxA , aBred – ɚɤɬɢɜɧɨɫɬɢ ɨɤɢɫɥɟɧɧɨɣ ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɧɨɣ ɮɨɪɦ ɪɟɞɨɤɫ-ɩɚɪɵ ɜ ɫɬɟɩɟɧɹɯ ɢɯ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɦɨɥɶ ɥ-1.

ɑɚɫɬɨ ɩɨɫɬɨɹɧɧɵɟ ɜɟɥɢɱɢɧɵ ɨɛɴɟɞɢɧɹɸɬ ɜ ɨɞɧɭ ɤɨɧɫɬɚɧɬɭ, ɚ ɧɚɬɭɪɚɥɶɧɵɣ ɥɨɝɚɪɢɮɦ ɡɚɦɟɧɹɸɬ ɞɟɫɹɬɢɱɧɵɦ. Ɍɨɝɞɚ ɩɪɢ 25qɋ:

	0		0,059		aA
E = E		+		lg	ox	.
			n		aB
					red

ȿɫɥɢ ɪɟɚɤɰɢɹ ɨɤɢɫɥɟɧɢɹ-ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɪɨɯɨɞɢɬ ɫ ɭɱɚɫɬɢɟɦ ɩɪɨɬɨɧɨɜ ɜɨɞɨɪɨɞɚ, ɬɨ ɫɤɨɪɨɫɬɶ ɟɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɫɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ.

* ɋɬɚɧɞɚɪɬɧɵɣ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥ ɫɢɫɬɟɦɵ – ɩɨɬɟɧɰɢɚɥ ɫɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɨɣ ɜɫɟ ɭɱɚɫɬɧɢɤɢ ɩɨɥɭɪɟɚɤɰɢɢ ɧɚɯɨɞɹɬɫɹ ɜ ɫɬɚɧɞɚɪɬɧɨɦ ɫɨɫɬɨɹɧɢɢ (ɩɪɢ ɚɤɬɢɜɧɨɫɬɢ, ɪɚɜɧɨɣ ɟɞɢɧɢɰɟ), ɚ ɪɚɫɬɜɨɪɟɧɧɵɟ ɜɟɳɟɫɬɜɚ – ɜ ɫɬɚɧɞɚɪɬɧɨɦ ɪɚɫɬɜɨɪɟ.

68

ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɢ ɪɟɚɥɶɧɵɣ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥ ɫɢɫɬɟɦɵ. ɇɚ-

ɩɪɢɦɟɪ, ɞɥɹ ɫɢɫɬɟɦɵ ɩɨɥɭɪɟɚɤɰɢɢ:

+ 3e + MnO4– + 4H+

MnɈ2p + 2H2O

(1)

E = E0 +

0,059

lg[MnO4 - ] [H+ ]4

(ɩɪɢ 25qɋ),

3

ɚ ɞɥɹ ɫɢɫɬɟɦɵ ɩɨɥɭɪɟɚɤɰɢɢ:

+ 5e + MnO4– + 8H+

Mn2+ + 4H2O

(2)

E = E0 +

0,059

lg

[MnO

-] [H+

]

8

4

ɩɪɢ

25q

ɋ

5

[Mn

2+

]

(

)

ȼɟɥɢɱɢɧɚ ȿ0 ɡɧɚɱɢɬɟɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɢɫɥɨɬɵ, ɢ ɜ ɩɪɢɫɭɬɫɬɜɢɢ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɣ H2SO4 ɟɟ ɡɧɚɱɟɧɢɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɨɬ + 1,51 ȼ ɞɨ + 1,9 ȼ (ɞɥɹ ɪɟɚɤɰɢɢ 2).

ɂɡɦɟɧɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɇ+ ɢɥɢ Ɉɇ– -ɢɨɧɨɜ ɜɥɢɹɟɬ ɧɟ ɬɨɥɶɤɨ ɧɚ ɢɡɦɟɧɟɧɢɟ ɜɟɥɢɱɢɧɵ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥɚ, ɧɨ ɢɧɨɝɞɚ ɢ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ ɯɨɞɚ ɪɟɚɤɰɢɢ. Ɍɚɤ, ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɚɪɫɟɧɢɬ-ɢɨɧɨɜ ɫ ɣɨɞɨɦ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɜ ɫɪɟɞɟ ɧɚɬɪɢɹ

ɝɢɞɪɨɤɚɪɛɨɧɚɬɚ (ɪɇ = 9) ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɹ:
- 2e	+ AsO2– + 4OH–							AsO43– + 2H2O	1	E0	= - 0,71 B
+ 2e	+ [I3]–				3I–				1	E0	= 0,545 B
AsO2– + [I3]–				+ 4OH – o AsO43– + 3I– + 2H2O
ȼ ɤɢɫɥɨɣ ɫɪɟɞɟ ɬɚɤɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɧɟɜɨɡɦɨɠɧɨ, ɬɚɤ ɤɚɤ
E0H3AsO4/HAsO2				= 0,56 B, ɱɬɨ ɛɨɥɶɲɟ E0[I3] – /3 I –						= 0,545 B ɢ ɩɨɬɨɦɭ ɢɡɦɟɧɹɟɬɫɹ
ɧɚɩɪɚɜɥɟɧɢɟ ɩɪɨɬɟɤɚɧɢɹ ɪɟɚɤɰɢɢ:
+ 2e	+ H3AsO4 + 2H+							HAsO2 + 2H2O	1	E0	= 0,56 B
- 2e	+ 3I–			[I3]–					1	E0	= 0,545 B

H3AsO4 + 3I– + 2H+ o HAsO2 + [I3]– + 2H2O

ɇɚ ɜɟɥɢɱɢɧɭ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥɚ ɨɤɚɡɵɜɚɸɬ ɜɥɢɹɧɢɟ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ, ɪɟɚɤɰɢɢ ɤɨɦɩɥɟɤɫɨɨɛɪɚɡɨɜɚɧɢɹ ɢ ɨɛɪɚɡɨɜɚɧɢɹ ɦɚɥɨɪɚɫɬɜɨɪɢɦɵɯ ɫɨɟɞɢɧɟɧɢɣ, ɬ.ɤ. ɷɬɢ ɩɪɨɰɟɫɫɵ ɜɥɢɹɸɬ ɧɚ ɮɨɪɦɭ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɢɨɧɨɜ ɢ ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɧɚ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɸ.

Ɂɧɚɱɢɬɟɥɶɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɫɤɨɪɨɫɬɶ ɨɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɯ ɪɟɚɤɰɢɣ, ɤɪɨɦɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɪɟɚɝɟɧɬɨɜ ɢ ɬɟɦɩɟɪɚɬɭɪɵ, ɨɤɚɡɵɜɚɟɬ ɜɜɟɞɟɧɢɟ ɤɚɬɚɥɢɡɚɬɨɪɨɜ ɢ ɢɧɝɢɛɢɬɨɪɨɜ. Ʉɚɬɚɥɢɡɚɬɨɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɩɨɫɬɨɪɨɧɧɟɟ ɜɟɳɟɫɬɜɨ, ɚ ɬɚɤɠɟ ɨɞɢɧ ɢɡ ɩɪɨɞɭɤɬɨɜ ɪɟɚɤɰɢɢ (ɚɜɬɨɤɚɬɚɥɢɡ). ɇɚɩɪɢɦɟɪ, ɤɚɬɚɥɢɡɚɬɨɪɨɦ ɪɟɚɤɰɢɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɳɚɜɟɥɟɜɨɣ ɤɢɫɥɨɬɨɣ ɩɟɪɦɚɧɝɚɧɚɬ-ɢɨɧɨɜ ɞɨ Mn2+ ɹɜɥɹɸɬɫɹ ɤɚɬɢɨɧɵ ɦɚɪɝɚɧɰɚ (II), ɬɨ ɟɫɬɶ ɩɪɨɞɭɤɬ ɪɟɚɤɰɢɢ.

ɉɨɥɧɨɬɚ ɩɪɨɬɟɤɚɧɢɹ ɨɤɢɫɥɢɬɟɥɶɧɨ-ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɯ ɪɟɚɤɰɢɣ ɡɚɜɢɫɢɬ ɨɬ ɫɥɟɞɭɸɳɢɯ ɮɚɤɬɨɪɨɜ:

x ȿȾɋ ɪɟɚɤɰɢɣ – ɪɚɡɧɨɫɬɢ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɫɢɫɬɟɦ; ɨɛɵɱɧɨ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɩɪɨɬɟɤɚɸɬ ɪɟɚɤɰɢɢ, ɗȾɋ ɤɨɬɨɪɵɯ ɛɨɥɶɲɟ 0,4 ȼ.

69

x ɜɟɥɢɱɢɧɵ ɤɨɧɫɬɚɧɬɵ ɪɚɜɧɨɜɟɫɢɹ ɪɟɞɨɤɫ-ɪɟɚɤɰɢɢ, ɤɨɬɨɪɭɸ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɭɪɚɜɧɟɧɢɸ:

Ʉɪ = 10ɚ, ɝɞɟ a =	n(E10 - E02 )	(ɩɪɢ 25qɋ), ɢɥɢ lgKp	=	n(E10 - E02 )	,
0,059			0,059

ɝɞɟ: n – ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɬɨɪɵɟ ɩɪɢɧɢɦɚɸɬ ɭɱɚɫɬɢɟ ɜ ɩɪɨɰɟɫɫɟ;

E10 , E02 – ɫɬɚɧɞɚɪɬɧɵɟ ɪɟɞɨɤɫ-ɩɨɬɟɧɰɢɚɥɵ ɫɢɫɬɟɦɵ ɨɤɢɫɥɢɬɟɥɹ ɢ ɜɨɫɫɬɚɧɨɜɢɬɟɥɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ȼ.

70