• CHB

7.2. Solubility of CuI in a dynamic redox system

120 Descriptive Inorganic Chemistry Researches of Metal Compounds

�<sup>2</sup> = 3I�<sup>1</sup> + S4O6

S4O6 �2 , I3

H2SO3 + S [80].

between S2O3

<sup>ð</sup>ZCu–2Þð½Cuþ<sup>2</sup>

þðZCu � <sup>1</sup>Þð½Cuþ<sup>1</sup>

<sup>þ</sup> <sup>4</sup> � ðZS–2:5Þ½S4O�<sup>2</sup>

6 � ðZS–2ÞÞ½CuðS2O3Þ

þ2

�1

þðZI � <sup>7</sup>Þð½H5IO6�þ½H4IO�<sup>1</sup>

ðV0þVNþVAcþVKIþVÞ ¼ 0

þ½CuðNH3Þ

þðZI þ 1Þ½I

follows:

ered separately.

�<sup>1</sup> + 2S2O3

7.3. Formulation of the system

S (ZS = 16). Note that sulfur in the core SO4

�2

þ2

�1

�<sup>2</sup> and S4O6

• Generalized electron balance (GEB)

�þ½CuNHþ<sup>1</sup>

�þ½CuOH<sup>þ</sup><sup>1</sup>

<sup>3</sup> �þ½CuðNH3Þ

�þð3ZI þ 1Þ½I

�5

The system considered in this section is related to iodometric, indirect analysis of an acidified (H2SO4) solution of CuSO4 [14, 64]. It is a very interesting system, both from analytical and

0.153 V for (Cu+2, Cu+1), one could expect (at a first sight) the oxidation of Cu+1 by I2. However, such a reaction does not occur, due to the formation of sparingly soluble CuI precipitate (pKsp = 11.96). This method consists of four steps. In the preparatory step (step 1), an excess of H2SO4 is neutralized with NH3 (step 1) until a blue color appears, which is derived from Cu(NH3)<sup>i</sup>

complexes. Then the excess of CH3COOH is added (step 2), to attain a pH ca. 3.6. After subsequent introduction of an excess of KI solution (step 3), the mixture with CuI precipitate and dissolved iodine formed in the reactions: 2Cu+2 + 4I�<sup>1</sup> = 2CuI + I2, 2Cu+2 + 5I�<sup>1</sup> = 2CuI + I3

mildly acidic solutions (acetate buffer), where the thiosulfate species are in a metastable state. In strongly acidic media, thiosulfuric acid disproportionates according to the scheme H2S2O3 =

We assume that V mL of C mol/L Na2S2O3 solution is added into the mixture obtained after successive addition of: V<sup>N</sup> mL of NH3 (C1) (step 1), VAc mL of CH3COOH (C2) (step 2), VKI mL of KI (C3) (step 3), and V mL of Na2S2O3 (C) (step 4) into V<sup>0</sup> mL of titrand D composed of CuSO4 (C0)+H2SO4 (C01). To follow the changes occurring in particular steps of this analysis, we assume that the corresponding reagents in particular steps are added according to the

In this system, three electron-active elements are involved: Cu (atomic number ZCu = 29), I (ZI = 53),

The balances written according to Approach I to GEB, in terms of molar concentrations, are as

�1

<sup>3</sup> � þ 2ZIð½I2� þ <sup>a</sup> � ½I2ð<sup>s</sup>Þ�Þ þ ðZI � <sup>1</sup>Þð½HIO�þ½IO�<sup>1</sup>

<sup>3</sup> � � ððZCu � 2ÞC0V0 þ ðZI þ 1ÞC3VKI þ 2 � ðZS � 2ÞCVÞ=

<sup>3</sup> �þ½CuðOHÞ

<sup>6</sup> �Þ þ <sup>2</sup> � ðZS � <sup>2</sup>Þð½H2S2O3�þ½HS2O�<sup>1</sup>

�<sup>2</sup> is completed; the reactions proceed quantitatively in

�<sup>2</sup> is not involved here in electron-transfer equilibria

<sup>4</sup> �þ½CuNHþ<sup>2</sup>

<sup>3</sup> �Þ þ ½S2O�<sup>2</sup>

�þ½CuðCH3COOÞ2�Þ þ ðZCu � <sup>2</sup> <sup>þ</sup> ZI � <sup>5</sup>Þ½CuIO<sup>þ</sup><sup>1</sup>

<sup>3</sup> �þ½CuðNH3Þ

<sup>3</sup> �Þ

�3

<sup>2</sup> �

<sup>2</sup> �þðZCu–1þ

�Þ þ ðZI � <sup>5</sup>Þð½HIO3�þ½IO�<sup>1</sup>

þ2 <sup>2</sup> �

<sup>3</sup> �

<sup>3</sup> �Þ

ð78Þ

; then the concentration balance for sulfate species can be consid-

�2

<sup>2</sup> �Þ þ ðZCu <sup>þ</sup> ZIÞ½CuIð<sup>s</sup>Þ�þðZCu <sup>þ</sup> 2ZI <sup>þ</sup> <sup>1</sup>Þ½CuI�<sup>1</sup>

<sup>3</sup> �þðZCu–1 þ 4 � ðZS–2ÞÞ½CuðS2O3Þ

) exceeds E<sup>0</sup> =

+2

�1

�<sup>2</sup> = 2I�<sup>1</sup> +

physicochemical viewpoints. Because the standard potential E<sup>0</sup> = 0.621 V for (I2, I�<sup>1</sup>

is titrated with Na2S2O3 solution (step 4), until the reduction of iodine: I2 + 2S2O3

titrimetric mode, and the assumption of the volumes additivity is valid.

�þ½CuðOHÞ2�þ½CuðOHÞ

þ1

<sup>4</sup> �þ½CuCH3COO<sup>þ</sup><sup>1</sup>

<sup>3</sup> �þ½CuðNH3Þ

<sup>6</sup> �þ½H3IO�<sup>2</sup>

<sup>6</sup> �þðZCu–<sup>1</sup> <sup>þ</sup> <sup>2</sup> � ðZS–2ÞÞ½CuS2O�<sup>1</sup>

<sup>½</sup>Hþ<sup>1</sup> �–½OH�<sup>1</sup> �þ½Kþ<sup>1</sup> �þ½Na<sup>þ</sup><sup>1</sup> ��½HSO4 �<sup>1</sup>� � <sup>2</sup>½SO4 �<sup>2</sup>�þ½NH4 <sup>þ</sup><sup>1</sup>��½CH3COO�<sup>1</sup> � þ <sup>2</sup>½Cuþ<sup>2</sup> � þ½CuOH<sup>þ</sup><sup>1</sup> ��½CuðOHÞ<sup>3</sup> �<sup>1</sup>�–2½CuðOHÞ<sup>4</sup> �<sup>2</sup>� þ <sup>2</sup>½CuðNH3<sup>Þ</sup> þ2 � þ 2½CuðNH3Þ<sup>3</sup> <sup>þ</sup><sup>2</sup>� þ <sup>2</sup>½CuðNH3Þ<sup>3</sup> þ2� þ2CuðNH3Þ<sup>4</sup> <sup>þ</sup><sup>2</sup>�þ½CuCH3COO<sup>þ</sup><sup>1</sup> ��½I �1 ��½I3 �<sup>1</sup>�–½IO�<sup>1</sup> ��½IO3 �<sup>1</sup>��½H4IO6 �<sup>1</sup>� � <sup>2</sup>½H3IO6 �2� þ½Cuþ<sup>1</sup> �þ½CuNH3 <sup>þ</sup><sup>1</sup>�þ½CuðNH3Þ<sup>2</sup> <sup>þ</sup><sup>1</sup>��½CuI2 �<sup>1</sup>�þ½CuIO3 <sup>þ</sup><sup>1</sup>��½HS2O3 �<sup>1</sup>� � <sup>2</sup>½S2O3 �2� �2½S4O6 �<sup>2</sup>��½CuS2O3 �<sup>1</sup>� � <sup>3</sup>½CuðS2O3Þ<sup>2</sup> �<sup>3</sup>� � <sup>5</sup>½CuðS2O3Þ<sup>3</sup> �<sup>5</sup>� ¼ <sup>0</sup> ð79Þ

• F(Cu)

$$\begin{aligned} \left[\mathbf{Cu}^{+2}\right] &+ \left[\mathbf{CuOH}^{+1}\right] + \left[\mathbf{Cu(OH)}\_{2}\right] + \left[\mathbf{Cu(OH)}\_{3}\right]^{-1} + \left[\mathbf{Cu(OH)}\_{4}\right]^{-2} + \left[\mathbf{CuSO}\_{4}\right] + \left[\mathbf{CuNH}\_{3}\right]^{+2} \\ &+ \left[\mathbf{Cu(NH\_3)}\_{3}\right]^{2+} + \left[\mathbf{Cu(NH\_3)}\_{3}\right]^{+2} + \left[\mathbf{Cu(NH\_3)}\_{4}\right]^{+2} + \left[\mathbf{Cu(NH\_3)CO}^{+1}\right] + \left[\mathbf{Cu(CH\_3COO)}\_{2}\right] \\ &+ \left[\mathbf{Cu}^{+1}\right] + \left[\mathbf{Cu(NH\_3)}^{+1}\right] + \left[\mathbf{Cu(NH\_3)}\_{2}\right]^{+1} + \left[\mathbf{CuI}\_{2}^{-1}\right] + \left[\mathbf{CuI}\_{(8)}\right] + \left[\mathbf{CuO}\_{3}^{+1}\right] + \left[\mathbf{CuS\_2O\_3}^{-1}\right] \\ &+ \left[\mathbf{Cu(S\_2O\_3)}\_{2}\right]^{-3} + \left[\mathbf{Cu(S\_2O\_3)}\_{3}\right]^{-5} \end{aligned} \tag{80}$$

• F(SO4)

$$\left[\text{HSO}\_4^{-1}\right] + \left[\text{SO}\_4^{-2}\right] + \left[\text{CuSO}\_4\right] \cdot \text{C}\_{01}V\_0/(\text{V}\_0 + \text{V}\_{\text{N}} + \text{V}\_{\text{Ac}} + \text{V}\_{\text{KI}} + \text{V}) = 0\tag{81}$$

• F(NH3)

$$\begin{aligned} \text{[NH}\_4\text{}^+\text{]} + \text{[NH}\_3\text{]} + \text{[CuNH}\_3\text{}^+\text{]} + 2\text{[Cu(NH}\_3\text{)}\_2\text{]}^+ &+ 3\text{[Cu(NH}\_3\text{)}\_3\text{]}^+ + 4\text{[Cu(NH}\_3\text{)}\_4\text{]}^+ \\ &+ \text{[CuNH}\_3\text{]}^+ \text{]} + 2\text{[Cu(NH}\_3\text{)}\_2\text{]}^+ \text{]} \cdot \text{C}\_1\text{V}\_\text{N}/(\text{V}\_0 + \text{V}\_\text{N} + \text{V}\_\text{Ac} + \text{V}\_\text{KI} + \text{V}) = 0 \end{aligned} (82)$$

• F(CH3COO)

$$\begin{aligned} \left[\text{CH}\_3\text{COOH}\right] + \left[\text{CH}\_3\text{COO}^{-1}\right] + \left[\text{CuCH}\_3\text{COO}^{+1}\right] + 2\left[\text{Cu}(\text{CH}\_3\text{COO})\_2\right] \\ -\text{C}\_2\text{V}\_{\text{Ac}}/(\text{V}\_0 + \text{V}\_{\text{N}} + \text{V}\_{\text{Ac}} + \text{V}\_{\text{KI}} + \text{V}) &= 0 \end{aligned} \tag{83}$$

• F(K)

$$\mathbf{[K^{+1}]} = \mathbf{C\_3}V\_{\mathbf{Kl}}/(\mathbf{V\_0} + V\_{\mathbf{N}} + \mathbf{V\_{Ac}} + \mathbf{V\_{Kl}} + \mathbf{V})\tag{84}$$

• F(I)

$$\begin{aligned} \left[\mathbf{I}^{-1}\right] + 3\left[\mathbf{I}\_3^{-1}\right] + 2\left(\left[\mathbf{I}\_2\right] + \left[\mathbf{I}\_{2(s)}\right]\right) + \left[\mathbf{H}\mathbf{IO}\right] + \left[\mathbf{IO}^{-1}\right] + \left[\mathbf{H}\mathbf{IO}\_3\right] + \left[\mathbf{IO}\_3^{-1}\right] + \left[\mathbf{H}\_5\mathbf{IO}\_6\right] + \left[\mathbf{H}\_4\mathbf{IO}\_6^{-1}\right] \\ + \left[\mathbf{H}\_3\mathbf{IO}\_6^{-2}\right] + 2\left[\mathbf{CuI}\_2^{-1}\right] + \left[\mathbf{CuI}\_{(s)}\right] + \left[\mathbf{CuIO}\_3^{+1}\right] - \mathbf{C}\_3\mathbf{V}\_{\text{KI}}/\left(V\_0 + V\_\text{N} + V\_\text{Ac} + V\_\text{KI} + V\right) = 0 \end{aligned} \tag{85}$$

$$\begin{aligned} &2[\text{H}\_{2}\text{S}\_{2}\text{O}\_{3}] + 2[\text{H}\text{S}\_{2}\text{O}\_{3}^{-1}] + 2[\text{S}\_{2}\text{O}\_{3}^{-2}] + 4[\text{S}\_{4}\text{O}\_{6}^{-2}] + 2[\text{CuS}\_{2}\text{O}\_{3}^{-1}] + 4[\text{Cu}(\text{S}\_{2}\text{O}\_{3})\_{2}^{-3}] \\ &+ 6[\text{Cu}(\text{S}\_{2}\text{O}\_{3})\_{3}^{-5}] - 2\text{CV}/(V\_{0} + V\_{\text{N}} + V\_{\text{Ac}} + V\_{\text{KI}} + V) = 0 \Rightarrow [\text{H}\_{2}\text{S}\_{2}\text{O}\_{3}] + [\text{HS}\_{2}\text{O}\_{3}^{-1}] + [\text{S}\_{2}\text{O}\_{3}^{-2}] \\ &+ 2[\text{S}\_{4}\text{O}\_{6}^{-2}] + [\text{CuS}\_{2}\text{O}\_{3}^{-1}] + 2[\text{Cu}(\text{S}\_{2}\text{O}\_{3})\_{2}^{-3}] + 3[\text{Cu}(\text{S}\_{2}\text{O}\_{3})\_{3}^{-5}] \\ &- \text{CV}/(\text{V}\_{0} + \text{V}\_{\text{N}} + \text{V}\_{\text{Ac}} + \text{V}\_{\text{KI}} + \text{V}) = 0 \end{aligned}$$

$$\left[\text{Na}^{+1}\right] = 2\text{CV}/(V\_0 + V\_\text{N} + V\_{\text{Ac}} + V\_{\text{KI}} + V) \tag{87}$$

$$\begin{split} \left[\text{Cu}^{+}\right] &= \left[\text{Cu}^{+}\right] \cdot 10^{\text{A(E=0.53)}} / \left[\text{I}\_{2}\right] = [\text{I}^{-1}]^{2} \cdot 10^{\text{2A(E=0.62)}} / s = 1.33 \cdot 10^{-3} \text{ mol/L} (\text{solubility of } \text{I}\_{2(s)}) \\ \left[\text{I}\_{3}^{-}\right] &= [\text{I}^{-1}]^{3} \cdot 10^{2\text{A(E=0.545)}} / \left[\text{IO}^{-1}\right] = [\text{I}^{-}] \cdot 10^{2\text{A(E=0.49)} + 2\text{pH-28}} \\ &= [\text{I}^{-1}] \cdot 10^{6\text{A(E=1.08)} + 6\text{pH}} \\ \left[\text{HIO}\_{3}\right] &= 10^{0.79} \cdot \left[\text{H}^{+}\right] \left[\text{IO}\_{3}^{-1}\right] \left[\text{H}\_{5}\text{IO}\_{6}\right] = [\text{I}^{-1}] \cdot 10^{8\text{A(E=1.24)} + 7\text{pH}} / \left[\text{H}\_{4}\text{IO}\_{6}^{-1}\right] \\ &= [\text{H}\_{5}\text{IO}\_{6}] \cdot 10^{-3.3 + \text{pH}} / \text{H}\_{5}\text{IO}\_{6}^{-2} = [\text{I}^{-1}] \cdot 10^{8\text{A(E=0.37)} + 9\text{pH} - 126} . \end{split}$$

In the calculations made in this system according to the computer programs attached to Ref. [64], it was assumed that V<sup>0</sup> = 100, C<sup>0</sup> = 0.01, C<sup>01</sup> = 0.01, C<sup>1</sup> = 0.25, C<sup>2</sup> = 0.75, C<sup>3</sup> = 2.0, C<sup>4</sup> = C = 0.1; V<sup>N</sup> = 20, VAc = 40, V<sup>K</sup> = 20. At each stage, the variable V is considered as a volume of the solution added, consecutively: NH3, CH3COOH, KI, and Na2S2O3, although the true/factual titrant in this method is the Na2S2O3 solution, added in stage 4.

The solubility s [mol/L] of CuI in this system (Figures 8a and b) is put in context with the speciation diagrams presented in Figure 9. This precipitate appears in the initial part of titration with KI (C3) solution (Figure 8a) and further it accompanies the titration, also in stage 4 (Figure 8b). Within stage 3, at V ≥ C0V0/C3, we have

$$\begin{split} s = s\_3 &= [\mathbf{Cu}^{+2}] + \sum\_{i=1}^{4} [\mathbf{Cu}(\mathbf{OH})\_i^{+2-i}] + \sum\_{i=1}^{4} [\mathbf{Cu}(\mathbf{NH}\_3)\_i^{+2}] + [\mathbf{CuSO}\_4] + [\mathbf{CuIO}\_3^{+1}] \\ s &+ \sum\_{i=1}^{2} [\mathbf{Cu}(\mathbf{CH}\_3\mathbf{COO})\_i^{+2-i}] + [\mathbf{Cu}^{+1}] + [\mathbf{CuI}\_2^{-1}] + \sum\_{i=1}^{2} [\mathbf{Cu}(\mathbf{NH}\_3)\_i^{+1}] \end{split} \tag{88}$$

and in stage 4

• F(S)

2½H2S2O3� þ 2½HS2O3

�<sup>2</sup>�þ½CuS2O<sup>3</sup>

–CV=ðV0 þ VN þ VAc þ VKI þ VÞ ¼ 0

þ6½CuðS2O3Þ<sup>3</sup>

þ2½S4O6

• F(Na)

<sup>½</sup>Hþ<sup>1</sup>

½CuðOHÞ<sup>3</sup>

½CuðNH3Þ

½CuI�<sup>1</sup>

½CuS2O�<sup>1</sup>

� ¼ <sup>10</sup>�pH, <sup>½</sup>OH�<sup>1</sup>

<sup>¼</sup> 1013:<sup>68</sup> � ½Cuþ<sup>2</sup>

<sup>¼</sup> 103:<sup>39</sup> � ½Cuþ<sup>2</sup>

<sup>¼</sup> 1012:<sup>03</sup> � ½Cuþ<sup>2</sup>

<sup>½</sup>CuSO4� ¼ <sup>10</sup><sup>2</sup>:<sup>36</sup> � ½Cuþ<sup>2</sup>

<sup>½</sup>CH3COOH� ¼ 104:<sup>65</sup> � ½Hþ<sup>1</sup>

<sup>2</sup> � ¼ 108:<sup>85</sup> � ½Cuþ<sup>1</sup>

<sup>¼</sup> 102:<sup>32</sup> � ½Hþ<sup>1</sup>

<sup>¼</sup> 1013:<sup>8</sup> � ½Cuþ<sup>1</sup>

<sup>¼</sup> <sup>10</sup><sup>2</sup>:<sup>24</sup> � ½Cuþ<sup>2</sup>

� 2 ½S2O�<sup>2</sup> <sup>3</sup> �,

<sup>½</sup>CuðCH3COOÞ2� ¼ 103:<sup>30</sup> � ½Cuþ<sup>2</sup>

<sup>3</sup> � ¼ 103:<sup>30</sup> � ½Cuþ<sup>1</sup>

Applying A = 16.92 [16], we have

þ2

�<sup>1</sup>� þ <sup>2</sup>½S2O3

122 Descriptive Inorganic Chemistry Researches of Metal Compounds

<sup>½</sup>Naþ<sup>1</sup>

lated in 35 independent equilibrium constants:

�½OH�<sup>1</sup> � 2 ,

�½NH3�,

�½NH3� 4 ,

> �½I �1 � 2

�½S2O�<sup>2</sup> <sup>3</sup> � 3

�½SO�<sup>2</sup>

�<sup>1</sup>� ¼ 1017:<sup>0</sup> � ½Cuþ<sup>2</sup>

<sup>2</sup> � ¼ 107:<sup>33</sup> � ½Cuþ<sup>2</sup>

�<sup>1</sup>� þ <sup>2</sup>½CuðS2O3Þ<sup>2</sup>

�<sup>2</sup>� þ <sup>4</sup>½S4O6

�<sup>5</sup>�–2CV=ðV<sup>0</sup> <sup>þ</sup> <sup>V</sup><sup>N</sup> <sup>þ</sup> <sup>V</sup>Ac <sup>þ</sup> <sup>V</sup>KI <sup>þ</sup> <sup>V</sup>Þ ¼ <sup>0</sup> ) ½H2S2O3�þ½HS2O3

The GEB is presented here in terms of the Approach I to GEB, based on the "card game" principle, with Cu (Eq. (80)), I (Eq. (85)) as S (Eq. (86)) as "players," and H, O, S (Eq. (81)), C (from Eq. (83)), N (from Eq. (82)), K, Na as "fans." There are together 47 species involved in 2 + 6 = 8, Eqs. (78)–(83), (85), (86) and two equalities; [K+1] (Eq. (84)) and [Na+1] (Eq. (87)) are not involved in expressions for equilibrium constants, and then are perceived as numbers (not variables), at a particular V-value. Concentrations of the species in the equations are interre-

� ¼ 10pH�<sup>14</sup>ðpK<sup>W</sup> <sup>¼</sup> <sup>14</sup>Þ, <sup>½</sup>CuOH<sup>þ</sup><sup>1</sup>

, ½CuðOHÞ

, ½CuðNH3Þ

<sup>4</sup> � ¼ 109:<sup>35</sup> � ½Hþ<sup>1</sup>

�, <sup>½</sup>Cuþ<sup>1</sup> �½I �1

<sup>3</sup> � ¼ <sup>10</sup><sup>0</sup>:<sup>82</sup> � ½Cuþ<sup>2</sup>

� 2

�3

, <sup>½</sup>HS2O�<sup>1</sup>

<sup>2</sup> � ¼ 1012:<sup>2</sup> � ½Cuþ<sup>1</sup>

�2

2þ

�½OH�<sup>1</sup> � 3

�½NH3� 2

<sup>4</sup> �, <sup>½</sup>NHþ<sup>1</sup>

�½CH3COO�<sup>1</sup>

�,

�½CH3COO�<sup>1</sup>

<sup>3</sup> �, ½CuðS2O3Þ

, <sup>½</sup>CuIO<sup>þ</sup><sup>1</sup>

�½CH3COO�<sup>1</sup>

�½S2O�<sup>2</sup>

�<sup>2</sup>� þ <sup>2</sup>½CuS2O3

�<sup>3</sup>� þ <sup>3</sup>½CuðS2O3Þ<sup>3</sup>

�<sup>1</sup>� þ <sup>4</sup>½CuðS2O3Þ<sup>2</sup>

�5�

� ¼ 2CV=ðV<sup>0</sup> þ V<sup>N</sup> þ VAc þ VKI þ VÞ ð87Þ

� ¼ 107:<sup>0</sup> � ½Cuþ<sup>2</sup>

�½NH3�, <sup>½</sup>HSO�<sup>1</sup>

<sup>3</sup> � ¼ 101:<sup>72</sup> � ½Hþ<sup>1</sup>

<sup>4</sup> � ¼ 1018:<sup>5</sup> � ½Cuþ<sup>2</sup>

<sup>3</sup> � ¼ 1010:<sup>06</sup> � ½Cuþ<sup>2</sup>

�½IO�<sup>1</sup>

�½OH�<sup>1</sup>

�½OH�<sup>1</sup> � 4

> �½NH3� 3

�, ½CuðOHÞ2�

þ2 <sup>4</sup> �

�½SO�<sup>2</sup> <sup>4</sup> �,

, <sup>½</sup>CuNHþ<sup>2</sup> <sup>3</sup> �

, ½CuðNH3Þ

<sup>4</sup> � ¼ 101:<sup>8</sup> � ½Hþ<sup>1</sup>

�½S2O�<sup>2</sup>

�

, ½CuðS2O3Þ

<sup>3</sup> �, ½H2S2O3�

�5 <sup>3</sup> �

� ¼ <sup>10</sup>�11:<sup>96</sup>ðsolubitlity product for CuIÞ,

<sup>3</sup> �, <sup>½</sup>CuCH3COO<sup>þ</sup><sup>1</sup>

�½S2O�<sup>2</sup> <sup>3</sup> � 2 �3�

�<sup>1</sup>�þ½S2O3

�2�

ð86Þ

$$s = s\_4 = s\_3 + \sum\_{i=1}^{3} \left[ \text{Cu} (\text{S}\_2\text{O}\_3)\_i^{+1-2i} \right] \tag{89}$$

The small concentration of Cu+1 (Figure 9, stage 3) occurs at a relatively high total concentration of Cu+2 species, determining the potential ca. 0.53–0.58 V, [Cu+2]/[Cu+1] = 10A(E – 0.153), see Figure 10a. Therefore, the concentration of Cu+2 species determine a relatively high solubility s in the initial part of stage 3. The decrease in the s value in further parts of stage 3 is continued in stage 4, at V < Veq = C0V0/C = 0.01∙100/0.1 = 10 mL. Next, a growth in the solubility s4 at V > Veq is involved with formation of thiosulfate complexes, mainly CuS2O3 �1 (Figure 9, stage 4). The species I3 �<sup>1</sup> and I2 are consumed during the titration in stage 4 (Figure 9d). A sharp drop of E value at Veq = 10 mL (Figure 10b) corresponds to the fraction titrated Φeq = 1.

The course of the E versus V relationship within the stage 3 is worth mentioning (Figure 10a). The corresponding curve initially decreases and reaches a "sharp" minimum at the point corresponding to crossing the solubility product for CuI. Precipitation of CuI starts after

Figure 9. The speciation plots for indicated Cu-species within the successive stages. The V-values on the abscissas correspond to successive addition of V mL of: 0.25 mol/L NH3 (stage 1); 0.75 mol/L CH3COOH (stage 2); 2.0 mol/L KI (stage 3); and 0.1 mol/L Na2S2O3 (stage 4). For more details see text.

Figure 10. Plots of E versus V for (a) stage 3 and (b) stage 4.

addition of 0.795 mL of 2.0 mol/L KI (Figure 11a). Subsequently, the curve in Figure 10a increases, reaches a maximum and then decreases. At a due excess of the KI (C3) added on the stage 3 (V<sup>K</sup> = 20 mL), solid iodine (I2(s), of solubility 0.00133 mol/L at 25<sup>o</sup> C) is not precipitated.

Figure 11. Solubility s of CuI within stage 3 (a) and stage 4 (b).
