What is the minimum pH required to prevent the precipitation of ZnS in a solution which is 0.01 M `ZnCl_2` and saturated with 0.1 M `H_2S` ?
`K_(sp)" of " (ZnS)=10^(-21),K_(a_1)xxK_(a_2)(H_2S)=10^(-20)`

Options

A. 4
B. 3
C. 2
D. 1

Answer

To solve the problem of determining the minimum pH required to prevent the precipitation of ZnS in a solution that is 0.01 M ZnCl₂ and saturated with 0.1 M H₂S, we will follow these steps:

### Step 1: Write the dissociation reaction of ZnS
ZnS dissociates in water as follows:
\[ \text{ZnS} \rightleftharpoons \text{Zn}^{2+} + \text{S}^{2-} \]

### Step 2: Write the expression for Ksp of ZnS
The solubility product constant (Ksp) for ZnS can be expressed as:
\[ K_{sp} = [\text{Zn}^{2+}][\text{S}^{2-}] \]
Given that \( K_{sp} = 10^{-21} \).

### Step 3: Determine the concentration of Zn²⁺
Since the solution is 0.01 M ZnCl₂, the concentration of Zn²⁺ ions is:
\[ [\text{Zn}^{2+}] = 0.01 \, \text{M} \]

### Step 4: Substitute Zn²⁺ concentration into Ksp expression
Substituting the concentration of Zn²⁺ into the Ksp expression:
\[ 10^{-21} = (0.01)[\text{S}^{2-}] \]

### Step 5: Solve for [S²⁻]
Rearranging the equation to find the concentration of sulfide ions:
\[ [\text{S}^{2-}] = \frac{10^{-21}}{0.01} = 10^{-19} \, \text{M} \]

### Step 6: Write the dissociation reaction of H₂S
The dissociation of H₂S can be represented as:
\[ \text{H}_2\text{S} \rightleftharpoons 2\text{H}^{+} + \text{S}^{2-} \]

### Step 7: Write the expression for Ka
The dissociation constant for H₂S is given as \( K_{a1} \times K_{a2} = 10^{-20} \). The expression for the dissociation of H₂S is:
\[ K_a = \frac{[\text{H}^{+}]^2 [\text{S}^{2-}]}{[\text{H}_2\text{S}]} \]

### Step 8: Substitute known values into the Ka expression
Given that the concentration of H₂S is 0.1 M:
\[ 10^{-20} = \frac{[\text{H}^{+}]^2 (10^{-19})}{0.1} \]

### Step 9: Rearrange to find [H⁺]
Rearranging gives:
\[ [\text{H}^{+}]^2 = 10^{-20} \times 0.1 \times 10^{19} \]
\[ [\text{H}^{+}]^2 = 10^{-21} \]

### Step 10: Solve for [H⁺]
Taking the square root:
\[ [\text{H}^{+}] = 10^{-10} \, \text{M} \]

### Step 11: Calculate the pH
Now, we can calculate the pH:
\[ \text{pH} = -\log([\text{H}^{+}]) = -\log(10^{-10}) = 10 \]

### Conclusion
The minimum pH required to prevent the precipitation of ZnS is **10**.

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