Solubility of `MX_(2)` type electrolytes is `0.5xx10^(-4) mol//L`, then find out `K_(sp)` of electrolytes.

Options

A. `5xx10^(-12)`
B. `25xx10^(-10)`
C. `1xx10^(-13)`
D. `5xx10^(-13)`

Explanation

To find the solubility product constant (Ksp) for the MX₂ type electrolyte given its solubility, we can follow these steps:

### Step 1: Understand the Dissociation of MX₂
The electrolyte MX₂ dissociates in water according to the following equation:
\[ \text{MX}_2 (s) \rightleftharpoons \text{M}^{2+} (aq) + 2\text{X}^- (aq) \]

### Step 2: Define Solubility
Let the solubility of MX₂ be \( s \). Given that the solubility is \( 0.5 \times 10^{-4} \, \text{mol/L} \), we can denote:
\[ s = 0.5 \times 10^{-4} \, \text{mol/L} \]

### Step 3: Determine Ion Concentrations
From the dissociation equation, we can determine the concentrations of the ions at equilibrium:
- The concentration of \( \text{M}^{2+} \) will be \( s \).
- The concentration of \( \text{X}^- \) will be \( 2s \) (since there are 2 moles of \( \text{X}^- \) for every mole of MX₂).

### Step 4: Substitute Values
Substituting the value of \( s \):
- Concentration of \( \text{M}^{2+} = s = 0.5 \times 10^{-4} \, \text{mol/L} \)
- Concentration of \( \text{X}^- = 2s = 2 \times (0.5 \times 10^{-4}) = 1.0 \times 10^{-4} \, \text{mol/L} \)

### Step 5: Write the Ksp Expression
The solubility product \( K_{sp} \) is given by the expression:
\[ K_{sp} = [\text{M}^{2+}][\text{X}^-]^2 \]

### Step 6: Substitute Ion Concentrations into Ksp Expression
Now, substituting the concentrations:
\[ K_{sp} = (0.5 \times 10^{-4})(1.0 \times 10^{-4})^2 \]

### Step 7: Calculate Ksp
Calculating the above expression:
\[ K_{sp} = (0.5 \times 10^{-4}) \times (1.0 \times 10^{-4})^2 \]
\[ K_{sp} = (0.5 \times 10^{-4}) \times (1.0 \times 10^{-8}) \]
\[ K_{sp} = 0.5 \times 10^{-12} \]
\[ K_{sp} = 5.0 \times 10^{-13} \]

### Final Answer
Thus, the solubility product \( K_{sp} \) of the electrolyte MX₂ is:
\[ K_{sp} = 5.0 \times 10^{-13} \]

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