The solubility of `CaCO_(3)` in water is `3.05 xx 10^(-4)` moles/litre. Its solubility product will be

Options

A. `3.05 xx 10^(-4)`
B. 10
C. `6.1 xx 10^(-4)`
D. `9.3 xx 10^(-8)`

Explanation

To find the solubility product (Ksp) of calcium carbonate (CaCO₃) given its solubility in water, we can follow these steps:

### Step 1: Write the Dissolution Equation
When calcium carbonate (CaCO₃) dissolves in water, it dissociates into calcium ions (Ca²⁺) and carbonate ions (CO₃²⁻):
\[ \text{CaCO}_3 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + \text{CO}_3^{2-} (aq) \]

### Step 2: Define the Solubility
Let the solubility of CaCO₃ be represented by \( s \). According to the information provided, the solubility \( s \) is given as:
\[ s = 3.05 \times 10^{-4} \text{ moles/litre} \]

### Step 3: Determine Ion Concentrations
From the dissolution equation, we can see that for every mole of CaCO₃ that dissolves, one mole of Ca²⁺ and one mole of CO₃²⁻ are produced. Therefore, at equilibrium:
- The concentration of Ca²⁺ = \( s \)
- The concentration of CO₃²⁻ = \( s \)

### Step 4: Write the Expression for Ksp
The solubility product (Ksp) is defined as the product of the concentrations of the ions, each raised to the power of their coefficients in the balanced equation:
\[ K_{sp} = [\text{Ca}^{2+}][\text{CO}_3^{2-}] \]
Substituting the concentrations:
\[ K_{sp} = s \times s = s^2 \]

### Step 5: Substitute the Value of s
Now, we can substitute the value of \( s \) into the Ksp expression:
\[ K_{sp} = (3.05 \times 10^{-4})^2 \]

### Step 6: Calculate Ksp
Calculating \( (3.05 \times 10^{-4})^2 \):
\[ K_{sp} = 3.05^2 \times (10^{-4})^2 \]
\[ K_{sp} = 9.3025 \times 10^{-8} \]
Rounding this to two significant figures gives:
\[ K_{sp} \approx 9.3 \times 10^{-8} \]

### Final Answer
Thus, the solubility product \( K_{sp} \) of calcium carbonate is:
\[ K_{sp} = 9.3 \times 10^{-8} \]

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