How many grams of calcium oxalate should be dissolved in water to make one litre of saturated solution? (`K_sp` of `CaC_2O_4` is `2.5 X 10^-9` and its molecular weight is 128 u)

Options

A. `6.4*10^-3 g`
B. `8.0*10^-3 g`
C. `1.28*10^-3 g`
D. `6.4*10^3 g`

Answer

To determine how many grams of calcium oxalate (CaC₂O₄) should be dissolved in water to make one litre of a saturated solution, we will use the solubility product constant (Ksp) and the molecular weight of calcium oxalate.

### Step-by-Step Solution:

1. **Write the dissociation equation**:
Calcium oxalate dissociates in water as follows:
\[ \text{CaC}_2\text{O}_4 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + \text{C}_2\text{O}_4^{2-} (aq) \]

2. **Define the solubility (S)**:
Let the solubility of calcium oxalate in mol/L be \( S \). At equilibrium, the concentration of \(\text{Ca}^{2+}\) and \(\text{C}_2\text{O}_4^{2-}\) will both be \( S \).

3. **Write the expression for Ksp**:
The solubility product constant (Ksp) for calcium oxalate is given by:
\[ K_{sp} = [\text{Ca}^{2+}][\text{C}_2\text{O}_4^{2-}] = S \cdot S = S^2 \]
Given \( K_{sp} = 2.5 \times 10^{-9} \), we can set up the equation:
\[ S^2 = 2.5 \times 10^{-9} \]

4. **Calculate the solubility (S)**:
To find \( S \), take the square root of both sides:
\[ S = \sqrt{2.5 \times 10^{-9}} = 5.0 \times 10^{-5} \text{ mol/L} \]

5. **Calculate the number of moles in 1 litre**:
Since the volume of the solution is 1 litre, the number of moles of calcium oxalate in the saturated solution is:
\[ \text{Number of moles} = S \times \text{Volume} = 5.0 \times 10^{-5} \text{ mol} \]

6. **Convert moles to grams**:
To find the mass of calcium oxalate, use the formula:
\[ \text{mass} = \text{number of moles} \times \text{molar mass} \]
The molar mass of calcium oxalate (CaC₂O₄) is given as 128 g/mol. Thus:
\[ \text{mass} = 5.0 \times 10^{-5} \text{ mol} \times 128 \text{ g/mol} = 6.4 \times 10^{-3} \text{ g} \]

### Final Answer:
The mass of calcium oxalate that should be dissolved in water to make one litre of saturated solution is:
\[ \text{6.4} \times 10^{-3} \text{ g} \]