Under what vapour pressure of moisture in atmospheric conditions `CuSO_45H_2O` will be efflorescent , if `CuSO_(4)5H_2O(s) hArr CuSO_4 3H_2O(s) +2H_2O(g) ,K_p=62.72 mm^2` ?

Options

A. 3.95mm
B. 7.90mm
C. 39.5mm
D. 0.395mm

Answer

To determine the vapor pressure of moisture in atmospheric conditions under which `CuSO_4·5H_2O` will be efflorescent, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Reaction**:
The reaction for the efflorescence of copper sulfate pentahydrate can be represented as:
\[ CuSO_4·5H_2O(s) \rightleftharpoons CuSO_4·3H_2O(s) + 2H_2O(g) \]
Here, the solid copper sulfate pentahydrate loses water molecules to form solid copper sulfate trihydrate and water vapor.

2. **Identify the Equilibrium Constant**:
We are given the equilibrium constant \( K_p = 62.72 \, \text{mm}^2 \). For the above reaction, the expression for \( K_p \) is:
\[ K_p = (P_{H_2O})^2 \]
where \( P_{H_2O} \) is the partial pressure of water vapor at equilibrium.

3. **Set Up the Equation**:
From the expression for \( K_p \):
\[ 62.72 = (P_{H_2O})^2 \]

4. **Solve for \( P_{H_2O} \)**:
To find \( P_{H_2O} \), we take the square root of both sides:
\[ P_{H_2O} = \sqrt{62.72} \]

5. **Calculate the Value**:
Now we calculate the square root:
\[ P_{H_2O} \approx 7.93 \, \text{mm} \]

6. **Interpret the Result**:
This value indicates that under a vapor pressure of approximately \( 7.93 \, \text{mm} \) of moisture, the copper sulfate pentahydrate will effloresce.

### Final Answer:
The vapor pressure of moisture under which `CuSO_4·5H_2O` will be efflorescent is approximately **7.93 mm**.