If solubility of any gas in the liquid at 1 bar pressure is 0.05 mol/L. What will be its solubility at 3 bar pressure, keeping the temperature constant? `

Options

A. `0.05/3 mol //L`
B. `0.15 mol//L`
C. `0.05 mol //L`
D. `1.0 mol//L`

Answer

To solve the problem of finding the solubility of a gas in a liquid at a different pressure while keeping the temperature constant, we will use Henry's Law. Here’s a step-by-step solution:

### Step 1: Understand Henry's Law
Henry's Law states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid. This can be mathematically expressed as:
\[ S = k_H \cdot P \]
where:
- \( S \) is the solubility of the gas (in mol/L),
- \( k_H \) is Henry's law constant (which is temperature dependent),
- \( P \) is the pressure of the gas (in bar).

### Step 2: Identify Given Data
From the problem, we have:
- Initial solubility (\( S_1 \)) = 0.05 mol/L at pressure (\( P_1 \)) = 1 bar.
- We need to find the solubility (\( S_2 \)) at pressure (\( P_2 \)) = 3 bar.

### Step 3: Calculate Henry's Law Constant
Using the initial conditions, we can calculate \( k_H \):
\[ k_H = \frac{S_1}{P_1} = \frac{0.05 \, \text{mol/L}}{1 \, \text{bar}} = 0.05 \, \text{mol/L/bar} \]

### Step 4: Use Henry's Law to Find New Solubility
Now we can use the value of \( k_H \) to find the new solubility at the new pressure:
\[ S_2 = k_H \cdot P_2 \]
Substituting the values we have:
\[ S_2 = 0.05 \, \text{mol/L/bar} \cdot 3 \, \text{bar} \]
\[ S_2 = 0.15 \, \text{mol/L} \]

### Step 5: Conclusion
The solubility of the gas at 3 bar pressure is 0.15 mol/L.