`H_(2)S`, a toxic gas with rotten egg like smell, is used for the qualitative analysis.If the solubility of `H_(2)S` in water at `STP` is `0.195 m`, calculate Henry's law constant.

Options

A. 0.0263 bar
B. 69.16 bar
C. 192 bar
D. 282 bar

Explanation

To calculate Henry's law constant for hydrogen sulfide (H₂S) given its solubility in water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Solubility of H₂S in water at STP = 0.195 m (molarity).
- We need to calculate Henry's law constant (K_H).

2. **Identify the Formula:**
- Henry's law states that \( P = K_H \cdot x \)
- Where \( P \) is the partial pressure of the gas, \( K_H \) is Henry's law constant, and \( x \) is the mole fraction of the gas in the solution.

3. **Calculate the Number of Moles of H₂S:**
- Given that the molarity (0.195 m) corresponds to 0.195 moles of H₂S in 1 liter of solution, we can directly use this value:
\[ \text{Moles of H₂S} = 0.195 \, \text{mol} \]

4. **Calculate the Number of Moles of Water:**
- Assume we have 1 kg of water (which is approximately 1 liter).
- The molar mass of water (H₂O) = 18 g/mol.
- Therefore, the number of moles of water:
\[ \text{Moles of water} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.5 \, \text{mol} \]

5. **Calculate the Mole Fraction of H₂S:**
- The mole fraction \( x \) of H₂S is calculated as follows:
\[ x = \frac{\text{Moles of H₂S}}{\text{Moles of H₂S} + \text{Moles of water}} = \frac{0.195}{0.195 + 55.5} \approx 0.0035 \]

6. **Determine the Partial Pressure of H₂S:**
- At STP, the pressure of H₂S is given as 0.987 atm.

7. **Calculate Henry's Law Constant (K_H):**
- Rearranging the Henry's law equation gives:
\[ K_H = \frac{P}{x} = \frac{0.987 \, \text{atm}}{0.0035} \approx 282 \, \text{atm} \]

### Final Answer:
The Henry's law constant \( K_H \) for H₂S is approximately **282 atm**.