Question

Two vessels \( A \) and \( B \) are of the same size and are at the same temperature. Vessel \( A \) contains \( 1 \, \text{g} \) of hydrogen and vessel \( B \) contains \( 1 \, \text{g} \) of oxygen. \( P_A \) and \( P_B \) are the pressures of the gases in \( A \) and \( B \) respectively. Then \( \frac{P_A}{P_B} \) is:

• A. \( 8 \)
• B. \( 16 \)
• C. \( 32 \)
• D. \( 4 \)

Hint:

At constant temperature and volume, the pressure of a gas is directly proportional to its number of moles. For comparisons, use the relationship \( P \propto n \).

Answer 1

The Correct Option is B

The ideal gas equation relates pressure, volume, temperature, and the number of moles: \[ PV = nRT \quad \implies \quad P \propto n, \] where \( n \) is the number of moles of gas. Step 1: Determine the Number of Moles For hydrogen (\( H_2 \)): \[ M_{H_2} = 2 \, \text{g/mol}, \quad n_A = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{1}{2} = 0.5 \, \text{mol}. \] For oxygen (\( O_2 \)): \[ M_{O_2} = 32 \, \text{g/mol}, \quad n_B = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{1}{32} = 0.03125 \, \text{mol}. \] Step 2: Compute the Ratio of Pressures Since \( P \propto n \): \[ \frac{P_A}{P_B} = \frac{n_A}{n_B} = \frac{0.5}{0.03125}. \] Simplify: \[ \frac{P_A}{P_B} = 16. \] Final Answer: \[ \boxed{16} \]