Question

Two vessels A and B are of the same size and are at the same temperature. A contains 1 g of hydrogen and B contains 1 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. 16
• B. 8
• C. 4
• D. 32

Answer 1

The Correct Option is A

Step 1: Apply the Ideal Gas Law:

\[ \frac{P_A V_A}{P_B V_B} = \frac{n_A R T_A}{n_B R T_B} \]

- Given that \(V_A = V_B\) and \(T_A = T_B\), the equation simplifies to:

\[ \frac{P_A}{P_B} = \frac{n_A}{n_B} \]

Step 2: Determine the Molar Quantities of Each Gas:

- For hydrogen in vessel A:

\[ n_A = \frac{\text{mass of hydrogen}}{\text{molar mass of } H_2} = \frac{1 \text{ g}}{2 \text{ g/mol}} = \frac{1}{2} \text{ mol} \]

- For oxygen in vessel B:

\[ n_B = \frac{\text{mass of oxygen}}{\text{molar mass of } O_2} = \frac{1 \text{ g}}{32 \text{ g/mol}} = \frac{1}{32} \text{ mol} \]

Step 3: Compute the Pressure Ratio:

\[ \frac{P_A}{P_B} = \frac{n_A}{n_B} = \frac{\frac{1}{2}}{\frac{1}{32}} = \frac{1}{2} \times 32 = 16 \]

The result is: 16