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

Answer: (A)

16

Answer 2

Step 1: Use the Ideal Gas Equation:

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

- Given $V_A = V_B$ and $T_A = T_B$, the equation simplifies to:

$\frac{P_A}{P_B} = \frac{n_A}{n_B}$

Step 2: Calculate Moles 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: Calculate the Ratio of Pressures:

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

So, the correct answer is: 16