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. 8
• B. 16
• C. 32
• D. 4

Hint:

The pressure of a gas is directly proportional to the number of moles of gas when volume and temperature are kept constant.

Answer 1

The Correct Option is B

Step 1: {Ideal Gas Law}
The ideal gas law is defined as:\[PV = nRT\]where:
\( P \) signifies the gas pressure
\( V \) signifies the gas volume
\( n \) signifies the molar quantity of gas
\( R \) signifies the ideal gas constant
\( T \) signifies the gas temperature
Step 2: {Hydrogen Moles (\( n_H \))}
Hydron's ( \( H_2 \) ) molar mass is 2 g/mol.\[n_H = \frac{{mass of hydrogen}}{{molar mass of hydrogen}} = \frac{1 { g}}{2 { g/mol}} = \frac{1}{2} { mol}\]Step 3: {Oxygen Moles (\( n_O \))}
Oxygen's ( \( O_2 \) ) molar mass is 32 g/mol.\[n_O = \frac{{mass of oxygen}}{{molar mass of oxygen}} = \frac{1 { g}}{32 { g/mol}} = \frac{1}{32} { mol}\]Step 4: {Applying Ideal Gas Law to Both Containers}
Given that the containers are identical in size and at the same temperature, \( V \) and \( T \) are uniform for both. Consequently, the following can be stated:For container A (hydrogen):\[P_A V = n_H RT\]For container B (oxygen):\[P_B V = n_O RT\]Step 5: {Calculating the Ratio \( \frac{P_A}{P_B} \)}
Divide the equation for container A by the equation for container B:\[\frac{P_A V}{P_B V} = \frac{n_H RT}{n_O RT}\]\[\frac{P_A}{P_B} = \frac{n_H}{n_O} = \frac{\frac{1}{2}}{\frac{1}{32}} = \frac{1}{2} \times \frac{32}{1} = 16\]Therefore, \( \frac{P_A}{P_B} = 16 \).