Question

Four vessels of same volume consist equal masses of four gases \(\text{H}_2\), \(\text{Cl}_2\), \(\text{N}_2\), and \(\text{O}_2\) separately at same temperature. The pressure exerted by the gas is maximum for

• A. \(\text{H}_2\)
• B. \(\text{Cl}_2\)
• C. \(\text{N}_2\)
• D. \(\text{O}_2\)

Hint:

At constant \(m\), lower molar mass → higher pressure.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
According to the ideal gas law, pressure is directly proportional to the number of moles of gas when volume and temperature are constant.
Step 2: Key Formula or Approach:
\[ PV = nRT \implies P = \frac{nRT}{V} \] \[ \text{Since } n = \frac{\text{mass}}{\text{Molar mass}}, \text{ then } P = \frac{\text{mass} \times RT}{M \times V} \] Step 3: Detailed Explanation:
Given that mass, volume, and temperature are the same for all vessels, the pressure exerted by a gas is inversely proportional to its molar mass (\(P \propto 1/M\)).
Molar masses:
\(M(\text{H}_2) = 2\text{ g/mol}\)
\(M(\text{N}_2) = 28\text{ g/mol}\)
\(M(\text{O}_2) = 32\text{ g/mol}\)
\(M(\text{Cl}_2) = 71\text{ g/mol}\)
Hydrogen (\(\text{H}_2\)) has the lowest molar mass, which means it will have the highest number of moles for a given mass. Consequently, it will exert the maximum pressure.
Step 4: Final Answer:
The gas with maximum pressure is \(\text{H}_2\).