Question

A container contains equal masses of H$_{2}$, He, CO$_{2}$ and Ne at a certain temperature. Which of the following gases exerts minimum partial pressure?

• A. H$_{2}$
• B. He
• C. CO$_{2}$
• D. Ne

Hint:

For equal masses: Heavier gas = Fewer moles = Lower partial pressure.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
According to Dalton's Law of partial pressures and the ideal gas law, at constant volume and temperature, the partial pressure of a gas is directly proportional to its number of moles (\( p_{i} \propto n_{i} \)).
Step 2: Key Formula or Approach:
Number of moles (\( n \)) = \( \frac{\text{Mass}(m)}{\text{Molar Mass}(M)} \)
Since all gases have equal mass \( m \), then \( n \propto \frac{1}{M} \).
Partial pressure \( p_{i} \propto \frac{1}{M} \).
Minimum partial pressure corresponds to the maximum molar mass.
Step 3: Detailed Explanation:
Let's find the molar masses ($M$) of the given gases:
- \( M(H_{2}) = 2 \text{ g/mol} \)
- \( M(He) = 4 \text{ g/mol} \)
- \( M(Ne) = 20 \text{ g/mol} \)
- \( M(CO_{2}) = 12 + 2(16) = 44 \text{ g/mol} \)
Comparing the values: \( 44>20>4>2 \).
Since \( CO_{2} \) has the largest molar mass, it will have the lowest number of moles for a fixed mass.
Therefore, \( CO_{2} \) exerts the minimum partial pressure.
Step 4: Final Answer:
\( CO_{2} \) exerts the minimum partial pressure.