Question

The mass of 4.48 dm³ of certain gas is 5.6 g at STP. Assuming ideal behavior, identify the probable gas from the following.

• A. \( \text{Cl}_2 \)
• B. \( \text{O}_2 \)
• C. \( \text{N}_2 \)
• D. \( \text{CH}_4 \)

Hint:

At STP, 1 mole of an ideal gas occupies 22.4 dm³. Use this information to calculate the number of moles and identify gases based on their molar masses.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the volume and mass of a gas at standard temperature and pressure (STP). We need to calculate its molar mass to identify the gas.
Step 2: Key Formula or Approach:
1. Calculate the number of moles using the molar volume at STP (\( 22.4 \text{ dm}^3/\text{mol} \)).
\[ n = \frac{\text{Volume}}{\text{Molar Volume}} \] 2. Calculate the molar mass using the formula:
\[ \text{Molar Mass} = \frac{\text{Mass}}{\text{n}} \] Step 3: Detailed Explanation:
Given:
Volume = \( 4.48 \text{ dm}^3 \) at STP.
Mass = \( 5.6 \text{ g} \).
Number of moles (\( n \)):
\[ n = \frac{4.48}{22.4} = 0.2 \text{ mol} \] Molar Mass (\( M \)):
\[ M = \frac{5.6}{0.2} = 28 \text{ g/mol} \] Now, check the molar masses of the options:
(A) \( \text{Cl}_2 = 2 \times 35.5 = 71 \text{ g/mol} \)
(B) \( \text{O}_2 = 2 \times 16 = 32 \text{ g/mol} \)
(C) \( \text{N}_2 = 2 \times 14 = 28 \text{ g/mol} \)
(D) \( \text{CH}_4 = 12 + 4 = 16 \text{ g/mol} \)
Step 4: Final Answer:
The molar mass corresponds to nitrogen gas (\( \text{N}_2 \)).