Question

A cooking gas contains carbon and hydrogen only. A volume of 11.2 L of this gas is found to weigh 22 g at STP. Then the molecular formula of the gas is

• A. $C_2H_6$
• B. $C_2H_2$
• C. $C_2H_4$
• D. $C_3H_8$
• E. $C_3H_4$

Answer 1

The Correct Option is D

We are given:

• Volume of gas = 11.2 L
• Mass of gas = 22 g
• Conditions = STP (Standard Temperature and Pressure)

At STP, 1 mole of any ideal gas occupies 22.4 L. So,

Moles of gas = \( \frac{11.2}{22.4} = 0.5 \)

Molar mass = \( \frac{22}{0.5} = 44 \, \text{g/mol} \)

We are told the gas contains only carbon (C) and hydrogen (H). Let’s test molecular masses:

• \( C_3H_8 \): \( 3 \times 12 + 8 \times 1 = 44 \, \text{g/mol} \) ✅
• \( C_2H_2 \): \( 24 + 2 = 26 \, \text{g/mol} \)
• \( C_2H_4 \): \( 24 + 4 = 28 \, \text{g/mol} \)
• \( C_2H_6 \): \( 24 + 6 = 30 \, \text{g/mol} \)
• \( C_3H_4 \): \( 36 + 4 = 40 \, \text{g/mol} \)

Only \( C_3H_8 \) has the correct molar mass.

Correct Answer: (D) \( C_3H_8 \)