Question

Volume of a gas at NTP is \( 1.12 \times 10^{-7} \, \text{cm}^3 \). The number of molecules in it is:

• A. \( 3.01 \times 10^{12} \)
• B. \( 3.01 \times 10^{24} \)
• C. \( 3.01 \times 10^{23} \)
• D. \( 3.01 \times 10^{20} \)

Hint:

To calculate the number of molecules for a given volume, use the relation: \[ \text{Number of molecules} = \frac{\text{Volume of gas}}{22,400 \, \text{cm}^3} \times 6.02 \times 10^{23}. \] This allows you to scale the number of molecules for any given volume at NTP conditions.

Answer 1

The Correct Option is A

At NTP, \( 22,400 \, \text{cm}^3 \) of gas contains \( 6.02 \times 10^{23} \) molecules. For \( 1.12 \times 10^{-7} \, \text{cm}^3 \), the number of molecules is calculated by proportionality:\[\text{Number of molecules} = \frac{6.02 \times 10^{23}}{22,400} \times 1.12 \times 10^{-7}.\]Simplifying yields:\[\text{Number of molecules} = \frac{6.02 \times 1.12 \times 10^{23} \times 10^{-7}}{22,400}.\]The calculation results in:\[\text{Number of molecules} = 3.01 \times 10^{12}.\] Final Answer:\[\boxed{3.01 \times 10^{12}}.\]