Question

Volume of a gas at NTP is 1.12 × 10⁻⁷ cm³. The number of molecules in it is :

• A. 3.01 × 10¹²
• B. 3.01 × 10²⁴
• C. 3.01 × 10²³
• D. 3.01 × 10²⁰

Hint:

Key Exam Tip:
At NTP, the molar volume of a gas is 22.4 L or 22400 cm³. Use Avogadro's number ($6.022 \times 10^{23}$) to convert moles to the number of molecules.

Answer 1

The Correct Option is A

At Normal Temperature and Pressure (NTP), 1 mole of any gas occupies a volume of 22.4 dm³, which is equivalent to 22,400 cm³. Avogadro's number ($N_A$) is approximately $6.022 \times 10^{23}$ molecules/mol.
First, calculate the number of moles ($n$) of the gas using its given volume at NTP:
$n = \frac{\text{Given Volume}}{\text{Molar Volume at NTP}}$
$n = \frac{1.12 \times 10^{-7} \text{ cm³}}{22400 \text{ cm³/mol}}$
$n = \frac{1.12 \times 10^{-7}}{2.24 \times 10^4} \text{ mol}$
$n = 0.5 \times 10^{-11} \text{ mol} = 5 \times 10^{-12} \text{ mol}$
Next, calculate the number of molecules by multiplying the number of moles by Avogadro's number:
Number of molecules = $n \times N_A$
Number of molecules = $(5 \times 10^{-12} \text{ mol}) \times (6.022 \times 10^{23} \text{ molecules/mol})$
Number of molecules = $30.11 \times 10^{11}$
Number of molecules = $3.011 \times 10^{12}$ molecules.
Rounding to three significant figures, the number of molecules is $3.01 \times 10^{12}$.
Final Answer: \(\boxed{A}\)