Question

If $1litre$ of $N_2$ at ${27}^{o}C$ and $760mm$ contains $N$ molecules, $4$ litres of $O_2$, under the same conditions of temperature and pressure, shall contain:

• A. $N$ molecules
• B. $2N$ molecules
• C. $\frac{N}{4}$ molecules
• D. $4N$ molecules

Answer 1

The correct option is D $4N$ molecules

Ideal gas equation: $PV=nRT$

Applying ideal gas equation for both the cases:

(i) V = 1 L, P = 1 atm or 760 mm, T = 300 K, Gas is Nitrogen

$⟹1\times 1=n_{N_2}\times R\times 300.......\left(1\right)$

(ii) V = 4 L, P = 1 atm or 760 mm, T = 300 K, Gas is Oxygen

$⟹1\times 4=n_{O_2}\times R\times 300.......\left(2\right)$

Dividing (1) by (2)

$⟹\frac{1\times 1}{1\times 4}=\frac{n_{N_2}\times R\times 300}{n_{O_2}\times R\times 300}$

$⟹n_{O_2}=4\times n_{N_2}$

$⟹\frac{N_{O_2}}{N_A}=4\times \frac{N_{N_2}}{N_A}$

$⟹N_{O_2}=4\times N_{N_2}=4\times N$

Hence, Option "D" is the correct answer.