Question

A mixture of hydrogen and oxygen has volume 2000 $cm^3$, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:[Take gas constant R = 8.3 $JK^{–1}$ $mol^{–1}$]

• A. $\frac{1}{3}$
• B. $\frac{3}{1}$
• C. $\frac{1}{16}$
• D. $\frac{16}{1}$

Answer 1

Answer: (B)

$\frac{3}{1}$

Answer 2

$P_1V = n_1RT$

$P_2V = n_2RT$

$⇒ (100 kPa) V = (n_1 + n_2)RT$

$⇒n_1+n_2=\frac{(100 kPa)(2000 cm)^3)}{8.3×300}….(1)$

Also, $n_1 × 2 + n_2 × 32 = 0.76 ….(2)$

Solving (1) and (2),

$n_1 = 0.06$

$n_2 = 0.02$

$⇒ \frac{n_1}{n_2} = 3$

Hence, the correct option is (B): $\frac{3}{1}$