JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Heat & Thermodynamics

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 :

(A) $\frac{1}{3}$
(B) $\frac{3}{1}$ ✓ Correct
(C) $\frac{1}{16}$
(D) $\frac{16}{1}$

Answer: (B)

Solution

Using ideal gas law

P V = n R T

: total moles

n = \frac{100 \times 1 0 ^{3} \times 2 \times 1 0 ^{- 3}}{8.314 \times 300} = 0.08

mol. Let

n_{1}

and

n_{2}

be moles of H₂ and O₂. Then

n_{1} + n_{2} = 0.08

and

2 n_{1} + 32 n_{2} = 0.76

. Solving:

n_{2} = 0.02

n_{1} = 0.06

. Ratio

\frac{n _{1}}{n _{2}} = \frac{3}{1}

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Single correct option

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