A mixture of hydrogen and oxygen has volume $500 \mathrm{~cm}^{3}$, temperature 300 K , pressure 400 kPa and mass 0.76 g . The ratio of masses of oxygen to hydrogen will be :-

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Heat & Thermodynamics

A mixture of hydrogen and oxygen has volume

500 cm^{3}

, temperature 300 K , pressure 400 kPa and mass 0.76 g . The ratio of masses of oxygen to hydrogen will be :-

(A) $3 : 16$
(B) $16 : 3$ ✓ Correct
(C) $3 : 8$
(D) $8 : 3$

Answer: (B)

Solution

Using the ideal gas equation:

P V = n R T

n = \frac{P V}{R T} = \frac{400 \times 1 0 ^{3} \times 500 \times 1 0 ^{- 6}}{8.3 \times 300} = 0.08

mol

Let

m_{1}

= mass of H₂,

m_{2}

= mass of O₂.

\frac{m _{1}}{2} + \frac{m _{2}}{32} = 0.08

and

m_{1} + m_{2} = 0.76

Solving:

16 m_{1} + m_{2} = 2.56

and

m_{1} + m_{2} = 0.76

This gives

m_{1} = 0.12

g and

m_{2} = 0.64

g

Ratio:

\frac{m _{2}}{m _{1}} = \frac{0.64}{0.12} = \frac{16}{3}

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Single correct option

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