JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Some Basic Concepts of Chemistry

A home owner uses

4.00 \times 1 0^{3} m^{3}

of methane

(CH_{4})

gas, (assume

CH_{4}

is an ideal gas) in a year to heat his home. Under the pressure of 1.0 atm and 300 K, mass of gas used is

x \times 1 0^{5} g

. The value of

x

is ______. (Nearest integer)
(Given

R = 0.083 L atm K^{- 1} mol^{- 1}

)

Answer: 26

Solution

One cubic metre is

1 0^{3}

L, so the volume used is

4.00 \times 1 0^{3} m^{3} = 4.00 \times 1 0^{6}

L. From

P V = n R T

n = \frac{P V}{R T} = \frac{1.0 \times 4.00 \times 1 0 ^{6}}{0.083 \times 300} = 1.606 \times 1 0^{5} mol

Methane has a molar mass of

16 g mo l^{- 1}

, so the mass burnt is

1.606 \times 1 0^{5} \times 16 = 2.57 \times 1 0^{6} g = 25.7 \times 1 0^{5} g

. To the nearest integer the value asked for is

26

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Integer answer