Q28 / 90 · JEE Main 2021 (25 Jul Shift 1) · Chemistry

A home owner uses $4.00 \times 10^{3} m^{3}$ 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 $x \times 10^{5} g$ . The value of $x$ is ______. (Nearest integer)
(Given $R = 0.083 L atm K^{- 1} {mol}^{- 1}$ )

Correct answer: 26

Solution

$n ({CH}_{4}) = \frac{PV}{RT}$

$= \frac{1 \times 4 \times 10^{3} \times 1000}{0.083 \times 300}$

Weight of ${CH}_{4}$

$= \frac{40 \times 16 \times 10^{5}}{0.083 \times 300} gm$

$= 25.7 \times 10^{5} gm$

Hence, the correct answer is 26.