Q. A home owner uses $4.00 \times 10^{3} m ^{3}$ of methane $\left( CH _{4}\right)$ 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) $\left(\right.$ Given $R=0.083\, L\,atm\K ^{-1} mol ^{-1}$ )

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Solution:

$n\left( CH _{4}\right)=\frac{P V}{R T}$
$=\frac{1 \times 4 \times 10^{3} \times 1000}{0.083 \times 300}$
Weight of $CH _{4}$
$=\frac{40 \times 16 \times 10^{5}}{0.083 \times 300} gm$
$=25.7 \times 10^{5} gm$

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$n\left( CH _{4}\right)=\frac{P V}{R T}$ $=\frac{1 \times 4 \times 10^{3} \times 1000}{0.083 \times 300}$ Weight of $CH _{4}$ $=\frac{40 \times 16 \times 10^{5}}{0.083 \times 300} gm$ $=25.7 \times 10^{5} gm$