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# A home owner uses

Question:

A home owner uses $4.00 \times 10^{3} \mathrm{~m}^{3}$ of methane $\left(\mathrm{CH}_{4}\right)$ gas, (assume $\mathrm{CH}_{4}$ is an ideal gas) in a year to heat his home. Under the pressure of $1.0 \mathrm{~atm}$ and $300 \mathrm{~K}$, mass of gas used is $\times \times 10^{5} \mathrm{~g}$. The value of $x$ is _________ (Nearest integer)

(Given $\mathrm{R}=0.083 \mathrm{~L}$ atm $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$ )

Solution:

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

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

Weight of $\mathrm{CH}_{4}$

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

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