A container is filled with $5.6 L$ methane gas at $N T P .$ Calculate (i) the number of moles of gas (ii) the mass of gas and (iii) the number of molecules of gas.

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Solution

At $N T P$ means $T = 20^{0} C = 293.15 K$ .
Pressure $= 1 a t m = 101325 P a$ .
$5.6$ litre of methane $= \frac{5.6}{1000} = 5.6 \times 10^{- 3}$ Cubic meter.
(i) The amount of methane $= \frac{101325 \times 5.6 \times 10^{- 3}}{293.15 \times 8.3144} = 232.806 \times 10^{- 3}$ moles.
(ii) $5.6 L$ of gas at $N T P$ are found to have a mass of $11 g$ .
$22.4 L$ of gas at $S T P = 1$ mole
$5.6 L$ of gas at $S T P = \frac{5.6}{22.4} \times 16 = 4 g m$ of methane.
(iii) Number of molecules of ${C H}_{4}$ in $5.6$ lit.
$= \frac{5.6 \times 6.022 \times 10^{23}}{22.4 l i t} = 1.5 \times 10^{23}$ molecules.

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