The number of molecules in one litre of an ideal gas at 300 K and 2… | JEE Main 2021 (27 Jul, Shift 1)

Q33JEE Main 2021 · 27 JUL · SHIFT 1Medium

Pressure & Kinetic Energy of a Gas

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $\times$ 10 $-$ 9 J per molecules is:

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Answer: (c)

$PV = \frac{2}{3}N\bar{E}$ , so $N = \frac{3PV}{2\bar{E}}$ .
$P = 2$ atm $= 2.026 \times 10^{5}$ Pa, $V = 10^{-3}$ m $^3$ , $\bar{E} = 2 \times 10^{-9}$ J
$N = \frac{3 \times 2.026 \times 10^{5} \times 10^{-3}}{2 \times 2 \times 10^{-9}} \approx 1.5 \times 10^{11}$
So the answer is (c) $1.5 \times 10^{11}$ .

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