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laws

Question

The number of molecules in a litre of a gas at temperature of 27°C and a pressure of $10^{6} dyne {cm}^{- 2}$ is [UP CPMT 2013]

Easy

A

$2.4 \times 10^{20}$
B

$2.4 \times 10^{21}$
C

$2.4 \times 10^{22}$
D

$2.4 \times 10^{23}$

Solution

The number of molecules (n) in a volume (V) at pressure p and temperature T is given by
$n = \frac{p V}{k_{B} T}$
Here, p = $10^{6} dyne {cm}^{- 2}$ , V = 100 cm³,
T = 273 + 27 = 300 K,
$k_{B} = 1.38 \times 10^{- 16}$ erg per kelvin
$∴ n = \frac{(10^{6}) (1000)}{1.38 \times 10^{- 16} \times 300} \approx 2.4 \times 10^{22}$

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