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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]

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2.4 × 1020

2.4 × 1021

2.4 × 1022

2.4 × 1023

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detailed solution

Correct option is C

The number of molecules (n) in a volume (V) at pressure p and temperature T is given by n=pVkBTHere, p = 106 dyne cm-2, V = 100 cm3, T = 273 + 27 = 300 K, kB= 1.38 × 10-16 erg per kelvin∴ n=106(1000)1.38×10-16×300≈2.4×1022

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The number of molecules in a litre of a gas at temperature of 27°C and a pressure of 106 dyne cm-2 is [UP CPMT 2013]

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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]