A container of volume of 50 cm3
contains hydrogen at a pressure of 1.0 Pa
and at a temperature of 27 0
C. Calculate (a) the number of molecules of the
gas in the container, and (b)their root-mean square speed.
( R= 8.3 J mol–1 K–1 , N = 6 × 1023 mol–1. Mass of 1 mole of hydrogen
molecule = 20 × 10–3 kg mol–1)
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volume of container , V = 50cm³ = 50ml
pressure of hydrogen, P = 1Pa = 9.869 × 10^-6 atm
temperature, T = 27°C = 27 + 273 = 300K
(a) using formula, PV = nRT
⇒9.869 × 10^-6 × 50 = n × 0.082 × 300
⇒n = 9.869 × 10^-6 × 50/(0.082 × 300)
≈ 2 × 10^-5 mol
number of molecules in the container = no of moles × 6.023 × 10²³
= 2 × 6.023 × 10²³ × 10^-5
= 1.2046 × 10^19
(b) rms speed = √{3RT/M}
R = 25/3 J/mol.K
T = 300 K
M = 20 × 10^-3 Kg/mol
so, rms speed = √{3 × 25/3 × 300/20 × 10^-3}
= √{25 × 300 × 1000/20}
= √{25 × 15 × 1000}
= 612.37 m/s
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