Question

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)

Answer 1

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