Question

The density of hydrogen at 0°C and 760 mm Hg pressure is 0.00009 g/cc. What is the rms speed (cm/sec) of hydrogen molecules?
(A) 3.9 × 104 (B) 2.5 × 104 (C) 1.0 × 104 (D) 1.84 × 105

Answer 1

answer : option (D) 1.84 × 10^5

explanation : we know, rms Velocity is given as V = √{3RT/M}.....(1)

and density of an ideal gas is given as, ρ = PM/RT......(2)

from equations (1) and (2),

v = √{3P/ρ}

here, v represents rms velocity, P is pressure and ρ is density of gas.

here given, P = 760 mmHg ≈ 101325 Pascal.

ρ = 0.00009 g/cc = 9 × 10^-5 g/cm³

= 9 × 10^-5 (10^-3 kg)/(10^-6 m³)

= 9 × 10^-2 kg/m³

now rms velocity, v = √{3 × 101325/9 × 10^-2}

= 1837.8 m/s

= 1.8378 × 10^5 cm/s

≈ 1.84 × 10^5 cm/s

hence, option (D) is correct choice.