Question

At which temperature the velocity of O₂ molecules will be equal to the rms velocity of N₂ molecules at 0°C 

(A) 93°C 

(B) 40°C 

(C) 39°C 

(D) cannot be calculated.

Answer 1

The correct option (C) 39°C

Explanation:

V_rms = √(3RT/M_O) i.e. V_rms = √(T/M_O

as rms Velocities are same,

√(T_O2 / M_O2) = √(T_N2 / M_N2)

∴ (T_O2 / T_N2) = (M_O2 / M_N2)

given  T_N2 = 0°C = 273K

M_O2 = 32 & M_N2 = 28

∴ (T_O2 / 273) = (32 / 28)

∴ T_O2 = 273 × (8/7)

= 312K

= 312 – 273 = 39°C