Question

Molecular masses for O2 and N2 are 32 u and 28 u, respectively.

a) What is the ratio of the root mean square speeds of oxygen to nitrogen at 30 ◦ C?

b) What is the ratio at 98 ◦ C?

Answer 1

We know that, RMS = 3 k N T / M

RMS = 3 R T / M

(a) What is the ratio of the root mean square speeds of oxygen to nitrogen at 30 ⁰C?

(RMS)_oxy / (RMS)_N = (3 R T / M_oxy) / (3 R T / M_N)

(RMS)_oxy / (RMS)_N = (3 R T / M_oxy) x (M_N / 3 R T)

(RMS)_oxy / (RMS)_N = (M_N / M_oxy)

(RMS)_oxy / (RMS)_N = [(0.0028 kg/mol) / (0.0032 kg/mol)]

(RMS)_oxy / (RMS)_N = 0.875

(b) What is the ratio at 98 ⁰C?

same as part (a), we have

(RMS)_oxy / (RMS)_N = (M_N / M_oxy)

(RMS)_oxy / (RMS)_N = [(0.0028) / (0.0032)]

(RMS)_oxy / (RMS)_N = 0.875