Question

At what temperature is the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules at 46 oC? (Hint: The molar mass of hydrogen atoms is 1.008 g/mol and of nitrogen atoms is 14.007 g/mol. The molar mass of H2 is twice the molar mass of hydrogen atoms, and similarly for N2.) The answer is in degree C.

Answer 1

rms of speed of molecules is given by:

Vrms = sqrt (3kT/m)

T = m*Vrms^2/(3k)

Since we need equal rms speed for both hydrogen and nitrogen molecules, So from above equation we can see that Temperature of molecules is directly proportional to the molar mass of molecules. So

T2/T1 = m2/m1

m1 = Molar mass of hydrogen = 2*1.008

m2 = Molar mass of Nitrogen = 2*14.007

T1 = temperature of hydrogen atom = 46 C = 273.15 + 46 = 319.15 C

T2 = temperature of Nitrogen atom = ? C

So,

T2 = T1*(m2/m1)

T2 = 319.15*(2*14.007/(2*1.008))

T2 = 4434.86 K = 4434.86 - 273.15

T2 = 4161.71 C = Temperature of Nitrogen molecules