A gaseous mixture of O2 (molecular mass 32 u) and N2 (molecular mass 28 u) is maintained at constant temperature. What is the ratio vrms(N2)/vrms(O2) of the root-mean-square speeds of the molecules?
A. 7/8
B. √(7/8)
C. √(8/7)
D. (8/7)2
E. ln (8/7)
(GR0177 #48)
Solution:
Kinetic energy, E = 1/2 mv2
1/2 mv2 = 3/2 kT
v2 = 3kT/m
vrms = √(3kT/m)
vrms ∝ √(1/m)
vrmsN2 / vrmsO2
= √(mO2 / mN2 )
= √(32u/28u)
= √(8/7)
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