Physical Chemistry: Thermodynamics, Structure, and Change

Published by W. H. Freeman
ISBN 10: 1429290196
ISBN 13: 978-1-42929-019-7

Chapter 1 - Topic 1B - The kinetic model - Exercises - Page 56: 1B.2(b)

Answer

$CO_2: v_{rms} = 408 \space m/s$ $He: v_{rms} = 1.35 \times 10^3 \space m/s$

Work Step by Step

$$v_{rms} = \Bigg( \frac{3RT}{M} \Bigg)^{1/2}$$ $$R = 8.3145 \space JK^{-1}mol^{-1}$$ $$20^o \space C = (20 + 273)K = 293 \space K$$ $CO_2$: $M = 1*12.0 + 2*16.0 = 44.0 \space g/mol = 0.0440 \space kg/mol$ $$v_{rms} = \Bigg( \frac{3(8.3145 \space JK^{-1}mol^{-1})(293 \space K)}{0.0440 \space kg/mol} \Bigg)^{1/2}$$ $$v_{rms} = 408 \space m/s$$ $He$: $M = 4.00 \space g/mol = 0.00400 \space kg/mol$ $$v_{rms} = \Bigg( \frac{3(8.3145 \space JK^{-1}mol^{-1})(293 \space K)}{0.00400 \space kg/mol} \Bigg)^{1/2}$$ $$v_{rms} = 1.35 \times 10^3 \space m/s$$
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