On a hot summer day, the temperature is 40.0°C and the pressure is 1.01 × 105 Pa
Let us model the air as all nitrogen of molecular mass 28.0 g/mol having molecules of diameter
0.500 nm that are moving at their root-mean-square speed. Avogadro's number is
6.02 × 1023 molecules/mol, the ideal gas constant is 8.31 J/mol ? K, and the Boltzmann constant is 1.38 × 10-23 J/K. Calculate reasonable estimates for
(a) the root-mean-square speed of the nitrogen molecules.
(b) the average distance a typical molecule travels between collisions.
(c) the average time a molecule travels between collisions, assuming that the molecules are moving at their root-mean-square speeds.
(d) the number of collisions an average molecule undergoes per second.
What will be an ideal response?
Answer:
(a) 528 m/s (b) 3.85 × 10-8 m
(c) 7.29 × 10-11 s (d) 1.37 × 1010 collisions
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