College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 13 - Problems - Page 499: 57


The gas occupies a volume of $0.377~m^3$

Work Step by Step

An oxygen atom consists of 8 protons and 8 neutrons. An oxygen molecule $O_2$ consists of 16 protons and 16 neutrons. The mass of one oxygen molecule is $32~u$ We can find the mass of one $O_2$ molecule: $m = (32~u)(1.66\times 10^{-27}~kg/u) = 5.312\times 10^{-26}~kg$ We can find the number of oxygen molecules in the cylinder: $N = \frac{0.532~kg}{5.312\times 10^{-26}~kg} = 1.0\times 10^{25}$ We can find the volume: $PV = NkT$ $V = \frac{NkT}{P}$ $V = \frac{(1.0\times 10^{25})(1.38\times 10^{-23}~J/K)(273~K)}{1.0\times 10^5~Pa}$ $V = 0.377~m^3$ The gas occupies a volume of $0.377~m^3$
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