If you consider the ideal gas law to be an acceptable approximation for substances that have compressibility factors within 10% of 1 (i.e., between 0.90 and 1.10), determine the range of acceptable pressures for ideal gas behavior for a gas with a temperature of 300 K if the gas is (a) hydrogen, (b) oxygen, and (c) carbon dioxide.
Given: T = 300 K, 0.9 ? Z ? 1.10
What will be an ideal response?
The compressibility chart will be used to find the values of PR at the acceptable limits of
the compressibility chart for each gas.
(a) H2: Tc = 33.3 K, Pc = 1,300 kPa
TR = T/Tc = 9.01
So, for Z = 0.90: Never achieved: take P = 0
For Z = 1.10: PR = 9, so P = PcPR = 11,700 kPa
Acceptable Pressure range: 0 ? P ? 11,700 kPa
(b) O2: Tc = 154.8 K, Pc = 5,080 kPa
TR = T/Tc = 1.94
So, for Z = 0.90: Never achieved: take P = 0
For Z = 1.10: PR = 8.7, so P = PcPR = 44,200 kPa
Acceptable Pressure range: 0 ? P ? 44,200 kPa
(c) CO2: Tc = 304.2 K, Pc = 7,390 kPa
TR = T/Tc = 0.986
So, for Z = 0.90: PR = 0.28, so P = PcPR = 2,070 kPa, and PR = 6.8, so P = 50, 200 kPa
For Z = 1.10: PR = 9.5, so P = PcPR = 70,200 kPa
Acceptable Pressure range: P ? 2,070 kPa and 50,200 kPa ? P ? 70,200 kPa
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