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A mixture of gases consists of 0.1 kg of oxygen, 1 kg of
Chapter 13, Problem 88P(choose chapter or problem)
A mixture of gases consists of 0.1 kg of oxygen, 1 kg of carbon dioxide, and 0.5 kg of helium. This mixture is compressed to 17,500 kPa and \(20^{\circ} \mathrm{C}\). Determine the mass of this gas contained in a \(0.3 \mathrm{~m}^{3}\) tank
(a) treating it as an ideal gas mixture,
(b) using a compressibility factor based on Dalton’s law of additive pressures,
(c) using a compressibility factor based on the law of additive volumes, and
(d) Kay’s psuedocritical pressure and temperature.
Questions & Answers
QUESTION:
A mixture of gases consists of 0.1 kg of oxygen, 1 kg of carbon dioxide, and 0.5 kg of helium. This mixture is compressed to 17,500 kPa and \(20^{\circ} \mathrm{C}\). Determine the mass of this gas contained in a \(0.3 \mathrm{~m}^{3}\) tank
(a) treating it as an ideal gas mixture,
(b) using a compressibility factor based on Dalton’s law of additive pressures,
(c) using a compressibility factor based on the law of additive volumes, and
(d) Kay’s psuedocritical pressure and temperature.
ANSWER:Step 1 of 12
Given Data:
Mass of \({O_2}\), \({m_{{O_2}}} = 0.1\;{\rm{kg}}\)
Mass of \(C{O_2}\), \({m_{C{O_2}}} = 1\;{\rm{kg}}\)
Mass of \(He\), \({m_{He}} = 0.5\;{\rm{kg}}\)
Mixture pressure, \({P_{total}}\) = \(17,500\;{\rm{kPa}}\)
The volume of the tank, \(V = 0.3\;{{\rm{m}}^3}\)
Mixture temperature,
\({T_m} = 20^\circ {\rm{C}}\)
\( = 20 + 273.15\)
\( = 293.15\;{\rm{k}}\)
Volume of the tank, \({V_m} = 0.3\;{{\rm{m}}^3}\)
From the property tables, the molar masses are as follows.
\({M_{{O_2}}} = 31.999\;\frac{{{\rm{kg}}}}{{{\rm{kmol}}}}\)
\({M_{C{O_2}}} = 44.01\;\frac{{{\rm{kg}}}}{{{\rm{kmol}}}}\)
\({M_{He}} = 4.003\;\frac{{{\rm{kg}}}}{{{\rm{kmol}}}}\)
The gas constants are as follows.
\({R_{{O_2}}} = 0.2598\;\frac{{{\rm{kJ}}}}{{{\rm{kg}} \cdot {\rm{K}}}}\)
\({R_{C{O_2}}} = 0.1889\;\frac{{{\rm{kJ}}}}{{{\rm{kg}} \cdot {\rm{K}}}}\)
\({R_{He}} = 2.0769\;\frac{{{\rm{kJ}}}}{{{\rm{kg}} \cdot {\rm{K}}}}\)
The critical properties are as follows.
For \({O_2}\):
\({T_{cr,{O_2}}} = 154.8\;{\rm{K}}\)
\({P_{cr,{O_2}}} = 5080\;{\rm{kPa}}\)
For \(C{O_2}\):
\({T_{cr,C{O_2}}} = 304.2\;{\rm{K}}\)
\({P_{cr,C{O_2}}} = 7390\;{\rm{kPa}}\)
For \(He\):
\({T_{cr,He}} = 5.3\;{\rm{K}}\)
\({P_{cr,He}} = 230\;{\rm{kPa}}\)