Chem 338 Homework Set 5 Solutions Workseet Page 5
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55.21) Use the phase diagram in Fig. 5.17 to state what would be observed when a
sample of carbon dioxide, initially at 1.0 atm and 298 K, is subjected to the
following cycle: (a) constant-pressure heating to 320 K, (b) isothermal
compression to 100 atm, (c) constant-pressure cooling to 210 K, (d) isothermal
decompression to 1.0 atm, (e) constant-pressure heating to 298 K.
a) CO
is a gas at the initial conditions and as the gas heats at constant pressure, its
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molar volume increases
b) it stays a gas during the isothermal compression, but its molar volume greatly
decreases and it becomes very dense. Note that this final temperature and
pressure are above the critical point, hence the gas is now supercritical.
c) As the gas is cooled from 320 K it condenses to a liquid at the critical
temperature, but without a discernable phase transition. No pause in the
temperature drop would be observed if we were withdrawing heat at a constant
rate. During this process the molar volume decreases. At about 220 K, we
would observe a sharp liquid-solid phase transition with its accomanying pause in
the temperature drop. The molar volume also will decrease as all of the liquid is
converted into solid. At the final temperature, CO
is a solid.
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d) The molar volume slightly increases as we go from 100 atm to 1.0 atm at
constant temperature. At a pressure of about 2 atm, a sharp phase transition
would be observed as the solid sublimes directly to the gas phase. A large
increase in the molar volume is observed.
e) The gas expands slightly back to its original molar volume.
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