2.26.A refrigerator contains approximately 17 cubic feet, or
about 480 liters, of air. Assuming it acts as an ideal gas with a
CVof 12.47 J/molK, what is the change in Uin cooling the air
from normal room temperature (22°C) to refrigerator temper-
ature (4°C)? Assume an initial pressure of 1.00 atm.
2.27.What are the units on each term of the equation for CV
given in part b of Example 2.10?
2.28.Starting with equation 2.27 and the original definition
of enthalpy, derive the fact that CpCV+ R.
2.29.Derive the fact that ( H/ p)Tis also zero for an ideal gas.
2.30.Define isobaric, isochoric, isenthalpic, and isothermal.
Can a change in a gaseous system be isobaric, isochoric, and
isothermic at the same time? Why or why not?
2.7 Joule-Thomson Coefficients
2.31.Starting from the cyclic rule involving the Joule-
Thomson coefficient, derive equation 2.35.
2.32.The ideal gas law is the equation of state for an ideal
gas. Why can’t it be used to determine ( T/ p)H?
2.33.For a gas that follows the van der Waals equation of
state, the inversion temperature can be approximated as 2a/Rb.
Using Table 1.6, calculate the inversion temperatures of He
and H 2 and compare them to their values of 40 K and 202 K,
respectively. What are the implications of these inversion tem-
peratures with regard to liquefaction of these two gases?
2.34.Estimate the final temperature of a mole of gas at 200.00
atm and 19.0°C as it is forced through a porous plug to a fi-
nal pressure of 0.95 atm. The JTof the gas is 0.150 K/atm.
2.35.With regard to exercise 2.34, how accurate do you
think your answer is, and why?
2.36.Someone proposes that the Joule-Thomson coefficient
can also be defined as
JT(^ UC/^
Vp)T
Is this definition valid? Why or why not?
2.8 Heat Capacities
2.37.Why is equation 2.37 written in terms of CVand Cpand
not CVand Cp?
2.38.What are the numerical values of the heat capacities Cp
and CVof a monatomic ideal gas, in units of cal/molK and
Latm/molK?
2.39.In a constant-pressure calorimeter (that is, one that ex-
pands or contracts if the volume of the system changes), 0.145
mol of an ideal gas contracts slowly from 5.00 L to 3.92 L. If
the initial temperature of the gas is 0.0°C, calculate the U
and wfor the process.
2.40.What is the final temperature of 0.122 mole of ideal gas
that performs 75 J of work adiabatically if the initial tempera-
ture is 235°C?
2.41.Derive equation 2.44 from the previous step.
2.42.Show that (CpCV)/CVequals ^23 for a monatomic
ideal gas.
2.43.What is for an ideal diatomic gas? (See footnote in
section 2.8.)
2.44.In orbit about Earth, a weather balloon jettisons a weight
and ascends to a higher altitude. If the initial pressure inside
the balloon is 0.0033 atm and it ascends to an altitude where
the pressure is 0.00074 atm, by what fraction does the ab-
solute temperature change? Assume that the balloon is filled
with helium, a good approximation of an ideal gas, and that
the change is adiabatic.2.9 & 2.10 Phase and Chemical Changes
2.45.Take the volume change into account and calculate H
and Ufor exactly 1 g of ice melting into 1 g of water at stan-
dard pressure. The density of ice at 0° is 0.9168 g/mL; the
density of water at 0° is 0.99984 g/mL.
2.46.How much work is performed by 1 mole of water freez-
ing to 1 mole of ice at 0°C at standard pressure? Use the den-
sities from the previous exercise.
2.47.Why are steam burns so much worse than water burns
even if the H 2 O is at the same temperature for both phases?
(Hint:consider the heat of vaporization of water.)
2.48.How many grams of water at 0°C will be melted by the
condensation of 1 g of steam at 100°C?
2.49.Citrus farmers sometimes spray their trees with water if
the temperature is expected to go below 32°F, in the hopes
that this will keep the fruit from freezing. Why would farmers
think that?
2.50.Draw a diagram like Figure 2.11 that illustrates the
change in enthalpy for the chemical reaction
C (s) + 2H 2 (g) →CH 4 (g)
which is exothermic by 74.8 kJ/mol.
2.51.Determine the rxnH(25°C) of the following reaction:
H 2 (g) + I 2 (s) →2HI (g)
2.52.Determine rxnH(25°C) for the following reaction:
NO (g) + ^12 O 2 (g) →NO 2 (g)
This reaction is a major participant in the formation of smog.
2.53.Using Hess’s law, write out all of the formation reactions
that add up to, and calculate rxnH(25°C) for, the following
reaction:
2NaHCO 3 (s) →Na 2 CO 3 (s) + CO 2 (g) + H 2 O ()
(This reaction occurs when one uses baking soda to smother
a fire in the kitchen.)
2.54.The thermite reaction combines aluminum powder and
iron oxide and ignites the mixture to make aluminum oxide
and iron. So much energy is given off that the iron product
frequently is molten. Write a balanced chemical reaction for
the thermite process and determine its H(25°C).
2.55.Benzoic acid, C 6 H 5 COOH, is a common standard used
in bomb calorimeters, which maintain a constant volume. If
1.20 g of benzoic acid gives off 31,723 J of energy when
burned in the presence of excess oxygen at a constant tem-
perature of 24.6°C, calculate q, w, H, and Ufor the reaction.64 Exercises for Chapter 2