Download Chemistry 520 - Problem Set 2

Chemistry 520 - Problem Set 2
Due Wednesday January 22, 1997
For the problems below, you may assume that all gases behave ideally.
1. In lecture on Friday January 10, I proposed two reversible paths for converting H2 O(l)
at 298 K and 1 atm to vapor at the same temperature and pressure. One involved
raising the temperature to the normal boiling point of 373 K the other lowering
the pressure to the vapor pressure of water at 298 K. In class we calculated H =
44:75kJ=mol and E = 42:27kJ=mol for this process.
(a) Use this result to calculate the molar heat of vaporization (H vap ) of H2 O at
298 K and 0.0313 atm.
(b) Calculate the change in internal energy (E ) when water goes from the liquid
to the vapor phase at 298 K and 0.0313 atm.
2. The mechanism by which oxides of nitrogen (NOx) catalyze the decomposition of O3
is given below:
!
!
NO(g) + O3(g)
NO2 (g) + O(g)
NO2(g) + O2(g)
NO(g) + O2(g)
(1)
(2)
(a) Calculate H 0 and E 0 for reaction (1) above.
(b) Will your result to part (a) be dierent if ambient pressure were 0.100 atm and
the temperature was 263 K rather than 1.00 atm and 298 K? Explain why or
why not. If it is dierent, calculate E and H under these conditions. [You
can assume all of your gases behave ideally.]
3. A bomb calorimeter provides a way to measure qV for a reaction of interest by constraining it to take place in a closed vessel which is surrounded by a insulated container
of water. A gure depicting a bomb calorimeter is attached. In a typical experiment,
one rst calibrates the calorimeter by running a reaction with a known ER . By
knowing how much heat should have been released by the reaction and the change
in the temperature of the calorimeter, the heat capacity of the calorimeter can be
obtained. In a second experiment, the reaction of interest is run. By measuring the
change in the temperature of the calorimeter and equating it to the heat released by
the reaction, E R can be determined and H R can be calculated. [The calculations
you will perform for this problem are the same as those needed to analyze one of the
experiments in physical chemistry lab]
(a) A student in a physical chemistry laboratory performed such an experiment.
In the rst step, she burned a 0.825 g sample of benzoic acid (C6 H5COOH)
for which the internal energy of combustion is -3251 kJ/mol. She recorded a
temperature rise of 1.940 K. Given the above information, calculate the molar
heat capacity [in J/(mol K)] of the calorimeter.
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(b) Next a sample of the sugar D-ribose (C5 H10 O5) of mass 0.727 g was placed in the
same bomb calorimeter and then ignited in the presence of excess oxygen. The
temperature of the calorimeter rose by 0.910 K. What is E for the combustion
of D-ribose? [The products of the reaction are CO2 (g) and H2 O(l)]
(c) From your result in part (b), calculate H R , assuming that the reaction is run
at 298 K.
(d) Finally, calculate H f of D-ribose. [answer: -1267 kJ/mol]
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4. The diagram below depicts three paths by which sample of an ideal gas can go from
state A to state B.
B (0.5 L, 20 atm)
D (10 L, 20 atm)
p/atm
20
A (10 L, 1 atm)
1
C (0.5 L, 1 atm)
0.5
V/L
10
Figure 1: The cycle described in Problem 4.
(a) If the amount of gas is consistent with a temperature at point A of 313 K,
calculate the number of moles of gas and the temperature of the sample at the
three remaining points (B,C,D)
(b) Calculate the work done on the gas along the two irreversible paths ACB and
ADB.
(c) Calculate the work done on the gas if it is expanded reversibly along the isotherm
(path AB).
(d) Calculate q,E and H for each of the three paths. You may assume that the
gas behaves ideally.
5. Problem 30, Chapter 2 of Tinoco, et al.: Consider the reaction in which 1 mol of
aspartic acid (s) is converted to alanine (s) and CO2 (g) at 298 K and 1 atm of
pressure. The balanced reaction is:
H2 NCH(CH2COOH)COOH ! H2NCH(CH3)COOH + CO2
(3)
(a) How much heat is released or absorbed (in kJ/mol) by Reaction (3)?
(b) Write a cycle you could use to calculate H for the reaction at 323 K. State
what properties of the molecules you would need to know and the equations you
would use to calculate the answer.
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