Page 164 - Physical Chemistry

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are studied in a constant-volume calorimeter. Reactions not involving gases are stud- Section 5.4
ied in a constant-pressure calorimeter. Determination of Standard Enthalpies
of Formation and Reaction
The standard enthalpy of combustion H° of a substance is H° for the reac-
T
c
T
tion in which one mole of the substance is burned in O . For example, H° for solid ∆ H°
c
2
glycine is H° for reaction (5.7). Some H° values are plotted in Fig. 5.3. c 298
298
c
An adiabatic bomb calorimeter (Fig. 5.4) is used to measure heats of combus-
tion. Let R stand for the mixture of reactants, P for the product mixture, and K for the
bomb walls plus the surrounding water bath. Suppose we start with the reactants at
25°C. Let the measured temperature rise due to the reaction be T. Let the system be
the bomb, its contents, and the surrounding water bath. This system is thermally insu-
lated and does no work on its surroundings (except for a completely negligible amount
of work done by the expanding water bath when its temperature rises). Therefore q
0 and w 0. Hence U 0 for the reaction, as noted in step (a) of Fig. 5.4.
After the temperature rise T due to the reaction is accurately measured, one
cools the system back to 25°C. Then one measures the amount of electrical energy U el
that must be supplied to raise the system’s temperature from 25°C to 25°C T; this
is step (b) in Fig. 5.4. We have U U VIt, where V, I, and t are the voltage, cur-
el
b
rent, and time.
The desired quantity U 298 (where r stands for reaction) is shown as step (c).
r
The change in the state function U must be the same for path (a) as for path (c) (b),
since these paths connect the same two states. Thus U U U and 0
a
c
b
U 298 U . Hence U 298 U , and the measured U enables U 298 to be
el
r
r
r
el
el
found.
Instead of using U , we could use an alternative procedure. We have seen that
el
U 298 U (Fig. 5.4b). If we imagine carrying out step (b) by supplying heat q b
b
r
to the system K P (instead of using electrical energy), then we would have U Figure 5.3
b
q C K P T, where C K P is the average heat capacity of the system K P over the Standard enthalpies of combustion
b
temperature range. Thus at 25°C. The scale is logarithmic.
The products are CO (g) and
¢ U 298 C K P ¢T (5.8) H O(l). 2
r
2
To find C K P , we repeat the combustion experiment in the same calorimeter using ben-
zoic acid, whose U of combustion is accurately known. For burning the benzoic acid,
let U , P , and T denote U 298 of reaction, the reaction products, and the tem-
r
298
perature rise. Similar to Eq. (5.8), we have U 298 C K P T . Measurement of
r

R + K ∆U = 0 P + K
at 25°C (a) at 25°C + ∆T

(c) (b) U e1 Figure 5.4
∆ r U 298
P + K (a) An adiabatic bomb calorimeter.
at 25°C The shaded walls are adiabatic.
(b) Energy relations for this
(a) (b) calorimeter.