Page 162 - Physical Chemistry

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Reactants aA + bB (1) Products cC + dD Section 5.4
in their standard states in their standard states Determination of Standard Enthalpies
at T at T of Formation and Reaction

(2) (3)
Elements
in their standard states
at T

Figure 5.1
Steps used to relate H° of a reaction to H° of reactants and products.
f

where n is the stoichiometric number of substance i in the reaction and H° is the
i f T,i
standard enthalpy of formation of substance i at temperature T.
To prove (5.6), consider the reaction aA bB → cC dD, where a, b, c, and d are
the unsigned stoichiometric coefficients and A, B, C, and D are substances. Figure 5.1
shows two different isothermal paths from reactants to products in their standard
states. Step 1 is a direct conversion of reactants to products. Step 2 is a conversion of
reactants to standard-state elements in their reference forms. Step 3 is a conversion of
elements to products. (Of course, the same elements produced by the decomposition
of the reactants will form the products.) Since H is a state function, H is independent
of path and H H H . We have H H° for the reaction. The reverse of
1 2 3 1 T
process 2 would form aA bB from their elements; hence,
¢H a ¢ H°1A2 b ¢ H°1B2
2
f
T
f
T
where H°(A) is the standard enthalpy of formation of substance A at temperature T.
f T
Step 3 is the formation of cC dD from their elements, so
¢H c ¢ H°1C2 d ¢ H°1D2
f
3
T
T
f
The relation H H H becomes
1 2 3
¢H° a ¢ H°1A2 b ¢ H°1B2 c ¢ H°1C2 d ¢ H°1D2
T
T
f
T
T
f
T
f
f
which is Eq. (5.6) for the reaction aA bB → cC dD, since the stoichiometric
numbers n are negative for reactants.
i
There are many more chemical reactions than there are chemical substances.
Rather than having to measure and tabulate H° for every possible chemical reaction,
we can use (5.6) to calculate H° from tabulated H°values of the substances in-
f
volved, provided we have determined H° of each substance. The next section tells
f
how H° is measured.
f
5.4 DETERMINATION OF STANDARD ENTHALPIES
OF FORMATION AND REACTION
Measurement of H°
f
The quantity H° is H° for isothermally converting pure standard-state elements
T,i
f
in their reference forms to one mole of standard-state substance i. To find H° , we
T,i
f
carry out the following steps:
1. If any of the elements involved are gases at T and 1 bar, we calculate H for the
hypothetical transformation of each gaseous element from an ideal gas at T and
1 bar to a real gas at T and 1 bar. This step is necessary because the standard state