Physical Chemistry , 1st ed.

process that occurs at a temperature different from that cited by available data
(usually 25.0°C). In addition to Hat 25.0°C, we need to know the heat ca-
pacities of the products and reactants. Given that information,HT,where T
is any temperature, is given by the sum of:

1. The heat,q, needed to bring the reactants to the temperature specified by
   the data (usually 298 K)


2. The heat of reaction,H, at that temperature (which can be determined
   from tabulated data)


3. The heat,q, needed to bring the products backto the desired reaction
   temperature
   Using H 1 ,H 2 , and H 3 to label the three heat values listed above, we can
   write expressions for each step. Step 1 is a change-in-temperature process that
   uses the fact that H 1 qpmcT. The heat capacity used in this ex-
   pression is the combined heat capacity of all of the reactants, which must be
   included stoichiometrically. That is, if there are 2 moles of one reactant, its heat
   capacity must be included twice, and so on. One must consider whether H 1
   represents an exothermic (heat out;His negative) or an endothermic (heat
   in;His positive) change. For step 2,H 2 is simply rxnH°. For step 3,H 3
   is similar to H 1 , except that now it is the products that must be taken from
   the specified temperature to whatever final temperature is necessary (again,
   keeping track of whether the process is endothermic or exothermic). In this
   third step, the heat capacities of the productsare needed. The overall HTis
   the sum of the three enthalpy changes, as Hess’s law and the fact that enthalpy
   is a state function require. The following example illustrates.

Example 2.19

Determine H 500 for the following reaction at 500 K and constant pressure:

CO (g) + H 2 O (g) →CO 2 (g) + H 2 (g)

The following data are necessary:

Substance Cp fH(298 K)

CO 29.12 110.5

H 2 O 33.58 241.8

CO 2 37.11 393.5

H 2 29.89 0.0

where the units for Cpare J/molK and the units for fHare kJ/mol. Assume

molar quantities.

Solution

First, we have to take CO and H 2 O from 500 K to 298 K, a Tof202 K.

For one mole of each, the heat (which equals the enthalpy change) is

H 1 q

(1 mol)29.12 

mo

J

lK

(202 K) + (1 mol)33.58 

mo

J

lK

(202 K)

H 1 12,665 J 12.665 kJ

For the second step, we need to evaluate Hfor the reaction at 298 K. Using

the products-minus-reactants approach, we find

2.11 Changing Temperatures 59