Physical Chemistry Third Edition

2.7 Calculation of Enthalpy Changes of a Class of Chemical Reactions 93

changes (see Chapter 7). The calculation is more complicated. We will not discuss that

case.

EXAMPLE2.32

Find the final temperature if the reaction of Eq. (2.7-1) is carried out adiabatically at constant

pressure beginning at 298.15 K. Assume that a stoichiometric mixture is present before the

reaction and that the reaction proceeds to completion. Assume that the heat capacity of water

vapor is constant and equal to its value at 2000 K.

Solution

The reaction as written in Eq. (2.7-1) includes liquid water as the product. In our case

the water produced will be a vapor, so we calculate∆H◦at 298.15 K for the gaseous

product:

∆H◦(298.15 K) 2 ∆fH◦(H 2 O(g))− 0 − 0

2(− 241 .818 kJ mol−^1 )− 483 .636 kJ mol−^1 −483636 J mol−^1

CP(products)2(51.18JK−^1 mol−^1 ) 102 .36JK−^1 mol−^1

∫T 2

298 .15 K

(

102 .36JK−^1 mol−^1

)

dT−483636 J mol−^1  0

(

102 .36JK−^1 mol−^1

)

(T 2 − 298 .15 K)483636 J mol−^1

T 2 5023 K≈5000 K

This result might be inaccurate because of the actual dependence of the heat capacity of water

vapor on temperature.

Exercise 2.28

Find the final temperature if a stoichiometric mixture of methane and oxygen is ignited at

298.15 K and allowed to react adiabatically at a constant pressure. Assume that the reaction

proceeds to completion and that the heat capacities of the products are constant and equal to their

values at 2000 K.

If heat capacities are represented by polynomials as in Table A.6, a more nearly

accurate final temperature can be calculated. This leads to a nonlinear equation, which

can be solved by trial and error or by other numerical techniques.

Exercise 2.29

Using the parameters from Table A.6, find the final temperature after the adiabatic combustion

of the stoichiometric mixture of hydrogen and oxygen in Example 2.32.