Physical Chemistry Third Edition

2.7 Calculation of Enthalpy Changes of a Class of Chemical Reactions 91

All reactants and products are included in this sum. Because reactants have negative

stoichiometric coefficients,∆CPis the heat capacity of the appropriate numbers of

moles of products minus the heat capacity of the appropriate numbers of moles of

reactants. If∆CPcan be assumed to be constant, Eq. (2.7-19) becomes

∆H(T 2 )∆H(T 1 )+∆CP(T 2 −T 1 )(∆CPconstant) (2.7-21)

Remember that this equation applies only if the reactants and the products are both at

temperatureT 2.

EXAMPLE2.31

Using heat capacity data from Table A.8 of Appendix A and assuming the heat capacities to

be independent of temperature, find the standard-state enthalpy change at 373.15 K for the

reaction of Eq. (2.7-6).

Solution

∆CP◦ 2 C◦P, m(NO 2 )+(−1)C◦P, m(N 2 O 4 )

2(36.874JK−^1 mol−^1 )+(− 1 )(77.256JK−^1 mol−^1 )

− 3 .508JK−^1 mol−^1 − 0 .003508 kJ K−^1 mol−^1

Using the value of∆H◦(298.15 K) from the previous example,

∆H◦(298. 15 K) 57 .11 kJ mol−^1 +

(

− 0 .003508 kJ K−^1 mol−^1

)

(75.00 K)

 57 .11 kJ mol−^1 − 0 .263 kJ mol−^1  56 .85 kJ mol−^1

Reactions Other Than Standard-State Reactions

If the products and reactants are not at their standard states, the enthalpy change for

a reaction can have a different value from that of the standard-state reaction. For the

reactions in our present class this difference is small. The enthalpy of an ideal gas does

not depend on the pressure, and the enthalpies of real gases are nearly constant for

moderate pressure changes. The effect on the enthalpy of pure solids and liquids due

to moderate changes in pressures is also small. In a later chapter we will learn how to

calculate these effects, but unless there is some need for great accuracy we will use the

value of the standard-state enthalpy change at another pressure.

Adiabatic Chemical Reactions

We have discussed reactions in which the final temperature is the same as the initial

temperature. The enthalpy change will have a different value if the temperature of the

system changes during the reaction. One case of interest is that the chemical reaction

takes place adiabatically at constant pressure. In this case the enthalpy change is equal

to the heat transferred, which is equal to zero. In order to compute the final temperature