Physical Chemistry Third Edition

92 2 Work, Heat, and Energy: The First Law of Thermodynamics

Process 3: Temperature change of products (and possibly

remaining reactants) to final temperature of adiabatic reaction

Process 2: Isothermal reaction

at temperature T 1

T 2

T 1

Process 1: Adiabati

c reaction

Reactants Products

T

Figure 2.11 The Process to Calculate the Final Temperature of an Adiabatic

Reaction.

of a system in which a chemical reaction takes place adiabatically, we consider the

processes shown in Figure 2.11. Process 1 is the adiabatic reaction, for which∆His

equal to zero. Process 2 is the reaction carried out isothermally. Process 3 is the change

in temperature of the products plus any remaining reactants to the same final state as

process 1. Because enthalpy is a state function, the enthalpy change of process 1 is

equal to the sum of the enthalpy changes of processes 2 and 3:

∆H 1 ∆H 2 +∆H 3  0 (2.7-22)

If a stoichiometric mixture is taken and if the reaction proceeds to completion, there

are no remaining reactants, and we can write

∆H 3 

∫T 2

T 1

∑s

i 1

νiCP, m(i)dT

(products only in sum)

−∆H 2 (2.7-23)

This equation can be solved forT 2 if the values of the heat capacities are known as

a function of temperature. If there are remaining amounts of some reactants, their

heat capacities must be added to the sum in Eq. (2.7-23). If the reaction comes

to equilibrium short of completion, the equilibrium can shift as the temperature