Physical Chemistry Third Edition

90 2 Work, Heat, and Energy: The First Law of Thermodynamics

Process 2: Isothermal reaction at temperature T 2

Process 1: Isothermal reaction at temperature T 1

Reactants

T

T 1

T 2

Products

Process 3: Temperature change of

reactants from

T^2

to

T^1

Process 4: Temperature change of

products from

T^1

to

T^2

Figure 2.10 The Process to Calculate∆H(T 2 )from∆H(T 1 ).

T 1 toT 2. According to Hess’s law∆H(T 2 ) is equal to the sum of the enthalpy changes

of processes 1, 2, and 3:

∆H(T 2 )∆H 3 +∆H 1 +∆H 4 ∆H 3 +∆H(T 1 )+∆H 4 (2.7-16)

For 1 mol of reaction, process 3 consists of changing the temperature of an amount

of each reactant equal to the magnitude of its stoichiometric coefficient, so that

∆H 3 

∫T 1

T 2

∑s

i 1

|νi|CP, m(i)dT

(reactants only in sum)



∫T 2

T 1

∑s

i 1

νiCP, m(i)dT

(reactants only in sum)

(2.7-17)

whereCP, m(i) is the molar heat capacity of substancei. The second equality comes from

interchanging the limits of integration and realizing that the stoichiometric coefficients

of reactants are negative. Process 4 is the change in temperature of the products from

T 1 toT 2 , so that

∆H 4 

∫T 2

T 1

∑s

i 1

νiCP, m(i)dT

(products only in sum)

(2.7-18)

The sums in Eqs. (2.7-17) and (2.7-18) can be combined to give the expression

∆H(T 2 )∆H(T 1 )+

∫T 2

T 1

∆CPdT (2.7-19)

where

∆CP

∑s

i 1

νiCP, m(i) (2.7-20)