PHYSICAL CHEMISTRY IN BRIEF

CHAP. 5: THERMOCHEMISTRY [CONTENTS] 134

5.3 Kirchhoff’s law—dependence of the reaction enthalpy on temperature

For the derivative of the reaction enthalpy with respect to the temperature of the general
reaction (5.1) we have (
∂∆rH
∂T

)

p

= ∆Cp, (5.14)

where

∆Cp=r Cpm(R) +s Cpm(S) + ··· −a Cpm(A)−b Cpm(B)− ···=

∑n

i=1

νiCpmi. (5.15)

Equation (5.14) follows from the definition of the reaction enthalpy (5.3) and from the definition
of the isobaric heat capacity (3.18). By integrating (5.14) from temperatureT 1 toT 2 we obtain

∆rH(T 2 ) = ∆rH(T 1 ) +

∫T 2

T 1

∆CpdT , [p]. (5.16)

This relation is called Kirchhoff’s law. It allows us to convert reaction enthalpies from one
temperature to another if we know the dependence of the heat capacities of substances on
temperature.

Note:∆rH(T 2 ) is the reaction enthalpy of a reaction that took place at temperatureT 2 ,

i.e. both the reactants and products have the same temperatureT 2.

Example

Based on the result of the preceding example and the data on the molar isobaric heat capacities

of substances, calculate the enthalpy of combustion of methane at temperature 1500 K. How

will the enthalpy of combustion change if we use air (approximately 20 mole percent O 2 , 80

mole percent N 2 ) instead of oxygen for methane combustion? Data: Cpm(CO 2 ) = 51. 0 J/mol,

Cpm(H 2 O(g)) = 39. 8 J/mol,Cpm(CH 4 ) = 66. 9 J/mol,Cpm(O 2 ) = 33. 7 J/mol,Cpm(N 2 ) = 34. 8

J/mol.