PHYSICAL CHEMISTRY IN BRIEF

CHAP. 5: THERMOCHEMISTRY [CONTENTS] 129

whereHmiis the molar enthalpy of a pure substance i. If a reaction proceeds at constant
volume and no work is performed, the heat of reaction is equal to theinternal energy of
reaction, i.e. to the difference between the internal energies of the products and reactants

Qr = ∆rU=

∑

i=R,S,···

Ui−

∑

i=A,B,···

Ui

= rUm,R+sUm,S+···−aUm,A−bUm,B−···=

∑n

i=1

νiUmi, [T, V]. (5.4)

Other thermodynamic quantities of reaction, e.g. thereaction entropy∆rSor thereaction
Gibbs energy∆rG, are defined similarly as the reaction enthalpy and the reaction internal
energy.

Note:Note that the heat of reaction and thermodynamic quantities of reaction are defined

for an idealized process with both reactants and products in their respective standard

states (as pure substances). The changes in thermodynamic quantities caused by the

mixing of substances are not considered here.

5.1.1 Linear combination of chemical reactions

If we multiply all stoichiometric coefficients of the general reaction

a 1 A +b 1 B +···=r 1 R +s 1 S +··· (5.5)

by an arbitrary numberα, and the stoichiometric coefficients of the reaction

a 2 A +b 2 B +···=r 2 R +s 2 S +··· (5.6)

by an arbitrary numberβ, and add these two reactions, we obtain the reaction

(αa 1 +βa 2 ) A + (αb 1 +βb 2 ) B +···= (αr 1 +βr 2 ) R + (αs 1 +βs 2 ) S, (5.7)

which is called thelinear combination of reactions(5.5) and (5.6). The linear combination
of a greater number of chemical reactions is defined in a similar way.