Physical Chemistry Third Edition

2.7 Calculation of Enthalpy Changes of a Class of Chemical Reactions 87

In a mixture of ideal gases, each substance behaves as though the others were absent. If

all substances are either pure liquids or solids or ideal gases the enthalpy of the system

is a sum of contributions of the separate substances

H

∑s

i 1

niHm(i) (2.7-8)

whereHm(i) is the molar enthalpy (enthalpy per mole) of substance numberiandni

is the amount (in moles) of that substance.

Consider a chemical reaction that begins with reactants in equilibrium or metastable

states at some particular temperature and pressure and ends with products in equilibrium

states at the same temperature and pressure. The enthalpy change of the reaction is

given by

∆HH(final)−H(initial)

∑s

i 1

∆niHm(i) (2.7-9)

where∆niis the change in the amount of substance numberi. We say thatone mole

of reactionoccurs if

∆niνi (2.7-10)

for each substance. That is, a number of moles of a product appears that is equal to that

product’s stoichiometric coefficient, and a number of moles of a reactant disappear that

are equal to the magnitude of its stoichiometric coefficient. For 1 mol of reaction,

∆H

∑s

i 1

νiHm(i) (2.7-11)

We use dimensionless stoichiometric coefficients. One can think of the units ofνi

as moles of substanceiper mole of reaction. The enthalpy change in Eq. (2.7-11)

has the units of J mol−^1 (meaning joules per mole of the reaction as written). If all

stoichiometric coefficients are doubled,∆Hfor the reaction doubles. When we give a

value of∆Hfor a reaction, it is always for 1 mol of the reaction as the reaction equation

is written.

The molar enthalpy of any substance depends on its state. Thestandard stateof

a liquid or solid substance is specified to be the pure substance at a fixed pressure

of exactly 1 bar (100,000 Pa), which we denote byP◦. The standard state for a gas

is defined to be the corresponding ideal gas at pressureP◦. The difference between

the molar enthalpy of a real gas at 1 bar pressure and the corresponding ideal gas at

1 bar is numerically very small, but we will discuss this difference in a later chapter.

If substance numberiis in its standard state, its molar enthalpy is denoted byHm◦(i).

Astandard-state reactionis one in which all substances are in their standard states

before and after the reaction. The enthalpy change for a standard-state reaction is

denoted by∆H◦. The standard-state pressure was at one time defined to equal 1 atm

(101,325 Pa). The difference in numerical values is small, and the formulas involving

P◦are the same with either choice. For highly accurate work, one must determine

which standard pressure was used for an older set of data.

Actual values for standard-state molar enthalpies are not available because an arbi-

trary constant can be added to each internal energy without any physical effect. We

use thestandard-state enthalpy change of formationto calculate∆H◦for chemical

reactions. The standard-state enthalpy change of formation of substanceiis denoted