Physical Chemistry Third Edition

88 2 Work, Heat, and Energy: The First Law of Thermodynamics

by∆fH◦(i) and is defined to be the standard-state enthalpy change of the chemical

reaction that forms 1 mol of substanceiin the specified phase from the appropriate

elements in the standard state in their most stable forms. For example, the most stable

form of carbon at 1 bar is graphite, not diamond, so that standard enthalpy changes of

formation are relative to graphite, not diamond.^5 Standard-state enthalpy changes of

formation for a number of substances are listed in Table A.8 of Appendix A.

The enthalpy change for 1 mol of any standard-state reaction in our restricted class

is given by

∆H◦

∑s

i 1

νi∆fH◦(i) (2.7-12)

We can show this equation to be correct from the fact that the enthalpy is a state

function. Let process 1 convert the reactants into elements in their most stable form.

The standard-state enthalpy change for process 1 is

∆H 1 ◦Helements−Hreactants

∑s

i 1

νi∆fH◦(i)

(reactants only)

(2.7-13)

This process is equivalent to the reverse of all of the formation reactions multi-

plied by the magnitude of the stoichiometric coefficients. The sign in front of the

sum in Eq. (2.7-13) is positive because the stoichiometric coefficients are

negative.

The products of the reaction must contain the same elements in the same amounts

as in the reactants. Let process 2 be the production of the products of the reaction of

interest from the elements produced in process 1. The standard-state enthalpy change

of process 2 is

∆H 2 ◦

∑s

i 1

νi∆fH◦(i)

(products only)

(2.7-14)

We now invokeHess’s law, which states:The enthalpy change of any process that is

equivalent to successively carrying out two other processes is equal to the sum of the

enthalpy changes of those two processes.This law is a consequence of the fact that

enthalpy is a state function, so that its change is path-independent.

Germain Henri Hess, 1802–1850, was
a Swiss-Russian chemist whose law
first showed that thermodynamics
applies to chemistry.
Our reaction is equivalent to the sum of processes 1 and 2. By Hess’s law,

∆H

◦



∑s

i 1

νi∆fH◦(i)

(reactants only)

+

∑s

i 1

νi∆fH◦(i)

(products only)



∑s

i 1

νi∆fH◦(i) (2.7-15)

where the final sum includes all substances involved in the reaction. This equation is

the same as Eq. (2.7-12). This equation applies only if the final temperature is equal to

the initial temperature.

(^5) An exception is made for phosphorus, which has several solid forms (called allotropes). The less reactive
red form is specified instead of the more reactive white form, which is more stable in the absence of other
substances.