Concise Physical Chemistry

c04 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

ENERGIES AND ENTHALPIES OF FORMATION 57

we still measure the amount of heat in calories or kilocalories, related through the

conversion factor 4.184 to the number of joules or kilojoules.

4.2 ENERGIES AND ENTHALPIES OF FORMATION

Many compounds can be formed by direct combination of their elements. An example

is carbon dioxide (CO 2 ). When a small measured amount of carbon in the common

form of graphite, C(gr), is burned in O 2 in a closed steel container called abomb,

the process causes a small temperature rise
Tin the immediate surroundings called

thebath. The heat capacity of the bath having been previously determined by an

electrical calibration, one can findqV, the amount of heat given off by the combustion

at constant volume:

C(gr)+O 2 (g)→CO 2 (g)+qV

Straightforward proportional calculation gives the amount of heat that would have

been given off if the measured amount of C(gr) had been one gram (qV=

32 .76 kJ g−^1 ) or if it had been one mole (qV=
U^298 =− 393 .51 kJ mol−^1 ). The

latterqVgives themolar energy change
U^298 of the system, which is negative be-

cause the system gives off heat to the surroundings. The heat is given off at constant

volume of the closed bomb; hence it is anenergychange. In this reaction, the number

of moles of gas used up is the same as the number produced
ngas=0, so the energy

change is the same as theenthalpychange:

H=
U+
(pV)=
U+
ngasRT

We can write
fU^298 (CO 2 )=
fH^298 (CO 2 )=− 393 .5kJmol−^1 to indicate the

energy or theenthalpy of formationof CO 2 for an experiment carried out at 298 K.

The heat of combustion of a gas—for example, hydrogen—can be found using a

flame calorimetric apparatus in which a known amount of gas is burned and the heat

given off is measured by measuring the temperature rise of a suitably positioned bath.

The apparatus is a fancy Bunsen burner heating up a container of water equipped with

a thermometer. It functions at constant pressure, so the heat given out is the enthalpy

decrease of the system:

H 2 (g)+^12 O 2 (g)→H 2 O(l)+qp

which leads to the molar enthalpy of formation of liquid water:

qp=
fH^298 (H 2 O(l))=− 285 .6kJmol−^1

In the formation reaction,^32 mol of gas are consumed to produce 1.0 mol ofliquid

water, which has a negligible volume compared to the gas burned. Energy and enthalpy

are related byH=U+pV; hence
H=
U+p
V at constant pressure and