Page 108 - Essentials of physical chemistry

70 Essentials of Physical Chemistry

a mole of gas so we neglect the volumes of any liquids or solids and estimate the D(PV) term using
only the change in the moles of gas, Dn gas . Here we have the net of (6 – 7.5 mol) ¼ 1.5 mol of gas
during the reaction for 1 mol of benzene. Thus, we can compute DH comb (25 C) after dividing

through by the number of moles.

C V DT (Dn gas )(RT ave )n
DH comb ¼ þ
n n
So inserting the numbers, we obtain

( 2569 cal=deg)(2:332 )

þ ( 1:5 mol)(1:987 cal= K mol)(298 K),

0:600 g
DH comb ¼
78:11184 g=mol
and so we find that
DH comb ¼ 779, 934:7 cal 888:2 cal ¼ 780, 822:9 cal ¼ 3266:9 kJ:

We can extract additional meaning from this result. First, the reaction is very exothermic, a lot of
heat is given off since the number is large and the sign is negative. We easily convert calories to
joules using 1 cal ¼ 4.184 J and we have rounded the value of T ave to 2988K since the actual
knowledge about T ave is only that it is near 258C and we see that the whole D(PV) term is much
smaller than the main DU term. Throughout this text we follow the policy of keeping all the digits
on our calculator until rounding to the least number of significant figures at the final answer. The
CRC Handbook [8] lists the experimental value as 3267.6 kJ.
This method for obtaining heats of combustion has been extended to many thousands of
compounds and lists of the values are tabulated (see Table 4.1) in several sources including the
CRC Handbook [8].
A hint of the usefulness of heats of combustion can be seen in that the heat of combustion for
H 2 is the same as the heat of formation of water.

1
H 2 þ O 2 ! H 2 O
2
Reactions other than combustion can be treated using a definition for the heat of a reaction:

X X
0 0 0
rxn
f,i
DH (298:15 K) n i H n j H f, j
product i reactant j
Now we can see the usefulness of the definition of the heat of formation of elements being zero.
1 0
0
0
0
) DH rxn ¼ H (H 2 O) H (H 2 ) H (O 2 ) ¼ 285:8 kJ 0 0 ¼ 285:8 kJ:
f
f
f
2
Note that we have to use the stoichiometric coefficients from the balanced reaction along with the
0
molar H values. It turns out that many of the heats of combustion and use of the definition of the heats
f
of formation of elements as zero lead to a whole series of heats of formation of compounds, which
have also been tabulated (see Table 4.2) at length in places like the CRC Handbook [8] for thousands
of compounds. This is possible due to the algebraic summation of enthalpy values. Notice that at this
point all reactions are considered to be at 258C. To summarize, heats of combustion can be used to
calculate heats of reactions which lead to standard heats of formation at 258C.