Modern Engineering Thermodynamics

15.7 Heat of Reaction 607
EXAMPLE 15.7
The formation of 1 mole of water by the combustion of its elements can be written as
H 2 + 0:5 × O 2 ! H 2 O + q r
where q r is the heat transfer that occurs per mole of water formed. Suppose we wanted to make exactly 0.160 kg of liquid
water by this combustion reaction. Determine the heat transfer required to keep both the reactants (H 2 and O 2 ) and the products
(H 2 O) at the standard reference state (25.0°C and 0.100 MPa) while this reaction takes place.
Solution
For the isothermal (25.0°C) and isobaric (0.100 MPa) combustion of 1.00 kgmole of hydrogen gas with 0.500 kgmole of
oxygen gas, Eq. (15.6) gives
ðq r Þ SRS
= q
f ° = h°
f
and since the reaction is at 25.0°C, the water formed is in the liquid state. Then, from Table 15.1, we find that ðh°Þ f = H2OðlÞ
285.838 MJ/kgmole. So, ðq ° f Þ H2OðlÞSRS
= 285.838 MJ/kgmole, and the heat transfer required for this reaction on a mass rather
than a molar basis is
q r = q r
M
where M is the molecular mass. Finally, the total heat transfer required is Q r = mq r ,or
Q r = mq r = m q
r
−285:838 MJ/kgmole
= ð0:160 kgÞ
= −2:54 MJ
M 18:016 kg/kgmole
Exercises
19. Rework Example 15.7 and determine the heat transfer required for the formation of 0.160 kg of water vapor H 2 O(g) at
the SRS rather than liquid water. Answer: ðQ r Þ H2OðgÞ
= −2:15 MJ:
20. Repeat Example 15.7 and determine the heat transfer required for the formation of 1.00 kg of methane gas CH 4 (g) when
both the reactants and the products are at the standard reference state. Answer: ðQ r Þ CH4 ðgÞ = −4:67 MJ:
21. Use the technique of Example 15.7 to determine the heat transfer required for the formation of 1.00 gallon (6.25 lbm)
of liquid octane C 8 H 18(l) . Answer: ðQ r Þ C8H18ðlÞ
= −5880 Btu:
15.7 HEAT OF REACTION
In the previous section, we saw that the heat of formation of a compound was the same as the heat of reaction
when that compound was formed from its elements at the standard reference state. An oxidation reaction of a
fuel is normally called combustion; therefore, the heat of reaction of the oxidation of a fuel in air or pure oxygen
is also known as the heat of combustion or the heating value of the fuel.
A bomb calorimeter is a closed, rigid (constant volume) vessel that can be used to determine the heat of reaction
of a liquid or solid fuel sample (see Figure 15.6). When the final temperature in the bomb has been reduced to
its initial standard state temperature of 25.0°C by the water bath, the resulting energy balance on the bomb is
Q r = mðu P − u R Þ = nðu P − u R Þ = U P − U R (15.7)
Then, from the definition of enthalpy, we can write
H P − H R = U P − U R + ðpVÞ P − ðpVÞ R
and, since the reactants are likely to be solids or liquids with a small volume and a low pressure, we can ignore
them and set ðpVÞ R
≈ 0, then
H P − H R = U P − U R + ðpVÞ P = Q r + ðnRTÞ P
which provides a convenient relation between the constant volume heat of reaction measured by the bomb
calorimeter and the total enthalpy change of the reaction occurring inside the bomb calorimeter.
The heat of reaction of gases, liquids, and some solids is more often measured in a steady state, steady flow, aergonic
calorimeter, similar to that shown in Figure 15.5. An energy rate balance on this type of calorimeter gives
the heat transfer rate of the reaction as
_Q r = _H P − _H R