Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.5 REACTIONCALORIMETRY 334

R.T 1 /

P.T 2 /

P.T 1 /

H(expt)

H.rxn,T 1 /

H.P/



T

Figure 11.11 Enthalpy changes for paths at constant pressure (schematic). R denotes

reactants and P denotes products.

heating curve when no reaction is occurring, andt 1 andt 2 are the times at temperaturesT 1
andT 2. For an isothermal-jacket calorimeter, we evaluateÅH(expt) using Eq.7.3.28on
page 172 withwelset equal to zero.
The enthalpy change we wish to find is the reaction enthalpyÅH.rxn,T 1 /, which is
the change for the same advancement of the reaction atconstanttemperatureT 1. The paths
labeledÅH(expt) andÅH.rxn,T 1 /in the figure have the same initial state and different
final states. The path connecting these two final states is for a change of the temperature
fromT 1 toT 2 withfixed at its final value; the enthalpy change for this path is denoted
ÅH.P/.^11 The value ofÅH.P/can be calculated from

ÅH.P/DP.T 2 T 1 / (11.5.1)

wherePis the energy equivalent (the average heat capacity of the calorimeter) when the
calorimeter contains the products. To measureP, we can carry out a second experiment
involving work with an electric heater included in the calorimeter, similar to the methods
described in Sec.7.3.2.
Since the difference of enthalpy between two states is independent of the path, we can
writeÅH(expt)DÅH.rxn,T 1 /CP.T 2 T 1 /, or

ÅH.rxn,T 1 /DP.T 2 T 1 /CÅH(expt) (11.5.2)

The molar integral reaction enthalpy at temperatureT 1 is the reaction enthalpy divided
byÅ, the advancement during the experimental process:

ÅHm(rxn)DÅH.rxn,T 1 /=Å

D

P.T 2 T 1 /CÅH(expt)

Å

(11.5.3)

(constant-pressure

calorimeter)

Note thatÅH(expt) is small, so thatÅHm(rxn) is approximately equal toP.T 2 T 1 /=Å.
IfT 2 is greater thanT 1 (the process is exothermic), thenÅHm(rxn) isnegative, reflecting
the fact that after the reaction takes place in the calorimeter, heat would have to leave the

(^11) The symbol P refers to the final equilibrium state in which the reaction vessel contains products of the reaction
and any excess reactants.