CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES
11.5 REACTIONCALORIMETRY 337
R.T 1 /R.T 2 / P.T 2 /U.R/ U(expt)U.IBP;T 2 /TFigure 11.13 Internal energy changes for paths at constant volume in a bomb calo-
rimeter (schematic). R denotes reactants and P denotes products.increases over the course of several minutes. For a while the temperature in the system is
far from uniform, as energy is transferred by heat through the walls of the bomb vessel walls
to the water outside.
When the measured temperature is again observed to change at a slow and practically
constant rate, the reaction is assumed to be complete and the temperature is assumed once
more to be uniform. A second time is now designated as the final timet 2 , with final tem-
peratureT 2. For best accuracy, conditions are arranged so thatT 2 is close to the desired
reference temperatureTref.
Because the jacket is not gas tight, the pressure of the water outside the bomb vessel
stays constant at the pressure of the atmosphere. Inside the bomb vessel, the changes in
temperature and composition take place at essentially constant volume, so the pressure in-
side the vessel isnotconstant. The volume change of the entire system during the process
is negligible.
The isothermal bomb process
The relations derived here parallel those of Sec.11.5.1for a constant-pressure calorimeter.
The three paths depicted in Fig.11.13are similar to those in Fig.11.11on page 334 , except
that instead of being at constant pressure they are at constant volume. We shall assume the
combustion reaction is exothermic, withT 2 being greater thanT 1.
The internal energy change of the experimental process that actually occurs in the
calorimeter between timest 1 andt 2 is denotedÅU(expt) in the figure. Conceptually, the
overall change of state during this process would be duplicated by a path in which the tem-
perature of the system with the reactants present increases fromT 1 toT 2 ,^12 followed by the
isothermal bomb process at temperatureT 2. In the figure these paths are labeled with the
internal energy changesÅU.R/andÅU.IBP; T 2 /, and we can write
ÅU(expt)DÅU.R/CÅU.IBP; T 2 / (11.5.4)To evaluateÅU.R/, we can use the energy equivalentRof the calorimeter with reac-
tants present in the bomb vessel.Ris the average heat capacity of the system betweenT 1
andT 2 —that is, the ratioq=.T 2 T 1 /, whereqis the heat that would be needed to change
(^12) When one investigates a combustion reaction, the path in which temperature changes without reaction is best
taken with reactants rather than products present because the reactants are more easily characterized.