Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.5 REACTIONCALORIMETRY 339

HereCV(P) andCV(R) are the heat capacities at constant volume of the contents of the
bomb vessel with products and reactants, respectively, present.

Reduction to standard states

We want to obtain the value ofÅcU.Tref/, the molar internal energy change for the main
combustion reaction at the reference temperature under standard-state conditions. Once we
have this value, it is an easy matter to find the molarenthalpychange under standard-state
conditions, our ultimate goal.
Consider a hypothetical process with the following three isothermal steps carried out at
the reference temperatureTref:
1.Each substance initially present in the bomb vessel changes from its standard state to
the state it actually has at the start of the isothermal bomb process.
2.The isothermal bomb process takes place, including the main combustion reaction
and any side reactions and auxiliary reactions.
3.Each substance present in the final state of the isothermal bomb process changes to
its standard state.

The net change is a decrease in the amount of each reactant in its standard state and an
increase in the amount of each product in its standard state. The internal energy change of
step 2 isÅU.IBP; Tref/, whose value is found from Eq.11.5.8. The internal energy changes
of steps 1 and 3 are calledWashburn corrections.^13
Thus, we calculate the standard internal energy change of the main combustion reaction
at temperatureTreffrom

ÅU.cmb; Tref/DÅU.IBP; Tref/C(Washburn corrections)

X

i

ÅiÅrU.i/(11.5.9)

where the sum overiis for side reactions and auxiliary reactions if present. Finally, we
calculate the standardmolarinternal energy of combustion from

ÅcU.Tref/D

ÅU.cmb; Tref/

Åc

(11.5.10)

whereÅcis the advancement of the main combustion reaction in the bomb vessel.

Standard molar enthalpy change

The quantityÅcU.Tref/is the molar internal energy change for the main combustion reac-
tion carried out at constant temperatureTrefwith each reactant and product in its standard
state at pressurep. From the relationsÅcHD

P

iiHi(Eq.11.2.15) andHiDUiCpVi
(from Eq.9.2.50), we get

ÅcH.Tref/DÅcU.Tref/Cp

X

i

iVi (11.5.11)

(^13) Ref. [ 170 ].