The standard enthalpy data we find tabulated in thermodynamic tables is all for data at 25℃. This data may not be exactly the information we need. What if a reaction doesn’t actually happen at standard 25℃. We have two options: 1, we can assume that there is no significant difference in enthalpy change or, 2, we can calculate the effect.
In cases where there is only small temperature changes the former option may not be too bad. However, in some cases, especially where the temperature of reaction is far from 25℃ we should take the latter option.
Consider a reaction between chemicals A and B to produce C and D at some temperature T.
We could calculate the ΔH for the process 2 using standard thermodynamic data. Steps 1 and 2 involve temperature changes and we can calculate the ΔH for these steps if we know the heat capacities of the compounds involved. According to Hess’ law, the overall enthalpy change for the reaction at temperature T is the sum of the steps 1, 2 and 3.
|Step 1:||This is simply a temperature change and we can calculate the enthalpy change using the heat capacities of A and B.|
ΔH°1 = [a Cp° (A) + b Cp°(B)]ΔT1 (298 – T)
|Step 2:||ΔH2 = ΔHº298 (calculate from whatever means possible, for example you could use ΔfHº values.)|
|Step 3:||Like step 1, this is simply a temperature change. Calculate the enthalpy change using the heat capacities of C and D. Note that the process is the reverse direction of step 1 and the sign of the temperature change is opposite.ΔH3 = [c Cp°(C) + d Cp°(D)]ΔT3 (298 – T) NOTE: ΔT1= -ΔT3|
|Step T:||Δ HT= ΔH1 + ΔHº298 + ΔHº3= [a Cp°(A) + b Cp°(B)]ΔT1 + ΔHº298 + [c Cp° (C) + d Cp°(D)]ΔT3= ([c Cp°(C) + d Cp°(D)] – [a Cp°(A) + b Cp°(B)])ΔT3 + ΔH298°= (ΔCp°) ΔT3 + ΔH298°|
Where have defined a new parameter ΔCp°.
The change in heat capacity (capacity of products – capacity of reactants) is a actually slightly dependent on temperature and hence this formulation is not valid if the temperature T is very different from standard temp. (298 K). In most cases, the temperature effect is not extremely large but that is not general.
Like the general concepts involved in Hess’ Law, we simply add up the heats of the processes involved in order to determine the overall heat. This is merely another special application of Hess’ Law.