How do we obtain reaction energies from reaction enthalpies, or vice versa? How do we determine a reaction enthalpy at a nonstandard temperature given a value at 298K? These two questions take us to the end of Chapter Four and the "First Law Era".
It is straightforward to derive the relation ∆rxnU°=∆rxnH°-RT∆rxnνgas which can be used to interconvert between reaction energy and enthalpy. When using this equation, we must keep in mind that (a) we are implicitly assuming all gases are ideal and (b) that, for liquids and solids, molar enthalpies and internal energies are approximately equal. In principle, we could jam in a real gas equation of state and create a ghastly version that is more general or, as is always done, use this version anyway and take the hit in accuracy. Assumption (b) is rather good because, unless we encounter extreme pressures, the heat capacities CP,m and CV,m are nearly equal for condensed phases.
Adjusting to a nonstandard temperature is rather important since many (most?) reactions do not actually occur at 25°C and the difference is often quite significant. Once the heat capacity CP,m is known as a function of temperature, we can calculate ∆∆rxnH°=∫∆rxnC°PdT.
To make integration life easier, the heat capacities are fit to simple polynomials of T:
CP,m=a + bT +cT2+dT3+eT4 [Shomate] or
CP,m=a + bT +cT-2
Exam 1 on Thursday. If you are nervous, just remember that if you got through organic chemistry, calculus and physics, you can do this. I have posted solutions to the two questions I assigned from Chapter 4. I also updated the study sheet that had some equations missing and an error in one of the thermodynamic equations of state.