What is a good, simple definition for standard enthalpy change? Standard enthalpy of formation? And entropy? What about delta S and delta G?

Standard enthalpy change, #DeltaH^@#, is #q#, the flow of thermal energy in a system, at constant atmospheric pressure AND at thermodynamic standard temperature and pressure (this means #25^@ "C"# and #"1 bar"#).

Regular #DeltaH# is all that, but at any temperature and pressure. #DeltaH_(rxn)# is #Delta#, for a reaction.

Going off of that, the standard enthalpy of formation, #DeltaH_f^@#, is the standard enthalpy change of the reaction that forms #"1 mol"# of a substance in a given phase from its elements in their standard state (as they exist in nature at #25^@ "C"# and #"1 bar"#).

Example... #DeltaH_f^@# for #"NH"_4"Cl"(s)# is for this reaction at #25^@ "C"# and #"1 bar"#:

#1/2"N"_2(g) + 2"H"_2(g) + 1/2"Cl"_2(g) -> "NH"_4"Cl"(s)#

Nitrogen, hydrogen, and chlorine are diatomic in nature, and are all gases at #25^@ "C"# and #"1 bar"#. One could also call this #DeltaH_(rxn)^@# for the formation of #"NH"_4"Cl"(s)#.

How do you explain that the #DeltaH_f^@# for all the elements in their standard state is zero?

The standard molar entropy, #S^@#, is the amount of energy dispersal within a system, relative to #"0 K"#.

(We define #S^@("0 K") = "0 J/mol"cdot"K"# from the third law of thermodynamics.) This can be given for any substance, and is usually not zero at #25^@ "C"#.

#DeltaS# is simply the change in entropy of some sort (totally general), going from the initial state to the final state.

#DeltaS = S_f - S_i#

We could then have a change in entropy of reaction, #DeltaS_(rxn)#, at some temperature #T#. Then, if you want, you could define the change in standard molar entropy of reaction as:

#DeltaS_(rxn)^@ = sum_P n_P S_P^@ - sum_R n_R S_R^@#

with #P# being products, #R# reactants, and #n# moles of either one. #S_k^@# is the standard molar entropy of either products #P# or reactants #R#.

That then becomes a ready calculation exercise for students.

#DeltaG# is again an arbitrary change in the Gibbs' free energy of any process. This is basically the maximum amount of work you can do that is not expansion or compression, that can be extracted from a system.

#DeltaG = G_f - G_i#

For any temperature, we can then have a #DeltaG_(rxn)# for a reaction.

• If #DeltaG_(rxn) = 0#, the reaction is at equilibrium at that temperature.
• If #DeltaG_(rxn) < 0#, the reaction is spontaneous at that temperature.
• If #DeltaG_(rxn) > 0#, the reaction is nonspontaneous at that temperature.

We could then define the change in standard Gibbs' free energy of reaction by using the change in standard Gibbs' free energy of formation:

#DeltaG_(rxn)^@ = sum_P n_P DeltaG_(f,P)^@ - sum_R n_R DeltaG_(f,R)^@#

And this would be calculated just like the change in standard enthalpy of reaction:

#DeltaH_(rxn)^@ = sum_P n_P DeltaH_(f,P)^@ - sum_R n_R DeltaH_(f,R)^@#

Either one uses tabulated data of #DeltaH_f^@# and #DeltaG_f^@#, i.e. the two thermodynamic quantities of formation.

It is also important to note that #DeltaG_(rxn)^@# does NOT describe spontaneity or equilibrium because it is defined at a fixed temperature.