Thermodynamics Summary

DG° = - RT LN K

Example: From DG° for the reaction, HCl_(g) ® H⁺_(aq) + Cl^-_(aq)

Calculate K_a at 298 K.

DG° = [(0 + -131.2 ) – (-95.27) ]kJ = -35.93 (3 sf) Note the DG°_f H⁺_(aq) is defined to be = 0

DG° = - RT LN K

DG°/(-RT) = LN K

exp(DG°/(-RT)) = K

exp(-35.93 kJ/(-8.314 x 10^-3 kJ/Kmol x 298K)) = exp (14.5)

K_a =2 X 10⁶

We used pK_a = - log K_a, so HCl would have a pK_a of –6.3. The only place I have seen a number for pK_a of strong acids gave pK_a of HCl as ~ –7. I don’t know why these numbers are different.

Note the exponent has 3 significant figures (14.5). Since this number is an exponent, the number calculated from e^14.5 will just have 1 significant figure (from the .5)

Chemical focus is using thermodynamic measurements to determine conditions where a reaction is spontaneous.

1^st Law – The Energy of the Universe is constant. DE = q + w (the change in internal energy is equal to the heat + work). This has been paraphrased as “ You can’t win, you can only break even.”

2^nd Law – The entropy of the universe increases for a spontaneous process. This has been paraphrased as “You can’t even break even!” This law requires that disorder increase with time. Because all natural processes take place as time progresses and result in increased disorder, it is apparent that time and entropy “point” in the same direction. Because of this, entropy has been called “time’s arrow”.

Since most processes we that concern us at are constant pressure, we have focused our time on the change in Gibbs free energy. We saw how DS_unv >0, then DG_sys<0, and so a process is spontaneous. If DG<0, this quantity is the maximum work you can get out of a process. DG = w_max (at constant p and T). Achieving this maximum work from a spontaneous process can only occur via a hypothetical pathway. Any real pathway waste energy. For example, if we use a battery to turn a starter motor in a car, some useful energy is lost due to the friction of electrons flowing through wires. So some of our work has been transformed into heat. So all real processes convert useful energy into heat, increasing the entropy of the universe. Thus thermodynamics tells us the potential of a process but tells us we can never achieve this potential. Hence the two quotes from Henry Bent

1^st Law: “ You can’t win, you can only break even.”

2^nd Law: “You can’t break even!”

. If DG>0, this quantity represents the minimum work needed to perform a process.

We were using

DG = DH - TDS (at constant pressure and T)

We also saw the relationship between the Gibbs free energy, the reaction quotient, and the equilibrium constant.

DG = DG° + RT LN Q

At equilibrium DG = 0 and Q = K

DG° = - RT LN K

3^rd Law – The entropy of a pure, perfect, crystalline substance at 0 K is zero. This allows us to measure absolute entropy. This is different from DH and DG, which for compounds are measured relative to the elements that make them in their standard state under standard conditions.

Neither of the first two laws of thermodynamics has ever been proven. And there has never been a single example showing otherwise. Albert Einstein said about thermodynamics “...is the only physical theory of the universe content [which], within the framework of applicability of its basic concepts, will never be overthrown.”