[burkeas]

Hi,

I have a question that was sparked by a recent exam...
We are given the formula delta G standard=-RT*ln(K). However, I do not understand exactly what K to use there.

Generally, I have seen that K be referred to as K_eq. How does that relate to K_c and K_p? Or is there another value that is just K? My teacher seems to think that K_eq can be K_p or K_c, but I do not understand how that could be possible... since K_p=K_c (RT)^ΔN, it does not seem that K_p and K_c would be interchangeable in the above equation.

Hopefully my question is somewhat coherent. The exact question on the exam gave a delta G standard value and asked for the value of K_p... I used the ΔG standard=-RT*ln(K) equation, but I then used K_p=K_c (RT)^ΔN because I thought K in the first equation was K_c... I got it wrong because apparently K in the ΔG standard=-RT*ln(K) can be K_c OR K_p, according to my teacher. Help please?
Thanks in advance

[mjc123]

K_eq means the equilibrium constant and is the same as K. For gas phase reactions, K or K_eq can be expressed in terms of either the pressures (K_p) or concentrations (K_c), which are related, as you say, by K_p = K_c(RT)^Δn. The equation ΔG° = -RTlnK applies to both forms of K, but the reference standard states are different in each case. When you use pressures, the standard state is gases at 1 atm pressure. When you use concentrations, the standard state is a concentration of 1M. This means that ΔG° is different in the two cases. From the above relation, ΔG°(c) = ΔG°(p) + RTΔnln(RT). (Try confirming this by using ΔS = nRln(V₂/V₁) for the entropy change of a gas on expansion/contraction.)
But you will find that tabulated thermodynamic data for gases, e.g. ΔG°_f(CO₂), is usually referenced to a standard pressure of 1 atm, so if you are given a value of ΔG° for a gas reaction, you should assume unless specified otherwise that the standard state is 1 atm, and the corresponding value of K is K_p. If you want K_c you then work it out from K_p using the above relation.

[mjc123]

Just a caution about units. In  K_p = K_c(RT)^Δn, to convert atm to mol/L, you need to use a value of R in L atm/mol/K. In ΔG° = -RTlnK, in SI units R should be in J/mol/K. In the equation ΔG°(c) = ΔG°(p) + RTΔnln(RT), the two Rs must be in different units, so it's probably not a very good equation to use.