[Rutherford]

For the reaction CO+0.5O₂ CO₂ ΔH=-283kJ/mol abd ΔG=-257.1kJ/mol establish an expression for the temperature dependence of the equilibrium constant K_p.

I know that ΔG=-RTlnK_c. ΔG also depends on the temperature, so what to do now?

[Babcock_Hall]

Do you mean ΔG or ΔG°?

[Rutherford]

ΔG° is given.

[Babcock_Hall]

Do you know of an equation that relates ΔG° to temperature?

[Rutherford]

Aside the one I wrote I know ΔH-TΔS=ΔG, so ΔH-TΔS=RTlnK_c, but then I get the expression for K_c, but it should be K_p, right? Their expression for K_p is the one I got for K_c  Why?

[Big-Daddy]

You're getting confused by the Kp = Kc * (RT)^n relation (n is the change in number of moles of gas per mole of the forward reaction equation that occurs) here?

I think the crucial point is that ΔG=-RT*ln(K) actually has K referring not to concentrations or partial pressures but to activities, and if Kp is expressed in terms of partial pressures (fugacities to be exact) then ΔG=-RT*ln(Kp) holds because fugacities are activities for gases (I think), whereas Kc is never exact but in solution is often approximated to be equal to K.

[Rutherford]

Yes, that expression was in my head. By the way, how is it derived?

[Big-Daddy]

Units. Let's take generalized equilibrium aA + bB -> cC + dD, everything is gaseous. Kp has units Pa^(d+c-a-b), Kc has units M^(d+c-a-b), and to convert from concentration to pressure we have to use P=nRT/V=CRT (C=n/V). So the units of Kp are then those of (C * RT)^(d+c-a-b) which we can break up into C^(d+c-a-b) * (RT)^(d+c-a-b) which is Kc * (RT)^(d+c-a-b). (I used C and M interchangeably because M is the unit and C is the term, but hope there is no confusion )

[Rutherford]

Understood. Thank you for the explanation .