Equilibrium constants Ka, Kc, Kx, Kp and rate constants in reversible reactions

ymhiq

Is the statement Ke=k+/k- valid for all equilibrium constants like Ka, Kx, Kp, Kc? All of the expressions I have found for this statement relate Kc, k+ and k- only.

Chestermiller

At equilibrium, the rate of the forward reaction must equal the rate of the reverse reaction. If the rates are expressed in terms of activities, then the equilibrium constant will be equal to the ratio of the forward- to the reverse rate constant.

ymhiq

Thanks for your reply, I knew that but my doubt is exactly if Ke=Ka=Kc=Kx=Kp=(k+/k-) but in advance I Know that Ka≠Kc≠Kx≠Kp so the statement Ke=k+/k- is valid only valid for Kc according to my findings in literature. What about the others equilibrium constants? Is this statement valid for them If so what would be the differences in order to maintain the fact that Ka≠Kc≠Kx≠Kp?

Chestermiller

So that we are on the same page, please refresh my memory of the definitions of Ka, Kc, Kx, and Kp. Do all of these refer to equilibrium constants for chemical reactions using different concentration parameters (and units)?

ymhiq

Yes, Indeed. All of them are equilibrium constants for chemical reactions.

Kc is the most used. It is based on concentration or molarities. Kc=∏(cj^Sj) where Sj is the stoichiometric coefficient of j chemical compound and Cj is its concentration. Concentration is often written as [j]. It has [mol/volume]^Sj units.

Kp is used in reactions in vapor phase so its defined through partial pressures of j in the vapor phase. Kp=∏(pj^Sj). It has [pressure]^Sj units.

Kx is in terms of mole fractions. It used for liquid phase reactions. Kx=∏(xj^Sj). It's dimensionless.

Ka is the Thermodynamic Equilibrium Constant. By definition Ka=∏(aj^Sj). It's dimensionless.

All of them are different and I don't know if you can use the concept Ke=k+/k- for all of them. If so, what would be the differences?

Chestermiller

Yes, they are all related to one another. Start out by writing K_E in terms of activities or fugacities. Then express the activities in terms of concentration times activity coefficient, or fugacities in terms of pressure times fugacity coefficient. This will let you see how the different K's are related, and where the k₊ and k_- can come in.

ymhiq

Would it be correct if I'd wrote something like: Kc = k+/k- = Ka/[{(ƩCj)^(-ƩSj)}*{∏(P^Sj)}*{∏(∅j^Sj)}] ? Here, P is total pressure and ∅j is the fugacity coefficient of j.

Chestermiller

The easiest way to study this is to assume ideal gas behavior and ideal solutions (no heat of mixing). Start out simple, by relating Kp and Kc. The partial pressure of a species is related to the concentration by p = c RT. Substitute this into the expression for Kp. This should allow you to determine the relationship between Kc and Kp. Starting simple like this is very helpful. Why? If you can't solve for the simplest case, you certainly won't be able to do more complicated cases.

Chet