[xshadow]

Hi!!
First of all sorry for my bad  english but it isn't my 1st language!

I need some help to understand the different  meaning of [itex]K(T)[/itex] and [itex]Kc[/itex] where:

K(T)= K_c* [y( C)* y(D)]/[y(A)*y(B)] = K_c * k_y
where:
[itex] y(X)[/itex] is the activity coefficient of the X-th species
[itex]K_c [/itex] is the usual equilibrium constant with concentrations.

So looking this formula i don't understand if K(T) is a CONSTANT for a some  reaction at a  T=T_0 temperature or if his value change ??   same doubt  for    K_c !!


 For example, for the reaction   at the temperature [itex] T_0 = 298K [/itex] :
CH3COOH+H2O CH3COO- + H30+ 

1)the K(T) (the thermodynamics constant) can change his value?? for example  due to the ionic strenght and so  due to the  different values of the  activity coefficients??

2) and K_c can change  his value for the same reason?? (different ionic strenght ---> different activities coefficients)
At last what is the main differences (of meaning) between these two equilibrium constant??

If someone can help me...
Thanks

[mjc123]

I'm not entirely familiar with the terminology here but let's have a try.
First, let's introduce the concept of the reaction quotient Q. For a reaction
A + B  C + D
Q = [C][D]/[A][B ] (This may be at any point in the reaction, not necessarily equilibrium)
The equilibrium constant K_c is equal to the value of Q at equilibrium, Q_eq.
This is strictly true only at high dilution, when activity equals concentration. Let us call this equilibrium constant K_c∞.
Now we could define K_c ≡ K_c∞, and this is a constant. Then we would say that at higher concentrations, when activity differs from concentration, Q_eq may be different from K_c. K_c is constant, but Q_eq is variable.
Alternatively (and I don't know which practice is currently fashionable) we could define K_c ≡ Q_eq under all conditions, and then say that K_c, which is variable, differs from K_c∞, which is constant.
Now let's consider it in terms of activities, α. We define
Qα = α_Cα_D/α_Aα_B
and Kα ≡ Qα_eq = Q_eqγ_Cγ_D/γ_Aγ_B
This is always true, from the definition of activity - it is that quantity which behaves as concentration ideally should. Kα is constant.
At high dilution γ = 1, so Kα = K_c∞
If you take the second alternative above, where K_c = Q_eq and is variable, then
Kα = K_cγ_Cγ_D/γ_Aγ_B
and Kα corresponds to your K(T).
I hope this helps a little. The key point is that the equilibrium constant in terms of activities is a true constant - that's what activity means.

[xshadow]

Thanks!!
 I think to have understood  the point:

The general expression  for a reaction 1A+1B 1C+1D is:

K(T)= {a(C)*a(D)}/{a(A)*a(B)}= {[C]*[D]}/{[A]*[ B]}* Ky= Kc*ky


Here K(T) is a costant for a reaction at a certain temperature: in other words the expression {a(C)*a(D)}/{a(A)*a(B)} has  a constant value for a reaction.

What is change is Kc and Ky (the activity coefficients )...
When Ky changes, i.e. the activity coefficients change(due to ionic strenght,for example), the term Kc has to change in order to guarantee the numeric value espressed by  K(T)= {a(C)*a(D)}/{a(A)*a(B)} ,which is a constant and must be always respected.


When Ky=1  K(T)=Kc  and in this particular case Kc has the usual value that we find generally in the books for that reaction...for example for CH3COOH  at 25*C has the common value of  1,75*10^(-5)