[kapital]

How is equilibrium constant formed? How can an such an arbitrary expression have souch meaning?

[Borek]

It is not arbitrary. Although initially it was just guessed it can be derived from the ΔG calculation for the reaction.

[Zeppos10]

Van't Hoff was the first to derive relations between the equilibrium constant K and other quantities of the chemical system, in L'Equilibre chimique dans les systemes gazeux ou dissous a l'etat dilue (1885).
In 2001 an English translation was published in: Hornix, WJ, Mannaerts, SHWM, Van't Hoff and the emergence of Chemical Thermodynamics, Delft UP.
It is interesting that Van't Hoff used 'equivalents' to express concentrations and (by consequence) his K's have dimension [1].     

[kapital]

Ok. Thanks for answers. I have antother question.

Why  the criteria for spontaneity is ΔG<0. (since by equation ΔG=R*T*lnK, we calculate that even for positive ΔG some product should be formed.

[ramboacid]

Why  the criteria for spontaneity is ΔG<0. (since by equation ΔG=R*T*lnK, we calculate that even for positive ΔG some product should be formed.

ΔG = -RTln(K). I believe you missed a minus sign.

[Jorriss]

Ok. Thanks for answers. I have antother question.

Why  the criteria for spontaneity is ΔG<0. (since by equation ΔG=R*T*lnK, we calculate that even for positive ΔG some product should be formed.

ΔG<0 is a reformulation of the second law at constant T and P. It corresponds to increasing the entropy of the universe.

[kapital]

Ok, but why this both calculations give different result?

[Jorriss]

Ok, but why this both calculations give different result?

I'm not sure what you mean.

ΔG=-RTlnK predicts a large positive equilibrium constant has a large negative free energy and a small equilibrium constant has a large positive free energy, as expected.

Why  the criteria for spontaneity is ΔG<0. (since by equation ΔG=R*T*lnK, we calculate that even for positive ΔG some product should be formed.

Ah I missed this at first. First off, there's a negative sign there. It's ΔG=-R*T*lnK.

ΔG > 0 implies that there are more reactants than products, it does not mean there are zero products. ΔG gives information about the extent of reaction.

[kapital]

So when they say, thar ΔG is criteria for sponaniety, they are just wrong?

[Zeppos10]

if no distinction is made between ΔG and ΔG°, this discussion goes nowhere.
The proper eqn is ΔG°=-RTlnK: the equilibrium criterion applies to ΔG.

[kapital]

What is the difrernce betwen ΔG and ΔG°?

[Jorriss]

So when they say, thar ΔG is criteria for sponaniety, they are just wrong?

No, it's just a reformulation of the second law of thermodynamics in terms of quantities easily measured by the system.

[Zeppos10]

What is the difference betwen ΔG and ΔG°?

ΔG=ΔG°+RTln(Q), where Q is the (actual, ie non-equilibrium) reaction-quotient .
but at equilibrium ΔG=0 and Q=K, hence ΔG°=-RTln(K).
I wonder what text does not distinguish ΔG from ΔG°: it should be blacklisted.
However, see:

Quilez J, First-Year university chemistry textbook misconceptions of Gibbs energy. JCE. 2012; 89:87-93.

[Bryan Sanctuary]

How is equilibrium constant formed? How can an such an arbitrary expression have souch meaning?

Although several answers give the equilibrium constant in terms of the Gibbs energy,

ΔG°=-RTln(K_eq)

there is a bit more to the story.  I will do this without discussing activities.  Consider the generic equation,

2A + B  3C

Where A, B and C are chemical species.  We can find these on tables that give us the Standard Gibbs Energies of formation, which we can call, ΔG°_A, ΔG°_B, ΔG°_C.  Recall that these are pressure (or in solution concentration) dependent and the relationships are,

ΔG_A =ΔG°_A –RT lnP_A
ΔG_B =ΔG°_B –RT lnP_B
ΔG_C =ΔG°_C –RT lnP_C

Let us now write down the change in Gibbs energy for the reaction:

ΔG_Rx= 3ΔG_C - 2ΔG_A- ΔG_B = 3ΔG°_C - 2ΔG°_A- ΔG°_B + 3RT lnP_C - 2RT lnP_A - RT lnP_B
ΔG_Rx= ΔG°_Rx+ RT lnP_C³- RTlnP_A² - RT lnP_B= ΔG°_Rx+ RT ln[P_C³/(P_A²P_B)]=
ΔG_Rx= ΔG°_Rx+ RT ln[Q]

Where Q is the quotient product: it has the same form as the equilibrium constant but the pressures are not the equilibrium pressures, but just the pressures that happen to be present,

Q= P_C³/(P_A²P_B)  K_eq  as pressures become their equilibrium values.

You should easily be able to see that the ΔG_Rx gets more or less negative as those pressures change in the quotient product, thereby showing that Le Chatelier’s principle raises or lowers the Gibbs energy, shifting the equilibrium one way or the other. 

It also becomes the equilibrium constant when the pressures are their equilibrium pressures. However at equilibrium there is no change and the ΔG_Rx is zero, hence

ΔG_Rx= ΔG°_Rx+RT ln[Q]     0= ΔG°_Rx+ RT ln[K_eq]

or

ΔG°_Rx=- RT ln[K_eq]

In this you can see where the form of the equilibrium constant comes from.

[Bryan Sanctuary]

So when they say, thar ΔG is criteria for sponaniety, they are just wrong?

Not wrong but vague. You always have to specify the conditions:

If T and P are constant, (bench top experiment) then the Gibbs energy, ΔG,  is a minimum at equilibrium
If T and V are constant (bomb calorimeter experiment) then the Helmholtz energy, ΔA, is a minimum at equilibrium.

So now we look at a chemical reaction:

2A + B  3C  ΔG_Rx = so many kJ mol^-1

If this happens at constant T and P then ΔG_Rx gives the criterion for spontaneity.  The more negative ΔG_Rx is, the greater the chemical push or potential. 

The same can be said at constant T and V for ΔA_Rx

Finally what does the value of ΔG_Rx mean in the chemical equation:

2A + B  3C  ΔG_Rx = so many kJ mol^-1?

First is says if you react 2 moles of A with one mole of B to get three moles of C, then the amount of energy transferred to the surroundings is ΔG_Rx.

It says that after the bonds have been broken and formed (energetics) and the system has rearranged (entropics) then there is a certain amount of energy left over to do useful work.  This is the reason the word "FREE" energy is used because after satisfying energetics and entropics (G = H-TS) we have some energy left over. So the energy left over goes to the surroundings.