[ussername]

[tex]\Delta G_{eq}=G_{eq}-G_{0}=-RTlnK_{eq}=-RTln\frac{\prod [product]_{eq}}{\prod [reactant]_{eq}}[/tex]
where [itex]0[/itex] is the state before the reaction, [itex]eq[/itex] is the equilibrium state. Is the relation correct?

If so, I don't understand how the change of state variable can depend just upon the final state, rather than both initial and final state (R = constant, T = constant, K = describes the final state).

[mjc123]

-RTlnK_eq = ΔG° = G°_products - G°_reactants where the superscript ° indicates standard states (e.g. [] = 1M)

The problem with your formulation is that G_eq and G₀ are arbitrarily (though not independently) variable. You can start with any values of initial concentrations, and the equilibrium concentrations will vary in a manner determined by the initial concentrations and K_eq - think of how you use an ICE table. The above equation relates K to a fixed standard ΔG value. Note that this is the difference between the Gibbs energies of products and reactants in standard states. It is not the value of the Gibbs energy at equilibrium, i.e. the minimum of the G-α curve (where α is extent of reaction).

I don't understand how the change of state variable can depend just upon the final state, rather than both initial and final state

I don't understand the question. State variable values are determined by the state; change in a state variable depends on the initial and final states.
G_eq depends on the equilibrium concentrations, which as I have said depend both on the initial concentrations and on K - ICE table again.

[ussername]

Thank you.
Also ΔG = G°(P) - G°(R) is difference between Gibbs energies of products and reactants in the state of equilibrium of chemical reaction. What is the meaning of this difference? (Why is there some special meaning compared to e.g. difference between Gibbs energies of components in gaseous mixture)?

[ussername]

Well obviously, as Gibbs energy of products (resp. reactants) is a function of its concentration in reaction mixture, the difference of Gibbs energies is a function of reaction mixture composition, i.e. a function of an extent of the reaction.

[mjc123]

Did you get my point?

ΔG = G°(P) - G°(R) is difference between Gibbs energies of products and reactants in the state of equilibrium of chemical reaction

No it is not! It is the difference between the Gibbs energies of products and reactants IN THEIR STANDARD STATES. Not in the equilibrium state.

as Gibbs energy of products (resp. reactants) is a function of its concentration in reaction mixture, the difference of Gibbs energies is a function of reaction mixture composition, i.e. a function of an extent of the reaction

The Gibbs energy of the system is a function of the extent of reaction, but ΔG° (and K) is a constant at a given temperature. The position of equilibrium depends on K and the initial concentrations.

What is the meaning of this difference? (Why is there some special meaning compared to e.g. difference between Gibbs energies of components in gaseous mixture)?

I don't understand what you're getting at here.

[ussername]

[tex]aA + bB \leftrightharpoons  cC + dD[/tex]
[tex]k_{1}[A]^{a}[ B]^{b} = k_{2}[C]^{c}[D]^{d}[/tex]
[tex]K_{eq}=\frac{k_{1}}{k_{2}}=\frac{[C]^{c}[D]^{d}}{[A]^{a}[ B]^{b}}[/tex]
[tex]\Delta G^{0} = -RT lnK_{eq}[/tex]
[tex]G_{P}^{0} = -RT ln([C]^{c}[D]^{d})[/tex]
[tex]G_{R}^{0} = -RT ln([A]^{a}[ B]^{b})[/tex]

No it is not! It is the difference between the Gibbs energies of products and reactants IN THEIR STANDARD STATES. Not in the equilibrium state.

As I see, [itex][C]^{c}[D]^{d}[/itex] resp. [itex][A]^{a}[ B]^{b}[/itex] are concentrations in the equilibrium state. Then I don't understand why Gibbs energies ([itex]G_{P}^{0}[/itex] resp. [itex]G_{R}^{0}[/itex]) don't describe the equilibrium state.
By standard state you mean concentrations of pure compounds under ([itex]T=298.15K[/itex], [itex]p=101.325 kPa[/itex]) conditions?

[mjc123]

Then I don't understand why Gibbs energies (G0P  resp. G0R) don't describe the equilibrium state

For the simple reason that at equilibrium G_P = G_R and ΔG = 0. It is ΔG° that tells us the equilibrium constant. (And G_P° = -RTln([C]^c[D]^d) is just wrong.)
Let's work it out. (Standard states by the way, means standard conditions at the specified temperature - which can be whatever you want, not necessarily 298.15K. For pure substances, standard state at that temp (pure liquids and solids have activity 1); gases 1 atm, solutions 1M.) Let's consider a solution reaction
aA + bB  cC + dD
Molar Gibbs energy of  compound A at concentration [A] is given by
G_A = G_A° + RT ln([A]/[A]°) = G_A° + RT ln[A] since [A]° = 1M
ΔG = cG_C + dG_D - aG_A - bG_B
= cG_C° + dG_D° - aG_A° - bG_B° + RT (cln[C] + dln[D] - aln[A] - bln[B ])     {Incidentally B in square brackets is code for bold text - put a space in if you want it to appear like conc of B}
= ΔG° + RT ln([C]^c[D]^d/[A]^a[B ]^b)
At equilibrium ΔG = 0, so
ΔG° = -RTln([C]_eq^c[D]_eq^d/[A]_eq^a[B ]_eq^b) = -RTlnK
So K depends on ΔG°, which refers to reactants and products in their standard states.

[Corribus]

@ussername

We've had some good discussions in the recent past about the difference between ΔG° and ΔG, if this is a point of confusion for you. For example, you might want to take a look at this post. This thread and this thread may also be relevant to you.