[mrlucky0]

The problem:

For a reaction A<-->B, the activities for reactants A and products B are a_a and a_b=0.25 in equilibrium and at 310 K. Calculate the equilibrium constant K and the standard Gibbs energy, Gs.

My attempt:

my textbook said the chemical activity is the "effective concentration" (what does that mean?) so I think I can write:

k = a_b / a_a = .25 / 2.00 = .125
hence:
Gs = -R*T*ln(k) = -8.3J/(mol*k)*310K*ln(.125) = -5.4kJ

I am almost confident I have the second part right but what's confusing me is the meaning of chemical activity (and chemical potential) and how I am using it. Why is would this is correct or incorrect? I'm not fully understanding the difference between chemical activity and chemical potential. Any help would be appreciated.

[Hunt]

The change in the chemical potential of a closed system is nothing but the change in the molar gibb's free energy. Equilibrium of a system then signifies that the change in its chemical potential is zero. If you consider a closed system , say of a volatile ideal solution of chemical potential u*, then if some solute is added, the change in the chemical potential of the solvent is : u - u*= RTLnX. This follows from raoult's law for ideal solutions.

u = the new chem potential , X = mol fraction of the solvent

Inorder to fit an equation that describes a real solution , X is replaced by a , the acitivity. In this sense, chemical activity is an 'effective concentration' that describes correctly the decrease in the chemical potential of a system undergoing a favourable process. Activity expression depends on the type of system you're working on. If you want a more fundamental explanation , you can start with the Debye-huckel theory of ionic solutions.

In the example above , deltaG computed should be positive and not negative.