A reaction A ( aq ) + B ( aq ) − ⇀ ↽ − C ( aq ) has a standard free‑energy change of − 5.43 kJ / mol at 25 °C. What are the concentrations of A , B , and C at equilibrium if, at the beginning of the reaction, their concentrations are 0.30 M, 0.40 M, and 0 M, respectively?

Answer : The concentrations of A, B, and C at equilibrium is, 0.11 M, 0.21 M and 0.19 M respectively.

Explanation :

The relation between the equilibrium constant and standard Gibbs, free energy is:

where,

= standard Gibbs, free energy  = -5.43 kJ/mol = -5430 J/mol

R = gas constant = 8.314 J/mol.K

T = temperature  =

K = equilibrium constant = ?

Now put all the given values in the above relation, we get:

Now we have to calculate the concentrations of A, B, and C at equilibrium.

The balanced equilibrium chemical reaction is:

Initial conc.     0.30       0.40         0

At eqm.        (0.30-x)    (0.40-x)     x

The expression for equilibrium constant for this reaction is,

Now put all the given values in this expression, we get:

As we know that the concentration at equilibrium can not be more than initial concentration. So, neglecting the value of x = 0.62 M

The value of 'x' will be, 0.19 M

Thus, the concentrations of A at equilibrium = (0.30-x) = (0.30-0.19) = 0.11 M

The concentrations of B at equilibrium = (0.40-x) = (0.40-0.19) = 0.21 M

The concentrations of C at equilibrium = x = 0.19 M

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