Question

The main ingredient of vinegar is acetic acid (HAc) that will dissociate into acetate (Ac^-) and hydrogen ion

      (H⁺) in water: HAc < = > Ac^- (aq) + H⁺ (aq) . K_{HAc(room temp)} = 1.8x10^-5. If [HAc]_t = 0.001M, [Ac^-]_t =

      0.0001M, and [H⁺] _t = 2x10^-4M, T = 25 °, R = 8.3145 J/mol·K, please calculate ΔG° and ΔG.

     (a) DG°_rxn = 11754.0 J/mol ; ΔG = 130 J/mol   the reverse rxn direction is favored,

     (b) DG°_rxn = 11754.0 J/mol ; ΔG = 130 J/mol   the forward rxn direction is favored,

     (c) DG°_rxn = 27069.4 J/mol ; ΔG = 261 J/mol   the reaction direction can not be decided.

     (d) DG°_rxn = 27069.4 J/mol ; ΔG = 261 J/mol   the forward rxn direction is favored,

     (e) DG°_rxn = 27069.4 J/mol ; ΔG = 261 J/mol   the reverse rxn direction is favored,

Answer 1

The dissociation of acetic acid is written as

It is given that the equilibrium constant is .

We know that equilibrium constant and standard free energy change of the reaction are related as follows:

Where

Hence,

Now, the free energy change of the reaction, is calculated as follows:

Where

Q is the reaction quotient defined as follows for our reaction

Using the given concentrations, we can calculate the value of Q as follows:

Hence,

Hence, we can calculate the value of free energy change as follows:

Now, we know that

If , the reverse reaction is favoured,

If , the reaction is at equilibrium.

If , the forward reaction is favoured.

Hence, since we have which is greater than zero, the reverse reaction will be favoured.

Hence, the option with the correct values and statement is