which of the following gives the relative size of Ka and pH of a 0.10 M solution of HEX3(aq)?

Question

HEX₃(aq) + H₂O(l) ⇌ H₃O⁺(aq) + EX₃⁻(aq)

∆G^o = +47 kJ/mol_rxn

The reaction between the acid HEX₃(aq) and water is shown above. Based on the chemical equation and the value of ∆G^o given above, which of the following gives the relative size of Ka and pH of a 0.10 M solution of HEX₃(aq)?

1. Ka = 1 and pH < 1

1. Ka << 1 and pH = 1

1. Ka > 1 and pH > 1

1. Ka << 1 and pH > 1

Answer 1

G is positive, so K is much less than 1.

+G = forward reaction is unfavorable / nonspontaneous

Therefore, [reactants]equilibrium >> [products]equilibrium and it lies far to the left.

All that to say, Since G is positive, K is much less than 1.

G=-RTlnK

Since G is positive, (-RTlnK) has to be negative, and lnK will be positive when K is less than one..

Since K is much less than 1, the reaction below barely increases [H3O+] at all, so the pH is relatively close to 7, and slightly lower due to the slight increase of [H3O+] due to HEX3 acting as a bronsted acid.

HEX₃(aq) + H₂O(l) ⇌ H₃O⁺(aq) + EX₃⁻(aq)