Chapter 10, Problem 116AE

Interpretation Introduction

Interpretation:

The pH of a 0.125 M solution of a weak base if ΔH° = -28.0 kJ and ΔS°=-175 J/K for the following equilibrium needs to be estimated.

  ${\text{B(aq) + H}}_{\text{2}}\text{O(l)}\rightleftharpoons {\text{BH}}^{\text{+}}(\text{aq})+{\text{OH}}^{-}(\text{aq})$

Concept Introduction:

• The Gibbs free energy change (ΔG) for a given reaction depends on the enthalpy change (ΔH), entropy change (ΔS) and temperature T i.e.

${\text{ΔG}}^0{\text{ = ΔH}}^0-{\text{TΔS}}^0\text{------(1)}$

The sum of the two terms in the above equation determines the sign of ΔG. Thus, for a reaction to be spontaneous ΔG< 0 i.e. negative

• The Gibbs free energy for a reaction at equilibrium is related to the equilibrium constant (K) through the Gibbs-Helmholtz isotherm:

$\Delta {\text{G}}_{\text{R}}^0=-\text{RTlnK -----(2)}$

where R = 8.314 J/mol-K and T is the temperature