Chapter 23, Problem 23.34P

Interpretation Introduction

Interpretation:

Value of ${\text{ΔG}}_{rxn}^o$ at $25°C$ has to be calculated. The direction in which the reaction is spontaneous under standard conditions has to be identified. Also, the value of value of ${\text{ΔG}}_{rxn}$ when $\left[C{o}^{3+}\right]=0.0050\text{ M}$, $\left[{\text{NH}}_3\right]=0.10\text{ M}$ and ${\left[Co{\left(N{H}_3\right)}_6\right]}^{3+}=1.00\text{ M}$ has to be calculated and direction in which the reaction is spontaneous under standard conditions has to be identified.

Concept Introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by $\text{ΔG}$. Value of $\Delta G_{rxn}^o$ is determined as follows,

  ${\text{ΔG}}_{rxn}^o=-\text{RT}\text{ln K}$

Under standard conditions, the reaction is spontaneous when $\Delta G_{rxn}^o$ is negative whereas the reaction is not spontaneous when $\Delta G_{rxn}^o$ is positive.

The formula of ${\text{ΔG}}_{\text{rxn}}$ in is given below,

    ${\text{ΔG}}_{rxn}=\text{RT}\text{ln }\left(\frac{{\text{Q}}_c}{K_c}\right)$

If $\Delta G_{rxn}<0$ then the reaction is spontanous in forward reaction and so the reaction will favor products.

If $\Delta G_{rxn}>0$ then the reaction is spontanous in backward reaction and so the reaction will favor reactants.

If $\Delta G_{rxn}=0$ then the reaction is at equilibrium.