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(A) The equilibrium constant $K_{eq}$ is defined as the ratio of the rate constant of the forward reaction to the rate constant of the backward reacti

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$6$

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(A) The equilibrium constant $K_{eq}$ is defined as the ratio of the rate constant of the forward reaction to the rate constant of the backward reaction: $K_{eq} = \frac{K_{f}}{K_{b}}$.Given $K_{f} = 10^{3}$ and $K_{b} = 10^{2}$,we have $K_{eq} = \frac{10^{3}}{10^{2}} = 10$.The standard Gibbs energy change is related to the equilibrium constant by the equation: $\Delta_{r} G^{\circ} = -RT \ln K_{eq}$.Given $T = 27^{\circ} C = 300 \ K$,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$,and $\ln 10 = 2.3$.Substituting the values: $\Delta_{r} G^{\circ} = -(8.3 	imes 300 	imes 2.3) \ J \ mol^{-1}$.$\Delta_{r} G^{\circ} = -5727 \ J \ mol^{-1} = -5.727 \ kJ \ mol^{-1}$.Rounding to the nearest integer,the magnitude is $6 \ kJ \ mol^{-1}$.

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