At 310 K a reaction A -> B has Delta G deg = +30.0 kJ mol^-1 and is coupled with C -> D with Delta G deg = -50.0 kJ mol^-1. Taking R = 8.314 J mol^-1K^-1, the equilibrium constant of the coupled reaction A + C -> B + D is nearest to

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At $310 K$ a reaction $A B$ has $Δ G^{\circ} = + 30.0 kJ mo l^{- 1}$ and is coupled with $C D$ with $Δ G^{\circ} = - 50.0 kJ mo l^{- 1}$ . Taking $R = 8.314 J mo l^{- 1} K^{- 1}$ , the equilibrium constant of the coupled reaction $A + C B + D$ is nearest to

For coupled reactions

Δ G^{\circ}

values add:

30.0 + (- 50.0) = - 20.0 kJ mo l^{- 1}

. Then

K = exp (20000/ (8.314 \times 310)) = exp (7.760) = 2.3 \times 1 0^{3}

. Using

298 K

or the wrong sign gives the other values.