# What is the standard state free energy for this reaction?

## Gold ions form complexes with cyanide ion according to the equation: Au+(aq) + 2 CN <-> Au(CN)2 kf=2x10^38 What is the standard state free energy for this reaction? Jun 27, 2018

$\Delta {G}^{\text{o" = -2.19 xx 10^5 color(white)(l) "J" * "mol}} ^ \left(- 1\right)$

The equation

## K_"eq" = e^(-(Delta G^ "o")/("R" cdot "T"))

Relates the equilibrium constant of a reaction, ${K}_{\text{eq}}$ to its change in Gibbs Free Energy per mole reaction $\Delta {G}^{\text{o}}$. $\text{R}$ is the ideal gas constant and $\text{T}$ the temperature in degree Kelvins. The question is asking for the Gibbs Energy Change under standard conditions. Thus $\text{T"=298 color(white)(l) "K}$.

Solve for $\Delta {G}^{\text{o}}$:

$\Delta {G}^{\text{o" = - ("R" * "T") * ln K_"eq}}$
color(white)(Delta G^"o") = - 8.314 color(white)(l) "J" * "mol"^(-1) * color(red)(cancel(color(black)("K"^(-1)))) * 298 color(white)(l) color(red)(cancel(color(black)("K"))) * ln (2 xx 10^38)
color(white)(Delta G^"o") = -2.19 xx 10^5 color(white)(l) "J" * "mol"^(-1)