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?enter image source here

1 Answer
Jacob T.
Jun 27, 2018

#Delta G^"o" = -2.19 xx 10^5 color(white)(l) "J" * "mol"^(-1)#

Explanation:

The equation

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

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

Solve for #Delta G^"o"#:

#Delta G^"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)#

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