You haven't given the relevant sf(E^@) values so I looked them up:
sf(Au^(3+)+3erightleftharpoonsAucolor(white)(xxxxxxxx)E^@=+1.42color(white)(x)V)
sf(Au^(+)+erightleftharpoonsAucolor(white)(xxxxxxxxxx)E^(@)=+1.68color(white)(x)V)
sf(Au^(3+)+2erightleftharpoonsAu^(+)color(white)(xxxxxxx)sf(E^@ is unknown
We need to convert these to free energy values and then apply the conservation of energy.
sf(DeltaG^@=-nFE^@)
sf(F) is the Faraday Constant
sf(n) is the no. of moles of electrons transferred.
Let sf(E^@) be the value we want to find.
We can say that:
sf(DeltaG^@[Au^(3+)rarrAu]=DeltaG^@[Au^(3+)rarrAu^(+)]+DeltaG^@[Au^(+)rarrAu])
:.sf(-3cancel(F)xx1.42=-2cancel(F)E^(@)-cancel(F)xx1.68)
:.sf(-2E^@=-4.26+1.68=-2.58color(white)(x)V)
sf(E^@=+2.58/2=+1.29color(white)(x)V)
