The equilibrium constant at 25°C for the process
`Co^(3+) (aq) +6NH_(3) (aq) hArr [Co(NH_(3))_(6)]^(3+) (aq)`
is `2.0 xx 10^(7)`. Calculate the value of `Delta_(r ) G^(Theta) ` at `25^(@)C`
`[R = 8314JK^(-1) "mol"^(-1)]`
In which direction is the reaction spontaneous when reactants and products are under standard conditions ?

Explanation

`Delta_(r ) G^(Theta) = -2.303 RT" log K"_( c)`
`K_(c ) = 2.10 xx 10^(7), R =8.314"J K"^(-1), T=25+273 =298K`
`:.Delta_(r )G^(Theta) = -2.303 xx 8.314 xx 298 log (2 xx 10^(7))`
`=-2.303 xx 8.314 xx 298[log 2 +7 log 10 ]`
`= -2.303 xx 8.314 xx 298 xx [0.3010+7]`
`= -41658.4J= -41.658kJ`
Since the value of `Delta_(r )G^(Theta)` is negative, the reaction is spontaneous in the forward direction.