Gvien the following value for the standard molar Gibbs free energy changes?
`G^(@)`, at `25^(@)C`
`Ag^(+) (aq) + 2NH_(3) (l) hArr Ag (NH_(3))_(2)^(+) (aq) ? G^(2) = -41.0KJ (mol Ag^(+))^(-1) Ag^(+) (aq) + Cl^(-)(aq) hArr AgCl (s) ? G^(@) = - 55.6 kJ (mol Ag^(+))^(-1)`
Calculate the value for the thermodynamic equilibrium constant. K, at `25^(@)C` for the reactions:
`AgCl (s) + 2NH_(3) (l) hArr Ag (NH_(3))_(2)^(+) (aq) + Cl (aq)`

Options

A. `3.62 xx 10^(2)`
B. `1.00`
C. `9.94 xx 10^(-1)`
D. `2.76 xx 10^(-3)`

Answer

D

Explanation

Reversing the 2nd equation and adding into 1 st equation gives
`Ag Cl (s) + 2NH_(3) (l) hArr Ag (NH_(3))_(2)^(+) (aq) + Cl^(-) (aq)`
`Delta G^(@) = 14.6 kJ` Also, `Delta G^(2) = 14.6 xx 100 J`
`=-2.303 xx 298 xx 8.314` log `K rArr K = 2.76 xx 10^(-3)`