Question
If the $${E^ \circ }_{cell}$$ for a given reaction has a negative value, then which of the following gives the correct relationships for the values of $$\Delta {G^ \circ }$$ and $${K_{eq}}?$$
A.
$$\Delta {G^ \circ } > 0;{K_{eq}} > 1$$
B.
$$\Delta {G^ \circ } < 0;{K_{eq}} > 1$$
C.
$$\Delta {G^ \circ } < 0;{K_{eq}} < 1$$
D.
$$\Delta {G^ \circ } > 0;{K_{eq}} < 1$$
Answer :
$$\Delta {G^ \circ } > 0;{K_{eq}} < 1$$
Solution :
Standard Gibbs free energy is given as
$$\Delta {G^ \circ } = - n{E^ \circ }F$$
If $${E^ \circ }_{cell} < 0\,\,i.e. - ve$$
$$\Delta {G^ \circ } > 0$$
Further $$\Delta {G^ \circ } = - RT\,\ell n\,{K_{eq}}$$