Question

For a homogeneous gaseous reaction, $K_p=K_c$
hence $\Delta n_g$ for the reaction will be:

Answer 1

For a homogeneous gaseous reaction, $K_p=K_c$
hence $\Delta n_g$ for the reaction will be $0$.
$K_p=K_c\times (RT{)}^{\Delta n_g}$
Substitute $K_p=K_c$ in the above expression
$K_c=K_c\times (RT{)}^{\Delta n_g}$
$1=\times (RT{)}^{\Delta n_g}$
This is possible when $\Delta n_g=0$
because $(RT{)}^0=1$