For which reaction does $K_p=K_c?$

${\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}(\mathrm{RT}{)}^{\mathrm{\Delta n}}$

If $\mathrm{\Delta n}=0,{\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}$

If $\mathrm{\Delta n}>0$, then ${\mathrm{K}}_{\mathrm{p}}>{\mathrm{K}}_{\mathrm{c}}$

If $\mathrm{\Delta n}<0,$ then ${\mathrm{K}}_{\mathrm{p}}<{\mathrm{K}}_{\mathrm{c}}$

For the reaction: ${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{g}\right)⟶2\mathrm{HI}\left(\mathrm{g}\right)$

$\mathrm{\Delta n}$ is the number of moles of gaseous products - number of moles of gaseous reactants in a balanced equation.

$\mathrm{\Delta n}=2-(1+1)=0$

$\therefore {\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}$