For this second-order reaction with respect to H$_2$ and I$_2$, the rate of the reaction is proportional to the product of the concentrations of H$_2$ and I$_2$.
When 1 mole of H$_2$ is added, assuming the concentration of I$_2$ remains constant, the rate of reaction will increase proportionally to the increase in the concentration of H$_2$.
Since the temperature is constant, the rate constant (k) remains unchanged.
Thus, the reaction rate increases with increased concentration of H$_2$.