For a second-order reaction involving H$_2$ and I$_2$, the reaction rate is directly proportional to the product of their respective concentrations.
If 1 mole of H$_2$ is added while the I$_2$ concentration is held constant, the reaction rate will increase proportionally to the augmented H$_2$ concentration.
As the temperature is constant, the rate constant (k) remains invariant.
Consequently, an increase in H$_2$ concentration leads to a higher reaction rate.