What is the order of the iodine clock reaction with respect to H+?

The equation I have been working with is H2O2(aq) + 2I-(aq) + 2H+(aq) → I2(aq) + 2H2O(l). From my experiments and graphs I think the order of the reaction with respect to all the reactants including H+ (from sulphuric acid) is first order but I'm not sure if it is right - when I tried calculating the rate constant from my data the rate constant was about the same for the experiments where I was changing the concentration of hydrogen peroxide and potium iodide but for the experiment where I changed the concentration of sulphuric acid the rate constant decreased as the concentrations of sulphuric acid increased. As I understand it the rate constant should never change when changing the concentration of the reactants. Any help would be appreciated!