The reaction rate is a direct function of the reactants concentrations,
aA+ bB → cC
$"Rate" = k[A]^x [B]^y$
Where
$a, b, c$: are the stoichiometric coefficients
$x, y$: are the reactant orders
The proposed mechanism is
$bb((1))color(white)(m)"I"_2 stackrelcolor(blue)(k_1)(⇌) "2I (fast)"$
$color(white)(mmmmll)stackrelcolor(blue)(k_text(-1)color(white)(m)$
$bb((2))color(white)(m)"I + I + H"_2 stackrelcolor(blue)(k_2color(white)(mm))(→) "2HI (slow)"$
It illustrates that the reaction is a function of reactant concentrations (only controlled by the slower reaction)
However, $"I"$ is an intermediate. We must express the rate law using the concentrations of the reactants.
From 2:
$bb((3))color(white)(m)"rate" = k["I"^2]["H"_2]$
From 1:
$bb((4))color(white)(m)k_1["I"_2] = k_text(-1)["I"]^2$
$bb((5))color(white)(m)["I"]^2 = k_1/k_text(-1)["I"_2]$
Substitute 5 into 3.
$bb((6))color(white)(m)"rate" =(kk_1)/k_text(-1)["I"_2]["H"_2]$
$color(blue)("rate" = k_text(obs)["H"_2]["I"_2])$
