For the reaction 2HI(g)→H2(g)+I2(g), the rate of the reaction is expressed as:
Rate=−21ΔtΔ[HI]=+ΔtΔ[H2]=+ΔtΔ[I2]
From this relationship, we can equate the rate of disappearance of HI with the rate of appearance of H2:
−21ΔtΔ[HI]=ΔtΔ[H2]
Rearranging this gives:
−ΔtΔ[HI]=2ΔtΔ[H2]