2.2.9 (HL)—Rate equations

Use experimental trials that vary one concentration independently. Compare the rate factor with the concentration factor to infer each exponent; the balanced overall equation alone cannot determine the rate equation.

If doubling [A] while holding [B] constant quadruples rate, the order in A is 2; if doubling [B] leaves rate unchanged, the order in B is 0, giving rate = k[A]². Choose trial pairs with only one changed concentration before combining exponents.

Worked initial-rate deduction: doubling $[\ce{Fe^{3+}}]$ from $1.00\times10^{-2}$ to $2.00\times10^{-2}\,\mathrm{mol\,dm^{-3}}$ at constant $[\ce{I^-}]$ doubles rate, so the order in $\ce{Fe^{3+}}$ is 1. Doubling $[\ce{I^-}]$ at constant $[\ce{Fe^{3+}}]$ increases rate from $3.24\times10^{-5}$ to $1.30\times10^{-4}\,\mathrm{mol\,dm^{-3}\,s^{-1}}$, approximately fourfold, so its order is 2. Therefore $v=k[\ce{Fe^{3+}}][\ce{I^-}]^2$, third order overall.