What is a Rate Law and Reaction Order?
A rate law expresses reaction rate as a mathematical function of reactant concentrations: rate = k[A]^m[B]^n. The exponents m and n are reaction orders; they determine how sensitive the rate is to concentration changes.
Rate law: rate = k[A]^m[B]^n, where k is the rate constant and m, n are the reaction orders. Orders are determined experimentally, not from stoichiometry.
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Step-by-step worked examples
For a reaction rate = k[A][B], with k = 0.5 M^-1·s^-1, [A] = 2 M, [B] = 0.3 M, find the rate.
rate = k[A][B] rate = 0.5 × 2 × 0.3 rate = 0.3 mol/(L·s)
A decomposition follows rate = k[A]^2 with k = 0.02 M^-1·s^-1 and [A] = 1.5 M. Rate?
rate = k[A]^2 rate = 0.02 × (1.5)^2 rate = 0.02 × 2.25 = 0.045 mol/(L·s)
If doubling [A] quadruples the rate, what is the reaction order with respect to A?
If rate ∝ [A]^m, and 2[A] → 4 × rate Then 2^m = 4 2^m = 2^2, so m = 2 The reaction is second order in A.
Flashcards
Quick quiz
Q1.For rate = 0.1[A]^2[B], if [A] = 2 M and [B] = 1 M, rate?
Q2.Tripling [A] increases rate 9×. Reaction order in A?
Q3.Which is determined experimentally?
Q4.For a zero-order reaction, doubling [A]…
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Common mistakes
Reaction order comes from the balanced equation coefficients. — Correct: Order is determined experimentally; it may differ from stoichiometry in complex reactions.
Rate constant k is always the same for a reaction. — Correct: k depends on temperature; it increases with increasing T.
All reactions are first or second order. — Correct: Reactions can be zero, fractional, or even complex orders depending on mechanism.
Higher order = faster reaction. — Correct: Order describes concentration sensitivity; a zero-order reaction rate is independent of [A].
FAQ
How do you determine the reaction order from data?
Use the method of initial rates or integrated rate laws. Compare rates as [A] varies; if rate ∝ [A]^m, m is the order.
Why is rate law determined experimentally, not from stoichiometry?
Because not all reactants participate at the same stage; rate laws reflect the reaction mechanism.
What are the units of the rate constant k?
Units depend on overall order: zero-order k has units mol/(L·s); first-order k has units s^-1; second-order k has units L/(mol·s).
Can a rate law have negative or fractional orders?
Fractional orders are possible (e.g., 0.5, 1.5) and indicate complex mechanisms. Negative orders are rare but can occur in special systems.