Reaction Rates
High-Yield Summary
- Rate of reaction = change in concentration of a reactant or product per unit time.
- Rate law: rate = k[A]^x[B]^y — x and y (reaction orders) are determined experimentally, NOT assumed from stoichiometry.
- Rate expression (definition of speed) ≠ rate law (empirical model of what controls speed) ≠ equilibrium constant expression (concentrations at equilibrium).
- The rate constant k is specific to a reaction AND a given temperature — it changes if temperature changes.
- Method of initial rates: compare experiment pairs where only one concentration changes to isolate each reactant's order, then solve for k.
Rate Expression
rate = −(1/a)Δ[A]/Δt = −(1/b)Δ[B]/Δt = (1/c)Δ[C]/Δt = (1/d)Δ[D]/Δt
- a, b, c, d = Stoichiometric coefficients for aA + bB → cC + dD
- Δ[X]/Δt = Rate of concentration change for species X
- Negative sign on reactants reflects their concentration decreasing over time; dividing by each coefficient keeps rate consistent regardless of which species is tracked.
Rate Law
rate = k[A]^x[B]^y
- k = Rate constant, specific to the reaction at a given temperature
- [A], [B] = Reactant concentrations
- x, y = Reaction orders — determined experimentally, not from stoichiometry
Rate Expression vs. Rate Law vs. Equilibrium Constant
| Expression | What It Answers |
|---|---|
| Rate expression | Definition of speed — how fast a reactant disappears/product appears |
| Rate law: rate = k[A]^x[B]^y | Empirical model of how rate depends on concentration, at any point during the reaction |
| Equilibrium constant: K = [C][D]/[A][B] | Ratio of concentrations at equilibrium only — not a statement about rate |
Method of Initial Rates
- 1Identify a pair of experiments where one reactant's concentration changes while all others stay constant.
- 2Compare the rate change between that pair — any change is attributable to that one reactant.
- 3Determine that reactant's order by comparing the ratio of rates to the ratio of concentrations.
- 4Once all orders are known, plug any trial's data into the rate law and solve for k.
Common MCAT Trap
- Reaction order does NOT have to match the stoichiometric coefficient — for 2A + B → C, the rate law could be rate = k[A][B] (first-order in A despite a coefficient of 2).
- Don't confuse the rate law (rate = k[A]^x[B]^y) with the equilibrium constant expression (K = [C][D]/[A][B]) — they look similar but answer different questions.
- k is NOT universal — it's specific to one reaction at one temperature; a temperature change means a new k.
- Equilibrium isn't only a 'final' state — forward and reverse rates can become equal (and stay equal) at any point, not just at the end of a reaction.
Quick Recall
For 2A + B → C, does a stoichiometric coefficient of 2 mean the reaction must be second-order in A?
In the method of initial rates, why must you compare experiments where only ONE concentration changes?
Is the rate constant k the same at every temperature?