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Must-know facts
20 facts
- 1Rate = −(1/a) d[A]/dt = (1/c) d[C]/dt for aA → cC: divide by the coefficient so every species gives one rate.
- 2Instantaneous rate is the slope of the tangent to the concentration-time curve; average rate is a slope across an interval.
- 3The rate law is found by experiment. Its powers need not match the coefficients in the balanced equation.
- 4Order = sum of the powers in the rate law; it can be 0, a fraction, or a whole number.
- 5Molecularity belongs to one elementary step, is a whole number 1-3, and is never zero or fractional.
- 6In a complex reaction, the slowest step sets the rate (rate-determining step).
- 7Units of k: (mol L⁻¹)^(1−n) s⁻¹. Zero order mol L⁻¹ s⁻¹; first order s⁻¹; second order L mol⁻¹ s⁻¹.
- 8Zero order: [R] = [R]₀ − kt; t½ = [R]₀/2k; straight line of [R] vs t.
- 9First order: k = (2.303/t) log([R]₀/[R]); t½ = 0.693/k; straight line of ln[R] vs t.
- 10First-order half-life does not depend on concentration; zero-order half-life is proportional to [R]₀.
- 11First order: 99.9% completion ≈ 10 half-lives; 99% ≈ 6.6 half-lives; after n half-lives (½)ⁿ remains.
- 12Pseudo first order: one reactant in large excess (ester hydrolysis in water; inversion of cane sugar).
- 13k changes with temperature and catalyst, never with concentration.
- 14Arrhenius: k = A e^(−Ea/RT); ln k vs 1/T is a straight line of slope −Ea/R.
- 15log(k₂/k₁) = [Ea/(2.303R)] (T₂ − T₁)/(T₁T₂).
- 16A 10 °C rise roughly doubles k for many reactions, because the fraction of molecules above Ea nearly doubles.
- 17e^(−Ea/RT) = fraction of molecules (or collisions) with energy ≥ Ea.
- 18A catalyst lowers Ea by an alternate path; it does not change ΔG, ΔH, K or the position of equilibrium.
- 19Collision theory: rate = P Z_AB e^(−Ea/RT); effective collisions need enough energy and the right orientation.
- 20Threshold energy = activation energy + average energy already possessed by the reactants.
Common traps
Where marks are lost
Writing the rate of 2N₂O₅ → 4NO₂ + O₂ as −d[N₂O₅]/dt and equating it to d[NO₂]/dt.
Reading the order straight off the balanced equation.
Calling a reaction of order ½ 'molecularity ½'.
Thinking k falls as the reaction slows down.
Using t½ = 0.693/k for every reaction.
Dropping the 2.303 when switching between ln and log.
Putting temperatures in °C into the Arrhenius equation.
Taking Ea in kJ mol⁻¹ while R is 8.314 J K⁻¹ mol⁻¹.
Saying a catalyst shifts equilibrium towards products.
Assuming a first-order reaction finishes after two half-lives.
Assuming every collision with enough energy leads to reaction.
Formulas
12 to know
Rate with stoichiometry
rate = −(1/a) Δ[A]/Δt = (1/c) Δ[C]/Δt
For aA + bB → cC + dD; instantaneous form uses d/dt.
Rate law
rate = k[A]^x[B]^y; order = x + y
x and y from experiment.
Units of k
(mol L⁻¹)^(1−n) s⁻¹
n = order. n = 0: mol L⁻¹ s⁻¹; 1: s⁻¹; 2: L mol⁻¹ s⁻¹.
Zero order, integrated
[R] = [R]₀ − kt
k = ([R]₀ − [R])/t.
Zero-order half-life
t½ = [R]₀/2k
Proportional to starting concentration.
First order, integrated
k = (2.303/t) log([R]₀/[R])
Same as [R] = [R]₀ e^(−kt).
First-order half-life
t½ = 0.693/k
Independent of concentration.
First order, gas pressure
k = (2.303/t) log[pᵢ/(2pᵢ − pₜ)]
For A(g) → B(g) + C(g) at constant volume.
Arrhenius equation
k = A e^(−Ea/RT)
ln k = ln A − Ea/RT.
Arrhenius, two temperatures
log(k₂/k₁) = [Ea/(2.303R)] × (T₂ − T₁)/(T₁T₂)
T in K; Ea in J mol⁻¹ with R = 8.314 J K⁻¹ mol⁻¹.
Fraction above Ea
fraction ≈ e^(−Ea/RT)
Fraction of molecules or collisions with energy ≥ Ea.
Collision theory
rate = P Z_AB e^(−Ea/RT)
Z_AB = collision frequency; P = steric (probability) factor.
Key terms
18 terms
- Chemical kinetics
- The study of how fast reactions go, what controls their speed, and the step-by-step routes (mechanisms) they follow.
- Average rate
- Change in concentration divided by a finite time interval.
- Instantaneous rate
- Rate at a single moment: the slope of the tangent to the concentration-time curve.
- Rate law
- The experimentally found expression of rate as k times reactant concentrations raised to powers.
- Rate constant (k)
- The proportionality constant in the rate law; the rate when all concentrations are 1 mol L⁻¹. Depends on temperature and catalyst.
- Order of reaction
- Sum of the powers of concentrations in the rate law; experimental, and may be zero or fractional.
- Elementary reaction
- A reaction that happens in a single step.
- Complex reaction
- An overall reaction made of a sequence of elementary steps.
- Molecularity
- Number of reacting species colliding at once in an elementary step: 1, 2 or 3.
- Rate-determining step
- The slowest step of a mechanism, which fixes the overall rate.
- Half-life (t½)
- Time for a reactant's concentration to fall to half of its starting value.
- Pseudo first order reaction
- A higher-order reaction that behaves as first order because one reactant is in large excess.
- Activation energy (Ea)
- The extra energy reactants must gain to reach the activated complex.
- Activated complex
- The short-lived, highest-energy arrangement between reactants and products, with bonds partly broken and partly formed.
- Arrhenius factor (A)
- The pre-exponential factor in k = A e^(−Ea/RT), also called the frequency factor.
- Catalyst
- A substance that speeds a reaction by giving it a lower-energy path, and is unchanged chemically at the end.
- Effective collision
- A collision with at least the threshold energy and the proper orientation, so it leads to products.
- Steric factor (P)
- The probability factor in collision theory that allows for collisions with the wrong orientation.