Chemical Kinetics: NEET notes.

01 · NCERT §3.1

Rate of a reaction

• Rate is the change in concentration of a reactant or product per unit time. Concentration is in mol L⁻¹ and time in s, min or h, so rate has units such as mol L⁻¹ s⁻¹; for gases, pressure in atm can replace concentration, giving atm s⁻¹.
• For R → P, rate = −Δ[R]/Δt = +Δ[P]/Δt. The minus sign makes the rate positive, because [R] falls.
• Average rate is the change over a finite interval. It hides the fact that the rate itself changes during that interval, usually falling as reactants are used up.
• Instantaneous rate is the limit as Δt → 0: r = −d[R]/dt = d[P]/dt. On a concentration-time graph it is the slope of the tangent at that moment.
• When coefficients differ, divide each rate of change by its coefficient so that every species gives the same number. For 2HI → H₂ + I₂: rate = −½ d[HI]/dt = d[H₂]/dt = d[I₂]/dt.
• For 2N₂O₅ → 4NO₂ + O₂, rate = −½ Δ[N₂O₅]/Δt = ¼ Δ[NO₂]/Δt = Δ[O₂]/Δt. If [N₂O₅] falls from 2.33 to 2.08 mol L⁻¹ in 184 min, the reaction rate is ½ × 0.25/184 = 6.79 × 10⁻⁴ mol L⁻¹ min⁻¹, and NO₂ forms at four times that, 2.72 × 10⁻³ mol L⁻¹ min⁻¹.
• Rates span a huge range: ionic precipitation (such as AgCl from Ag⁺ and Cl⁻) is almost instantaneous, the inversion of cane sugar and hydrolysis of starch go at a moderate pace, and the rusting of iron in moist air is very slow.

02 · NCERT §3.2; §3.2.1; §3.2.2

Rate law and rate constant

• Rate depends on the concentration of reactants (pressure for gases), temperature and catalyst.
• The rate law (rate equation) expresses rate as k times concentrations raised to powers: for aA + bB → products, rate = k[A]^x[B]^y.
• The powers x and y are found by experiment. They need not equal the coefficients a and b of the balanced equation.
• The standard method compares initial rates. For 2NO + O₂ → 2NO₂, doubling [NO] at fixed [O₂] makes the rate four times larger and doubling [O₂] at fixed [NO] makes it twice as large, so rate = k[NO]²[O₂].
• Two reactions from the book whose powers do not follow the equation: CHCl₃ + Cl₂ → CCl₄ + HCl has rate = k[CHCl₃][Cl₂]^½, and the acid hydrolysis of an ester has rate = k[ester][H₂O]⁰ in excess water.
• k, the rate constant, equals the rate when every concentration in the rate law is 1 mol L⁻¹. At a given temperature it is fixed for the reaction; it changes with temperature and with a catalyst, not with concentration.
• Rate falls as the reaction proceeds because concentrations fall; k stays the same throughout.

03 · NCERT §3.2.3

Order of a reaction and units of k

• Order is the sum of the powers in the experimental rate law. In rate = k[A]^x[B]^y the order is x + y; x alone is the order with respect to A.
• Order can be 0, 1, 2, 3, or a fraction. Zero order means the rate does not change with concentration of that reactant.
• An elementary reaction happens in one step. A complex reaction is a series of elementary steps (a mechanism), and its order comes from that mechanism, not from the overall equation.
• Units of k follow from rate = k[A]ⁿ: k has units (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 (mol⁻¹ L s⁻¹).
• Working backwards, the units of a stated k give its order: k = 3 × 10⁻⁴ s⁻¹ is first order; k = 2.3 × 10⁻⁵ L mol⁻¹ s⁻¹ is second order.
• Order is always an experimental quantity. It can change with conditions, as when a reactant is present in large excess.

04 · NCERT §3.2.4

Molecularity and mechanism

• Molecularity is the number of reacting species (atoms, ions or molecules) that must collide at once in an elementary step. It is always a whole number: 1, 2 or 3.
• Examples: NH₄NO₂ → N₂ + 2H₂O is unimolecular, 2HI → H₂ + I₂ is bimolecular, and 2NO + O₂ → 2NO₂ is termolecular.
• Molecularity above three is not seen, because a simultaneous collision of four or more particles is too improbable.
• A balanced equation with many molecules, such as KClO₃ + 6FeSO₄ + 3H₂SO₄ → KCl + 3Fe₂(SO₄)₃ + 3H₂O, cannot be one step; it is found to be second order and runs through several steps.
• In a sequence of steps, the slowest one limits the overall rate. It is called the rate-determining step, like the slowest runner holding back a relay team.
• Decomposition of H₂O₂ in alkaline medium with I⁻ has rate = k[H₂O₂][I⁻]. The proposed mechanism: slow step H₂O₂ + I⁻ → H₂O + IO⁻, then fast step H₂O₂ + IO⁻ → H₂O + I⁻ + O₂. IO⁻ is an intermediate that is made and then used up.
• Order applies to both elementary and complex reactions; molecularity applies only to elementary steps. For a complex reaction the order is set by the slowest step, and the molecularity of that step can equal its order.
• Order can be zero or fractional; molecularity cannot be zero or fractional.

05 · NCERT §3.3; §3.3.1

Zero-order reactions

• Integrating the rate law gives an equation linking concentration directly to time, which experiments can test; this is how order and k are found in practice.
• For zero order, rate = −d[R]/dt = k, a constant. Integration gives [R] = [R]₀ − kt.
• A plot of [R] against t is a straight line with slope −k and intercept [R]₀.
• So k = ([R]₀ − [R])/t. The reactant is used up entirely at t = [R]₀/k, after which the reaction simply stops.
• Zero order is uncommon and appears under special conditions, usually when a surface or an enzyme is saturated.
• NH₃ decomposing on a hot platinum surface at 1130 K at high pressure: 2NH₃ → N₂ + 3H₂ with rate = k. The surface is fully covered, so extra gas cannot speed the reaction.
• Thermal decomposition of HI on a gold surface is another zero-order example.

06 · NCERT §3.3.2

First-order reactions

• For first order, rate = −d[R]/dt = k[R]. Integration gives ln([R]₀/[R]) = kt, or [R] = [R]₀e^(−kt).
• In common logs: k = (2.303/t) log([R]₀/[R]).
• A plot of ln[R] against t is a straight line of slope −k; a plot of log([R]₀/[R]) against t is a straight line through the origin with slope k/2.303.
• Between two times t₁ and t₂: k = 2.303/(t₂ − t₁) × log([R]₁/[R]₂).
• Examples: hydrogenation of ethene (rate = k[C₂H₄]), natural radioactive decay such as that of radium, and the decomposition of N₂O₅ and N₂O.
• Worked number: [N₂O₅] falls from 1.24 × 10⁻² to 0.20 × 10⁻² mol L⁻¹ in 60 min at 318 K. k = (2.303/60) log 6.2 = 0.0304 min⁻¹.
• For a gas-phase reaction A(g) → B(g) + C(g) at constant volume, pressure follows the progress. If the initial pressure is pᵢ and the total pressure at time t is pₜ, then p_A = 2pᵢ − pₜ and k = (2.303/t) log(pᵢ/(2pᵢ − pₜ)).
• First-order decay is exponential: the reactant never quite reaches zero, but falls by the same fraction in every equal time interval.

07 · NCERT §3.3.3

Half-life and pseudo first order

• Half-life t½ is the time for the concentration of a reactant to fall to half its starting value.
• Zero order: t½ = [R]₀/2k. It is proportional to the starting concentration, so each successive half-life is half as long as the one before.
• First order: t½ = 0.693/k, independent of concentration. Every half-life of a first-order reaction takes the same time.
• Example: for k = 5.5 × 10⁻¹⁴ s⁻¹, t½ = 0.693/(5.5 × 10⁻¹⁴) = 1.26 × 10¹³ s.
• For first order, 99.9% completion takes (2.303/k) log 1000 = 6.909/k, which is about 10 half-lives; 99% completion takes 4.606/k, about 6.6 half-lives.
• After n half-lives of a first-order reaction, the fraction remaining is (½)ⁿ.
• A pseudo first order reaction is truly of higher order, but one reactant is in such large excess that its concentration barely changes. Its term is absorbed into k.
• Acid hydrolysis of ethyl acetate in a large excess of water behaves as first order: with 0.01 mol ester and 10 mol water, water only drops to 9.99 mol when the ester is gone. Rate = k′[CH₃COOC₂H₅], where k′ = k[H₂O].
• Inversion of cane sugar in acid (C₁₂H₂₂O₁₁ + H₂O → glucose + fructose) is another pseudo first order reaction: rate = k[C₁₂H₂₂O₁₁].

08 · NCERT §3.4

Temperature and the Arrhenius equation

• Most reactions speed up with temperature. N₂O₅ in the gas phase has a half-life of about 12 min at 50 °C, 5 h at 25 °C and 10 days at 0 °C. A mixture of KMnO₄ and oxalic acid decolourises faster when warm.
• For many reactions a rise of 10 °C roughly doubles the rate constant.
• Arrhenius equation: k = A e^(−Ea/RT). A is the Arrhenius (frequency) factor, Ea the activation energy in J mol⁻¹ and R = 8.314 J K⁻¹ mol⁻¹.
• Reactants must pass through a short-lived, high-energy activated complex before becoming products. For H₂ + I₂ → 2HI the complex has partly broken H–H and I–I bonds and partly formed H–I bonds. Ea is the energy needed to reach it from the reactants.
• At a given temperature molecules have a spread of kinetic energies (the Maxwell-Boltzmann distribution). The peak is at the most probable energy. A higher temperature flattens the curve and shifts the peak to higher energy; the total area stays the same because the number of molecules is fixed.
• e^(−Ea/RT) is the fraction of molecules with energy at least Ea. Raising T by 10 °C nearly doubles the area beyond Ea, which is why rate nearly doubles.
• Taking logs: ln k = ln A − Ea/RT. A plot of ln k against 1/T is a straight line with slope −Ea/R and intercept ln A.
• Two temperatures: log(k₂/k₁) = [Ea/(2.303R)] × [(T₂ − T₁)/(T₁T₂)]. For k = 0.02 s⁻¹ at 500 K and 0.07 s⁻¹ at 700 K, this gives Ea = 18.2 kJ mol⁻¹.
• If k doubles between 298 K and 308 K, Ea = 2.303R × log 2 × (298 × 308)/10 = 52.9 kJ mol⁻¹.

09 · NCERT §3.4.1

Effect of a catalyst

• A catalyst increases the rate of a reaction and is chemically unchanged at the end. MnO₂ speeds up the decomposition of KClO₃: 2KClO₃ → 2KCl + 3O₂.
• A substance added to slow a reaction is not called a catalyst; it is an inhibitor.
• Intermediate complex theory: the catalyst takes part by forming temporary bonds with a reactant to give an intermediate complex, which then breaks up into products and releases the catalyst.
• The catalyst provides a new pathway (mechanism) with a lower activation energy, so a larger fraction of molecules can cross the barrier at the same temperature.
• A small amount of catalyst is enough to change the rate greatly.
• A catalyst does not change ΔG of the reaction. It can speed up only a reaction that is already spontaneous; it cannot make a non-spontaneous reaction happen.
• It lowers the barrier equally for forward and reverse reactions, so equilibrium is reached sooner but the equilibrium constant and the equilibrium composition do not change.

10 · NCERT §3.5

Collision theory

• Collision theory (Max Trautz and William Lewis, 1916-18) treats molecules as hard spheres and says a reaction happens only when molecules collide.
• Collision frequency Z counts how many collisions happen each second in a unit volume of the reacting mixture.
• Only collisions carrying at least a threshold energy can succeed. Threshold energy = activation energy + energy the molecules already have.
• For A + B → products, rate = Z_AB e^(−Ea/RT), where e^(−Ea/RT) is the fraction of collisions energetic enough to react. This mirrors the Arrhenius equation, with Z_AB in the role of A.
• Proper orientation is also needed: for the formation of methanol from bromomethane and OH⁻, the OH⁻ must approach the carbon on the side away from bromine, or the collision fails even with enough energy.
• Energy and orientation together make an effective collision. Adding a probability (steric) factor P gives rate = P Z_AB e^(−Ea/RT).
• The theory's weakness is its hard-sphere picture of atoms and molecules; it ignores their structure, which is why P is needed at all.

Revise

Must-know facts

1. 01Rate = −(1/a) d[A]/dt = (1/c) d[C]/dt for aA → cC: divide by the coefficient so every species gives one rate.
2. 02Instantaneous rate is the slope of the tangent to the concentration-time curve; average rate is a slope across an interval.
3. 03The rate law is found by experiment. Its powers need not match the coefficients in the balanced equation.
4. 04Order = sum of the powers in the rate law; it can be 0, a fraction, or a whole number.
5. 05Molecularity belongs to one elementary step, is a whole number 1-3, and is never zero or fractional.
6. 06In a complex reaction, the slowest step sets the rate (rate-determining step).
7. 07Units 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.
8. 08Zero order: [R] = [R]₀ − kt; t½ = [R]₀/2k; straight line of [R] vs t.
9. 09First order: k = (2.303/t) log([R]₀/[R]); t½ = 0.693/k; straight line of ln[R] vs t.
10. 10First-order half-life does not depend on concentration; zero-order half-life is proportional to [R]₀.
11. 11First order: 99.9% completion ≈ 10 half-lives; 99% ≈ 6.6 half-lives; after n half-lives (½)ⁿ remains.
12. 12Pseudo first order: one reactant in large excess (ester hydrolysis in water; inversion of cane sugar).
13. 13k changes with temperature and catalyst, never with concentration.
14. 14Arrhenius: k = A e^(−Ea/RT); ln k vs 1/T is a straight line of slope −Ea/R.
15. 15log(k₂/k₁) = [Ea/(2.303R)] (T₂ − T₁)/(T₁T₂).
16. 16A 10 °C rise roughly doubles k for many reactions, because the fraction of molecules above Ea nearly doubles.
17. 17e^(−Ea/RT) = fraction of molecules (or collisions) with energy ≥ Ea.
18. 18A catalyst lowers Ea by an alternate path; it does not change ΔG, ΔH, K or the position of equilibrium.
19. 19Collision theory: rate = P Z_AB e^(−Ea/RT); effective collisions need enough energy and the right orientation.
20. 20Threshold energy = activation energy + average energy already possessed by the reactants.

Where marks go

Common traps

Reference

Formulas

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.

Glossary

Key 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.