CHEMICAL KINETICS | Rate of Reaction ◆ Integrated Rate Laws ◆ Half-Life ◆ Arrhenius Equation ◆ Catalysis CHEMISTRY | Class XII

 CHEMISTRY  |  Class XII

Chapter 4

CHEMICAL KINETICS

Rate of Reaction  ◆  Integrated Rate Laws  ◆  Half-Life  ◆  Arrhenius Equation  ◆  Catalysis

 

1. Introduction to Chemical Kinetics

Chemical Kinetics is the branch of physical chemistry that deals with the speed (rate) of chemical reactions, the factors that influence this rate, and the mechanisms by which reactions proceed at the molecular level. The word 'kinetics' comes from the Greek word 'kinetikos' meaning 'putting in motion'.

Chemical thermodynamics tells us whether a reaction is spontaneous (ΔG < 0) and what the equilibrium position will be — but it tells us nothing about how fast the reaction will reach equilibrium. A reaction may be thermodynamically highly favourable yet practically useless if it is extremely slow. For example, the conversion of diamond to graphite is thermodynamically spontaneous (graphite is more stable) but so kinetically slow at room temperature that diamonds last forever. Conversely, the combustion of fuel in an engine is both thermodynamically favourable and kinetically fast — making it practically useful.

Chemical kinetics has enormous practical importance: it guides the design of industrial reactors (choosing optimal temperature, pressure, catalysts), explains food preservation and spoilage (why refrigeration slows bacterial growth), informs drug half-life in pharmacology, helps understand atmospheric chemistry (ozone depletion), and is the basis of enzyme kinetics in biochemistry.

 

2. Rate of Chemical Reaction

The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. Since reactant concentrations decrease with time and product concentrations increase, the rate is always expressed as a positive quantity.

Consider a general reaction:  aA + bB → cC + dD

Rate of Reaction (General)

Rate  =  −(1/a) d[A]/dt  =  −(1/b) d[B]/dt  =  +(1/c) d[C]/dt  =  +(1/d) d[D]/dt

 

The negative signs for reactants ensure the rate is positive (reactant concentrations decrease). Division by stoichiometric coefficients ensures all expressions give the same rate value for the overall reaction.

Figure 1: Rate of Reaction — [A] decreases and [B] increases with time. Instantaneous rate = slope of tangent to concentration-time curve. Average rate = Δ[A]/Δt.

2.1 Average Rate vs Instantaneous Rate

Average Rate: The change in concentration over a finite time interval: r_avg = −Δ[A]/Δt. This is easy to measure but gives a 'blurred' picture — the rate changes continuously during that interval.

Instantaneous Rate: The rate at a specific instant in time: r_inst = −d[A]/dt. This is the slope of the tangent to the concentration-time curve at that particular point. At the start of the reaction (t = 0), the instantaneous rate is called the Initial Rate — this is most commonly used in rate law determination.

 

2.2 Factors Affecting Rate of Reaction

◆        Concentration of Reactants: For most reactions, increasing the concentration of reactants increases the rate. More molecules per unit volume means more frequent collisions.

◆        Temperature: Increasing temperature increases the rate exponentially (roughly doubles for every 10°C rise — the 'rule of ten' or Q10 rule). Higher temperature gives molecules more kinetic energy — more collisions exceed the activation energy.

◆        Nature of Reactants: Ionic reactions (e.g., precipitation, neutralisation) are very fast. Reactions involving breaking of strong covalent bonds are slower. Surface area matters for solids — smaller particles react faster.

◆        Presence of Catalyst: A catalyst provides an alternative reaction pathway with a lower activation energy, dramatically increasing the rate without being consumed.

◆        Pressure (for gaseous reactions): Increasing pressure increases concentration of gases, hence increases rate.

◆        Solvent and Ionic Strength: The medium affects how readily reactants can interact.

 

3. Rate Law and Order of Reaction

The rate law (or rate equation) is a mathematical expression that relates the rate of a reaction to the concentrations of reactants. It is determined experimentally and cannot be derived from the balanced stoichiometric equation alone (except for elementary reactions).

For a general reaction: aA + bB → Products

Rate Law (Rate Equation)

Rate  =  k [A]^m [B]^n

 

Here k is the rate constant (or specific rate constant), m is the order with respect to A, n is the order with respect to B, and (m + n) is the overall order of the reaction. The values of m and n are determined experimentally — they may or may not equal the stoichiometric coefficients a and b.

3.1 Order of Reaction

Order with respect to a reactant: The exponent of that reactant's concentration in the rate law. It tells us how the rate changes when that reactant's concentration is changed while keeping all others constant.

Overall Order: The sum of all exponents in the rate law: (m + n + ...). The order is always determined from experiment — it can be zero, fractional, negative, or a whole number.

 

Order (m)	Meaning	Example
Zero (m=0)	Rate is independent of the concentration of A. Doubling [A] has no effect on rate.	Decomposition of NH3 on hot Pt/W; H2/Cl2 photochemical reaction
First (m=1)	Rate doubles when [A] doubles. Rate ∝ [A].	Decomposition of N2O5; Radioactive decay; Inversion of sucrose (pseudo 1st order)
Second (m=2)	Rate quadruples when [A] doubles. Rate ∝ [A]²	Decomposition of NO2; Saponification of ethyl acetate
Fractional	Rate depends on [A] raised to a fraction.	Decomposition of CH3CHO (order ≈ 1.5); Some chain reactions
Negative	Rate decreases when [A] increases — inhibitor.	Some enzyme reactions where excess substrate inhibits

 

3.2 Rate Constant (k) — Units and Significance

The rate constant k is the proportionality constant in the rate law. It depends on temperature (increases with temperature according to the Arrhenius equation) but is independent of concentration. The units of k depend on the overall order of reaction.

Units of Rate Constant (general)

Units of k  =  [concentration]^(1−n) [time]^(−1)  =  mol^(1−n) L^(n−1) s^(−1)

 

Order	Units of k	Rate Expression
Zero	mol L⁻¹ s⁻¹  (or mol L⁻¹ min⁻¹)	Rate = k
First	s⁻¹  (or min⁻¹)  — time⁻¹ only	Rate = k[A]
Second	L mol⁻¹ s⁻¹  (or L mol⁻¹ min⁻¹)	Rate = k[A]² or k[A][B]
Third	L² mol⁻² s⁻¹	Rate = k[A]³ or k[A]²[B]
nth	mol^(1−n) L^(n−1) s⁻¹	Rate = k[A]^n

 

3.3 Determination of Order — Method of Initial Rates

The most common experimental method to determine the order of a reaction is the Method of Initial Rates (Method of Isolation). In this method, the initial rate is measured for different initial concentrations of reactants, while keeping all other concentrations constant.

If doubling [A] doubles the rate → first order in A. If doubling [A] quadruples the rate → second order in A. If doubling [A] has no effect → zero order in A. If doubling [A] halves the rate → order = −1 in A (inhibition).

Finding Order from Two Experiments

Rate1/Rate2  =  ([A]1/[A]2)^m  →  log(Rate1/Rate2)  =  m × log([A]1/[A]2)

 

 

4. Integrated Rate Laws

The rate law gives the instantaneous rate at any moment. By integrating the rate law (differential equation), we obtain the Integrated Rate Law — which gives the concentration of reactant as a function of time. This allows us to (1) determine concentration at any time t, (2) find the time for a given degree of completion, and (3) determine the rate constant k from experimental data.

Figure 2: Integrated rate laws — [A] vs time curves for zero order (straight line), first order (exponential decay), and second order (hyperbolic). Each gives a characteristic graph.

4.1 Zero Order Reaction

In a zero order reaction, the rate is constant and independent of the concentration of reactant. The concentration decreases linearly with time. A plot of [A] vs t is a straight line with slope = −k.

Integrated Rate Law (Zero Order)

[A]  =  [A]₀  −  kt

 

Rate Constant (Zero Order)

k  =  ([A]₀ − [A]) / t   [units: mol L⁻¹ s⁻¹]

 

Half-Life (Zero Order)

t½  =  [A]₀ / 2k     (depends on initial concentration)

 

Characteristics: [A] vs t is a straight line (slope = −k). Reaction proceeds at constant rate until all reactant is consumed. Half-life depends on initial concentration (unlike first order). Examples: Photochemical reactions, enzyme-catalysed reactions at saturating substrate concentration, reactions on solid catalysts.

 

4.2 First Order Reaction

First order reactions are the most important in chemistry — radioactive decay, many drug metabolisms, first-order thermal decompositions, and many biological processes are first order. The rate is proportional to the concentration of one reactant.

Integrated Rate Law (First Order)

[A]  =  [A]₀ · e^(−kt)

 

Logarithmic Form

ln [A]  =  ln [A]₀  −  kt     or     ln([A]₀/[A])  =  kt

 

Half-Life (First Order)

t½  =  0.693 / k  =  ln 2 / k     (CONSTANT — independent of [A]₀)

 

Figure 3: First Order Reaction — ln[A] vs t is a straight line (slope = −k, intercept = ln[A]₀). Half-life t½ = 0.693/k is constant — same regardless of starting concentration.

Why First Order Half-Life is Constant — Key Insight

For a first order reaction: [A] = [A]0 × e^(−kt). At t = t½:  [A] = [A]0/2  →  [A]0/2 = [A]0 × e^(−kt½)  →  1/2 = e^(−kt½)  →  t½ = ln2/k = 0.693/k. This result is independent of [A]0 — the half-life is the same no matter what concentration you start with. This is the basis of radioactive dating (carbon-14, uranium-238) and drug half-life in pharmacology. After n half-lives: [A] = [A]0 / 2^n.  After 1 t½: 50% remains. After 2 t½: 25%. After 7 t½: < 1%.

 

Pseudo First Order Reactions: When a reaction is second order overall (rate = k[A][B]) but one reactant (say B) is present in large excess (so [B] ≈ constant = [B]₀), the reaction appears to be first order. The effective rate constant k' = k[B]₀ is called the pseudo first-order rate constant. Example: Hydrolysis of ethyl acetate in aqueous solution — water is in large excess so the reaction is pseudo first order in ester concentration.

 

4.3 Second Order Reaction

Second order reactions show a characteristic hyperbolic decay in [A] vs t plots. The linearised plot is 1/[A] vs t — a straight line with slope = +k. The half-life increases with time (unlike first order).

Integrated Rate Law (Second Order in A)

1/[A]  =  1/[A]₀  +  kt

 

Half-Life (Second Order)

t½  =  1 / (k [A]₀)     (depends on initial concentration; increases as [A]₀ decreases)

 

4.4 Summary of Integrated Rate Laws

Order	Integrated Law	Linear Plot	Slope	Half-Life (t½)	Units of k
Zero	[A] = [A]₀ − kt	[A] vs t	−k	[A]₀/(2k) — depends on [A]₀	mol L⁻¹ s⁻¹
First	ln[A] = ln[A]₀ − kt	ln[A] vs t	−k	0.693/k — CONSTANT	s⁻¹
Second	1/[A] = 1/[A]₀ + kt	1/[A] vs t	+k	1/(k[A]₀) — depends on [A]₀	L mol⁻¹ s⁻¹

 

 

5. Temperature Dependence of Rate Constant — Arrhenius Equation

It is a well-established experimental observation that the rate of a chemical reaction increases dramatically with temperature. Svante Arrhenius (1889) proposed a quantitative equation that describes the relationship between the rate constant k and the temperature T.

Arrhenius Equation

k  =  A · e^(−Ea/RT)

 

Here: k = rate constant; A = pre-exponential factor (Arrhenius factor, frequency factor) with same units as k; Ea = activation energy (J/mol or kJ/mol) — the minimum energy required for reaction; R = universal gas constant = 8.314 J mol⁻¹ K⁻¹; T = absolute temperature (Kelvin). The factor e^(−Ea/RT) represents the fraction of collisions that have energy ≥ Ea.

5.1 Logarithmic Form of Arrhenius Equation

Arrhenius — Logarithmic Form

ln k  =  ln A  −  Ea/(RT)

 

A plot of ln k vs 1/T gives a straight line with slope = −Ea/R and y-intercept = ln A. This is the Arrhenius plot — used experimentally to determine Ea and A.

Ea from Arrhenius Plot

Ea  =  −R × slope  =  −8.314 × (slope in K)   [J/mol]

 

Figure 4: Arrhenius Plot — ln k vs 1/T is a straight line. Slope = −Ea/R. The steeper the slope, the higher the activation energy. Extrapolating to 1/T = 0 gives ln A.

5.2 Two-Temperature Form of Arrhenius Equation

The most useful form for numerical problems — when rate constants are known at two temperatures T₁ and T₂:

Two-Temperature Arrhenius

ln(k₂/k₁)  =  (Ea/R) × (1/T₁  −  1/T₂)

 

In log₁₀ form (at 298 K)

log(k₂/k₁)  =  (Ea/2.303R) × [(T₂ − T₁)/(T₁ × T₂)]

 

This formula allows us to: (1) Calculate Ea if k is known at two temperatures, (2) Predict k at a new temperature if Ea and k at one temperature are known, (3) Find the temperature needed to achieve a desired rate constant.

5.3 Activation Energy — Physical Meaning

The activation energy (Ea) is the minimum extra energy that reactant molecules must possess (over and above their average energy) for a collision to result in a chemical reaction. Molecules must reach the Transition State (or Activated Complex) — a high-energy unstable species at the peak of the energy barrier — for the reaction to proceed.

Figure 5: Energy Profile Diagram — Ea is the energy barrier from reactants to transition state. A catalyst lowers Ea without changing ΔH. Exothermic reaction: products are more stable (lower energy) than reactants.

Transition State Theory (Activated Complex Theory): At the peak of the energy profile diagram sits the Transition State (also called Activated Complex). It is not a stable intermediate — it is an unstable, fleeting configuration of atoms that exists at the highest energy point along the reaction pathway. It cannot be isolated. The transition state can either revert to reactants or proceed to form products.

 

Threshold Energy: The minimum energy required for an effective (product-forming) collision. Threshold energy = Ea + Average kinetic energy of reactants.

Effective Collision: A collision that leads to chemical reaction. An effective collision must satisfy two conditions: (1) Colliding molecules must have energy ≥ threshold energy (energetic criterion), and (2) Molecules must collide in the proper geometric orientation (steric/orientation criterion).

 

6. Collision Theory of Chemical Reactions

Collision Theory (Lewis, Trautz, 1916–1918) provides a molecular-level explanation of why reactions occur and why the rate depends on temperature and concentration. It is based on the kinetic molecular theory of gases.

Basic Postulates: (1) Reactant molecules must collide with each other for a reaction to occur. (2) Not all collisions lead to reaction — only those with sufficient energy AND correct orientation are effective (productive). (3) The rate of reaction is proportional to the number of effective collisions per unit time per unit volume.

 

Rate from Collision Theory

Rate  =  Z_AB × f × p  =  Z_AB × e^(−Ea/RT) × p

 

Where Z_AB = collision frequency (total number of collisions per second per unit volume between A and B molecules), f = fraction of collisions with energy ≥ Ea = e^(−Ea/RT) (Boltzmann factor), and p = steric factor or probability factor (0 < p ≤ 1, accounts for proper orientation requirement).

6.1 Maxwell-Boltzmann Energy Distribution

The Maxwell-Boltzmann distribution describes how the kinetic energies of molecules in a gas are distributed at a given temperature. At any temperature, molecules have a range of energies — a few with very low energy, most with intermediate energy (near the peak), and a few with very high energy. The fraction of molecules with energy ≥ Ea is given by the Boltzmann factor: f = e^(−Ea/RT).

Figure 6: Maxwell-Boltzmann Distribution — At higher temperature T2, the distribution broadens and shifts right. A larger fraction of molecules have energy ≥ Ea → faster reaction rate.

Why Temperature Has Such a Large Effect on Rate

At T = 300 K, Ea = 50 kJ/mol: f = exp(−50000/(8.314×300)) = exp(−20.05) ≈ 2×10⁻⁹ At T = 310 K, Ea = 50 kJ/mol: f = exp(−50000/(8.314×310)) = exp(−19.40) ≈ 3.7×10⁻⁹ The ratio f(310)/f(300) ≈ 1.85 — the fraction nearly DOUBLES with just 10°C rise! This explains the empirical 'rule of ten' (Q10 rule): reaction rate doubles for every 10°C increase. The effect is exponential — a small change in T causes a large change in the Boltzmann factor and hence the rate. Lower Ea → more sensitive to temperature changes (more molecules near the threshold).

 

 

7. Catalysis

A catalyst is a substance that increases the rate of a chemical reaction without itself being permanently consumed or chemically changed at the end of the reaction. The process of using a catalyst is called catalysis. Catalysts can be recovered unchanged after the reaction.

How does a catalyst work? A catalyst provides an alternative reaction pathway (or mechanism) with a lower activation energy (Ea') compared to the uncatalysed pathway. Since the Boltzmann factor e^(−Ea/RT) is larger for a lower Ea, a larger fraction of molecules can cross the energy barrier — dramatically increasing the rate.

Key Point: A catalyst lowers the activation energy Ea but does NOT change the thermodynamics of the reaction — it does not change ΔH, ΔG, or the equilibrium constant K. It only affects HOW FAST the equilibrium is reached, not the final equilibrium position.

 

7.1 Types of Catalysis

Type	Description	Examples	Mechanism
Homogeneous Catalysis	Catalyst and reactants are in the SAME phase (all gas or all liquid).	SO2 oxidation with NO as catalyst (all gas); Lead chamber process; H+ in ester hydrolysis	Catalyst forms intermediate compounds that react with reactant, then regenerates
Heterogeneous Catalysis	Catalyst and reactants are in DIFFERENT phases (usually solid catalyst with liquid/gas reactants).	Haber process (Fe catalyst); Contact process (V2O5); Catalytic converters (Pt/Pd/Rh)	Adsorption of reactants on catalyst surface → weakening of bonds → reaction → desorption of products
Enzyme Catalysis (Biochemical)	Biological catalysts (enzymes — large protein molecules) that catalyse reactions in living organisms.	Amylase (starch digestion), Pepsin (protein digestion), Carbonic anhydrase (CO2/H2CO3)	Lock-and-key model or induced-fit model — substrate fits into active site

 

7.2 Heterogeneous Catalysis — Surface Mechanism

The mechanism of heterogeneous catalysis involves the following steps:

◆        Adsorption: Reactant molecules from gas or liquid phase are adsorbed onto the surface of the solid catalyst. This can be physisorption (weak van der Waals forces) or chemisorption (strong chemical bonding). Chemisorption weakens the bonds within the adsorbed reactant molecules, making them more reactive.

◆        Diffusion: Reactant molecules diffuse on the surface of the catalyst and come into contact with each other at active sites.

◆        Reaction: The adsorbed, activated reactant molecules react to form product molecules on the catalyst surface. The activation energy for this surface reaction is much lower than for the gas-phase reaction.

◆        Desorption: The product molecules detach from the catalyst surface (desorb) and move back into the gas/liquid phase, freeing the active sites for the next cycle.

 

Catalyst Poisoning: Some substances called poisons or inhibitors can block the active sites of a catalyst, permanently destroying its activity. For example, CO poisons the iron catalyst in the Haber process. Lead in petrol poisoned the platinum catalyst in early catalytic converters (which is why unleaded petrol was developed).

Catalyst Promoters: Substances that by themselves have little catalytic activity but when added to a catalyst, increase its activity or selectivity. For example, Al₂O₃ and K₂O are promoters for the iron catalyst in the Haber process.

 

7.3 Enzyme Catalysis — Special Features

Enzymes are the most efficient catalysts known — they can increase reaction rates by factors of 10⁶ to 10¹⁴. They are highly specific (each enzyme catalyses one specific reaction or type of reaction), work at mild conditions (body temperature 37°C, near-neutral pH), and are present in living organisms in very small amounts.

Michaelis-Menten Kinetics (Enzyme)

Rate  =  V_max [S] / (K_m + [S])     (simplified — not in syllabus but mentioned)

 

At low [S]: Rate ∝ [S] — first order in substrate. At high [S] ([S] >> Km): Rate = Vmax — zero order in substrate (enzyme is saturated). This gives the characteristic hyperbolic rate vs [S] curve — Michaelis-Menten kinetics.

 

8. Important Named Reactions — Orders and Rate Constants

Reaction	Overall Order	Rate Law	Key Feature
Decomposition of H2O2 (in aq.)	First order	Rate = k[H2O2]	2H2O2 → 2H2O + O2; ln[H2O2] vs t = straight line
Decomposition of N2O5	First order	Rate = k[N2O5]	2N2O5 → 4NO2 + O2; t½ = 0.693/k
Inversion of sucrose (acid-catalysed)	Pseudo first order	Rate = k'[sucrose]  (k' = k[H+][H2O])	Water is in large excess; apparent 1st order
Hydrolysis of esters (acidic hydrolysis)	Pseudo first order	Rate = k'[ester]	Water is solvent (excess); apparent 1st order
Saponification of ethyl acetate	Second order	Rate = k[CH3COOC2H5][OH−]	Base (NaOH) and ester; bimolecular
Decomposition of NO2 (at high T)	Second order	Rate = k[NO2]2	2NO2 → 2NO + O2
H2 + I2 → 2HI	Second order	Rate = k[H2][I2]	Elementary bimolecular reaction; mechanism via I atoms
H2 + Br2 → 2HBr (thermal)	Fractional (~3/2)	Rate = k[H2][Br2]^(1/2)	Chain mechanism; fractional order from rate-determining step

 

 

9. Master Formula Table — Chemical Kinetics

Formula / Concept	Expression	Key Notes / Units
Rate of Reaction	r = −(1/a)d[A]/dt = +(1/c)d[C]/dt	Always positive; divide by stoichiometry
Rate Law	Rate = k[A]^m [B]^n	m,n from experiment; overall order = m+n
Units of k (nth order)	mol^(1−n) L^(n−1) s⁻¹	n=0: mol/L/s; n=1: s⁻¹; n=2: L/mol/s
Finding order	log(r1/r2) = m × log([A]1/[A]2)	From initial rate method
Zero Order Integrated	[A] = [A]0 − kt	[A] vs t → straight line, slope = −k
Zero Order t½	t½ = [A]0 / 2k	Depends on [A]0
First Order Integrated	[A] = [A]0 e^(−kt)  or  ln[A] = ln[A]0 − kt	ln[A] vs t → straight line
First Order t½	t½ = 0.693/k = ln2/k	CONSTANT; independent of [A]0
After n half-lives	[A] = [A]0 / 2^n	Same for 1st order radioactive decay
Second Order Integrated	1/[A] = 1/[A]0 + kt	1/[A] vs t → straight line, slope = +k
Second Order t½	t½ = 1/(k[A]0)	Depends on [A]0; increases with time
Arrhenius Equation	k = A × e^(−Ea/RT)	A = frequency factor; Ea = activation energy
Arrhenius (log form)	ln k = ln A − Ea/RT	Slope of ln k vs 1/T = −Ea/R
Arrhenius (two T)	ln(k2/k1) = (Ea/R)(1/T1 − 1/T2)	Most useful for numericals
Finding Ea	Ea = −R × slope (of ln k vs 1/T)	R = 8.314 J mol⁻¹ K⁻¹
Boltzmann factor	f = e^(−Ea/RT)	Fraction of molecules with E ≥ Ea
Collision theory rate	Rate = ZAB × f × p	p = steric factor (≤1)
Pseudo 1st order k'	k' = k[B]0 (B in large excess)	Apparent first-order constant

 

 

10. Quick Revision — Key Points

Rate Laws & Order — Must Know

* Rate = k[A]^m [B]^n. Order is determined experimentally — NOT from stoichiometry. * Units of k: n=0 → mol L⁻¹ s⁻¹; n=1 → s⁻¹; n=2 → L mol⁻¹ s⁻¹. Remember: only 1st order has time unit only. * Method of initial rates: keep one reactant varying, others constant. Use log(r1/r2) = m × log([A]1/[A]2). * Zero order: [A] vs t is linear. First order: ln[A] vs t is linear. Second order: 1/[A] vs t is linear. * Doubling [A] doubles rate → 1st order. Quadruples rate → 2nd order. No change → 0th order. * Pseudo first-order: when one reactant is in large excess (e.g., water in hydrolysis reactions).

 

Integrated Rate Laws & Half-Life — Must Know

* Zero order: t½ = [A]0/2k — depends on [A]0. Rate is constant throughout. * First order: t½ = 0.693/k — CONSTANT (independent of [A]0). This is the key hallmark. * First order: [A] = [A]0 × e^(−kt). After n half-lives: [A] = [A]0/2^n. * Second order: t½ = 1/(k[A]0) — depends on [A]0; gets longer as reaction proceeds. * Plot [A] vs t: Zero order = straight line. First order: exponential decay. Second order: hyperbola. * Linearising plots: Zero: [A] vs t; First: ln[A] vs t; Second: 1/[A] vs t. All give straight lines.

 

Arrhenius Equation & Temperature — Must Know

* k = A × e^(−Ea/RT). Higher T → larger k. Higher Ea → stronger temperature dependence. * ln k vs 1/T: straight line with slope = −Ea/R and y-intercept = ln A. * Two-temperature form: ln(k2/k1) = (Ea/R)(1/T1 − 1/T2). Most used formula in numericals. * Rule of Ten (Q10): rate roughly doubles for every 10°C rise in temperature. * Ea = −R × slope (slope from Arrhenius plot). R = 8.314 J mol⁻¹ K⁻¹. * Maxwell-Boltzmann: fraction with E ≥ Ea = e^(−Ea/RT). At higher T, larger fraction → faster rate. * Effective collision needs: (1) energy ≥ Ea AND (2) correct orientation of collision.

 

Catalysis — Must Know

* Catalyst lowers activation energy Ea — does NOT change ΔH, ΔG or equilibrium constant K. * Homogeneous catalysis: catalyst and reactants in same phase. Intermediate formation mechanism. * Heterogeneous catalysis: different phases. Steps: Adsorption → Diffusion → Reaction → Desorption. * Catalyst poisoning: impurities block active sites (e.g., CO poisons Fe catalyst in Haber process). * Enzyme catalysis: most efficient (10⁶–10¹⁴ times faster). Highly specific. Lock-and-key model. * At high [S] in enzyme reactions: rate = Vmax (zero order). At low [S]: rate ∝ [S] (first order). * Promoters enhance catalyst activity. Inhibitors/poisons reduce or destroy catalyst activity.

 

— End of Chapter 4: Chemical Kinetics (Chemistry) —