Study sheet: Chemical Kinetics

📋 Course Outline

1. Scope of Chemical Kinetics
2. Reaction Rate
3. Stoichiometric Rate Relations
4. Rate Laws and Rate Constants
5. Reaction Order
6. Molecularity and Mechanisms
7. Integrated Rate Equations
8. Half-Life and Pseudo-Order
9. Temperature Dependence
10. Catalysis and Collision Theory

📖 1. Scope of Chemical Kinetics

🔑 Key Concepts & Definitions

• Chemical kinetics : the branch of chemistry that studies reaction rates, the factors controlling them, and reaction mechanisms.

★ Must-know

📌 Thermodynamics predicts whether a reaction is feasible, whereas chemical kinetics determines how rapidly the reaction occurs and under what conditions its rate changes.

Further detail

• A reaction with ΔG < 0 at constant temperature and pressure is feasible, but diamond-to-graphite conversion remains imperceptibly slow despite being thermodynamically feasible.

💡 Memory Hook

Thermodynamics asks whether; kinetics asks how fast.

📖 2. Reaction Rate

🔑 Key Concepts & Definitions

• Reaction rate : the change in concentration of a reactant or product per unit time.

★ Must-know

📐 Formula — For a reaction R → P at constant volume, the average rate is $r_{av}=-\frac{\Delta[R]}{\Delta t}=\frac{\Delta[P]}{\Delta t}$.

📐 Formula — The instantaneous rate is $r_{inst}=-\frac{d[R]}{dt}=\frac{d[P]}{dt}$ and equals the slope of the tangent to a concentration–time curve.

Further detail

• Reaction-rate units are concentration per time, such as mol L⁻¹ s⁻¹, or atm s⁻¹ when gas concentration is represented by partial pressure.

💡 Memory Hook

Reactants disappear while products appear.

📖 3. Stoichiometric Rate Relations

★ Must-know

📐 Formula — For a reaction with stoichiometric coefficients, the rate is obtained by dividing each species’ concentration change by its coefficient, as in $aA+bB\rightarrow cC+dD$ and $r=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=\frac{1}{c}\frac{d[C]}{dt}=\frac{1}{d}\frac{d[D]}{dt}$.

Further detail

• For $2HI\rightarrow H_2+I_2$, the reaction rate is $r=-\frac{1}{2}\frac{d[HI]}{dt}=\frac{d[H_2]}{dt}=\frac{d[I_2]}{dt}$.

💡 Memory Hook

Divide each concentration change by its stoichiometric coefficient.

📖 4. Rate Laws and Rate Constants

🔑 Key Concepts & Definitions

• Rate law : the experimentally determined expression that relates reaction rate to the molar concentrations of reacting species.
• Rate constant : the proportionality constant in a rate law at a specified temperature.

★ Must-know

📐 Formula — For $aA+bB\rightarrow cC+dD$, a general rate law is $r=k[A]^x[B]^y$, where k is the rate constant.

Further detail

📐 Formula — For $2NO+O_2\rightarrow2NO_2$, experimental data give $r=k[NO]^2[O_2]$.

📖 5. Reaction Order

🔑 Key Concepts & Definitions

• Reaction order : the sum of the powers of reactant concentrations appearing in its experimentally determined rate law.

★ Must-know

• Reaction order can be zero, an integer, or a fraction, and a zero-order reaction has a rate independent of reactant concentration.

Further detail

📐 Formula — For $r=k[A]^{1/2}[B]^{3/2}$, the overall order is $\frac{1}{2}+\frac{3}{2}=2$.

📖 6. Molecularity and Mechanisms

🔑 Key Concepts & Definitions

• Molecularity : the number of reacting species that must collide simultaneously in a single elementary reaction.

★ Must-know

📌 Molecularity is always a positive integer from one to three, whereas reaction order may be zero, fractional, or negative.

• A complex reaction proceeds through a sequence of elementary steps, and its slowest step controls the overall rate.

Further detail

• In the iodide-catalysed decomposition of hydrogen peroxide in alkaline medium, IO⁻ is an intermediate and the first elementary step is slow and rate determining.

💡 Memory Hook

A relay team moves only as fast as its slowest runner.

📖 7. Integrated Rate Equations

★ Must-know

📐 Formula — For a zero-order reaction $R\rightarrow P$, the integrated rate law is $[R]=[R]_0-kt$ and the rate constant is $k=\frac{[R]_0-[R]}{t}$.

📐 Formula — For a first-order reaction $R\rightarrow P$, the integrated rate law is $\ln\frac{[R]_0}{[R]}=kt$ or $[R]=[R]_0e^{-kt}$.

Further detail

• A plot of [R] against time is linear with slope −k for a zero-order reaction, whereas a plot of ln[R] against time is linear with slope −k for a first-order reaction.

💡 Memory Hook

Zero order gives a linear concentration plot; first order gives a linear logarithmic plot.

📖 8. Half-Life and Pseudo-Order

🔑 Key Concepts & Definitions

• Half-life : the time required for the concentration of a reactant to decrease to half its initial value.
• Pseudo-first-order reaction : a higher-order reaction that behaves as first order because one reactant is present in large excess and its concentration remains nearly constant.

📝 Essential Points

📐 Formula — For a zero-order reaction, the half-life is $t_{1/2}=\frac{[R]_0}{2k}$ and therefore depends directly on the initial concentration.

📐 Formula — For a first-order reaction, the half-life is $t_{1/2}=\frac{0.693}{k}$ and is independent of the initial concentration.

💡 Memory Hook

Zero-order half-life depends on initial concentration; first-order half-life does not.

📖 9. Temperature Dependence

🔑 Key Concepts & Definitions

• Activation energy : the energy required to form the activated complex from the reacting molecules.

★ Must-know

📐 Formula — The Arrhenius equation is $k=Ae^{-E_a/(RT)}$, where A is the frequency factor, Ea is activation energy, R is the gas constant, and T is absolute temperature.

📐 Formula — The logarithmic Arrhenius form is $\ln k=-\frac{E_a}{RT}+\ln A$, so a plot of ln k against 1/T has slope $-E_a/R$ and intercept ln A.

Further detail

• Increasing temperature by 10 degrees approximately doubles the rate constant for many reactions.

💡 Memory Hook

Higher temperature or lower activation energy → larger rate constant.

📖 10. Catalysis and Collision Theory

🔑 Key Concepts & Definitions

• Catalyst : increases the reaction rate without undergoing permanent chemical change by providing an alternative pathway with lower activation energy.
• Collision frequency : the number of collisions between reactant molecules per second per unit volume of reaction mixture.

📝 Essential Points

📌 A catalyst accelerates both the forward and reverse reactions to the same extent, so equilibrium is reached faster without changing the equilibrium state.

📐 Formula — Collision theory gives the rate relation $r=Z_{AB}e^{-E_a/(RT)}P$, where P is the steric factor accounting for proper molecular orientation. — Max Trautz and William Lewis

📌 Effective collisions require energy at least equal to the activation threshold and suitable orientation, whereas collisions lacking either condition do not form products.

💡 Memory Hook

Collision frequency + sufficient energy + proper orientation → effective collision.

📊 Synthesis Tables

Zero- and First-Order Kinetics

Property	Zero order	First order
Integrated law	[R] = [R]₀ − kt	ln([R]₀/[R]) = kt
Linear plot	[R] versus t	ln[R] versus t
Half-life	t₁/₂ = [R]₀/(2k)	t₁/₂ = 0.693/k
Dependence on [R]₀	Depends on initial concentration	Independent of initial concentration