Reaction Kinetics notes

MDCAT Chemistry

Reaction kinetics is the study of the rate of chemical reactions, the factors that affect the rate, and the mathematical expressions used to describe reactions. This chapter explains rate law, order, molecularity, activation energy, activated complex, half-life, and rate constant.

Rate of Reaction

The rate of a chemical reaction is the change in concentration of a reactant or product per unit time. Concentration is commonly expressed in mol dm⁻³ and time in seconds. Reactant concentration decreases, so a negative sign is used to make the rate positive.

For a reaction A → B, rate can be written as rate = −Δ[A]/Δt for the reactant or rate = Δ[B]/Δt for the product. The rate may be average or instantaneous. The instantaneous rate is the rate at a particular moment and is obtained from the slope of the tangent to a concentration versus time curve.

Rate of reaction = change in concentration divided by change in time.
For a reactant, rate = −Δ[reactant]/Δt.
For a product, rate = Δ[product]/Δt.
The usual unit of rate is mol dm⁻³ s⁻¹.
The rate of forward reaction is the conversion of reactants into products per unit time.
At the start of a reaction, the instantaneous rate is generally higher than the average rate over a longer time interval.
As reactants are consumed, their concentration usually decreases and the rate also decreases.
A graph of concentration against time is generally a curve, not a straight line.

Rate in Terms of Stoichiometric Coefficients

For reactions involving different stoichiometric coefficients, the rate of disappearance or formation is divided by the relevant coefficient. This gives one common rate for the whole reaction.

For aA + bB → cC + dD, the reaction rate is −1/a Δ[A]/Δt = −1/b Δ[B]/Δt = 1/c Δ[C]/Δt = 1/d Δ[D]/Δt. The negative signs are used for reactants because their concentrations fall with time.

In 2H2 + O2 → 2H2O, hydrogen disappears twice as fast as oxygen when compared directly by concentration change.
For a single-step reaction A → B + 2C, the rate law is rate = k[A] because one molecule of A participates in that elementary step.
Greater reactant concentration generally gives a greater value of dx/dt, where x is the amount reacted per unit time.
The rate can be calculated by measuring the change in concentration of a reactant or product with time.
The amount of product formed increases with time for reactions of any order, although the rate of formation usually becomes smaller.

Factors Affecting Rate of Reaction

The rate of a reaction depends on the number of successful collisions between reacting particles. A collision is successful only when particles collide with suitable orientation and enough energy to overcome the activation energy.

Increasing the concentration of reactants increases the number of particles per unit volume. This usually increases collision frequency and therefore increases the rate. For gases, increasing pressure has a similar effect because particles become closer together.

Increase in temperature generally increases the rate of reaction.
Higher temperature increases both collision frequency and the fraction of particles having energy equal to or greater than activation energy.
Increasing concentration of reactants generally increases the rate.
Increasing pressure increases the rate of a gaseous reaction when the number of gaseous particles per unit volume increases.
Increasing surface area of a solid reactant increases the rate because more particles are exposed for collision.
A catalyst increases rate by providing an alternative pathway with lower activation energy.
A catalyst is not consumed overall and does not change the final equilibrium position.
The effect of concentration is determined experimentally and may differ for different reactions.

Collision Theory and Activated Complex

Collision theory states that reacting particles must collide to react. However, not every collision produces products. The particles must have sufficient kinetic energy and suitable orientation. Such a collision is called an effective collision.

During an effective collision, bonds in the reactants begin to break and new bonds begin to form. The unstable, high-energy arrangement at this stage is called the activated complex or transition state. It exists for a very short time and may form products or return to reactants.

An activated complex is formed as a result of an effective collision.
Effective collision requires suitable orientation of particles.
Effective collision also requires energy equal to or greater than activation energy.
The activated complex has higher energy than both the reactants and the products in an exothermic reaction.
Activation energy is the minimum extra energy required for reactant particles to form the activated complex.
A catalyst lowers the activation energy of the reaction pathway.
In an exothermic reaction, the forward reaction requires less energy than the reverse reaction because products have lower energy than reactants.
A higher temperature increases the number of particles able to form the activated complex.

Rate Law and Order of Reaction

The rate law or rate equation expresses the rate in terms of the concentrations of reactants. For a reaction involving A and B, it may be written as rate = k[A]m[B]n. The powers m and n are determined experimentally, not necessarily from the balanced chemical equation.

The order with respect to a reactant is the power of its concentration in the rate equation. The overall order is the sum of all powers in the rate equation. A reaction may be zero order, first order, second order, or a fractional order.

The rate equation is an experimental expression.
For rate = k[A]n, the order with respect to A is n.
For rate = k[A]m[B]n, overall order = m + n.
A zero-order reaction has rate = k and its rate is independent of reactant concentration.
For a reaction that is zero order with respect to P, changing the concentration of P does not change the rate.
A first-order reaction has rate = k[A].
A second-order reaction may have rate = k[A]2 or rate = k[A][B].
The order of a reaction is not always equal to the stoichiometric coefficient in the balanced equation.

Molecularity, Pseudo-Unimolecular Reactions and Irreversibility

Molecularity is the number of reacting species taking part in a single elementary step. It is always a whole positive number, such as one, two, or three. Molecularity is not assigned to an overall complex reaction, while order may be assigned to an overall reaction from experimental data.

When one reactant is present in large excess, its concentration remains almost constant during the reaction. Its concentration is then included in the rate constant, and a reaction that is actually bimolecular may appear to be first order. This is called a pseudo-unimolecular or pseudo-first-order reaction.

Molecularity is defined only for an elementary reaction step.
Molecularity is always a positive integer and cannot be zero or fractional.
Order is obtained experimentally and may be zero, fractional, or a whole number.
For an elementary reaction, the order and molecularity may be equal.
For a complex reaction, overall order and molecularity need not be equal.
In A + B → products, if B is in large excess, the reaction behaves as pseudo-unimolecular with respect to A.
For A + B → products, rate = k[A][B]. If [B] is constant, rate = k′[A], where k′ = k[B].
An irreversible process cannot be reversed by simply reversing the controlling conditions or factors.

Integrated Rate Equations and Half-Life

Half-life, written as t1/2, is the time required for the concentration of a reactant to become half of its initial value. Its relation with the rate constant depends on the order of the reaction.

For a first-order reaction, t1/2 = 0.693/k. It is independent of the initial concentration. For a second-order reaction involving one reactant, t1/2 = 1/(k[A]0), so it depends on the initial concentration. For a zero-order reaction, t1/2 = [A]0/(2k).

For a first-order reaction, t1/2 = 0.693/k.
The half-life of a first-order reaction is independent of initial concentration.
For a second-order reaction involving one reactant, t1/2 = 1/(k[A]0).
The relation t1/2 = 1/(k[A]0) belongs to a second-order reaction.
After one half-life, concentration becomes 1/2 of the initial value.
After two half-lives, concentration becomes 1/4 of the initial value.
After three half-lives, concentration becomes 1/8 of the initial value.
If the first-order half-life is 14 s, the time to reach 1/8 of the initial concentration is 3 × 14 = 42 s.

Rate Constant and Units

The rate constant, k, is the proportionality constant in the rate equation. Its value is constant for a particular reaction at a fixed temperature and in the presence of the same catalyst. It changes when temperature or catalyst conditions change.

The units of k depend on the overall order of the reaction. These units are obtained by rearranging the rate equation. The rate has units mol dm⁻³ s⁻¹ and concentration has units mol dm⁻³.

For a zero-order reaction, rate = k, so the unit of k is mol dm⁻³ s⁻¹.
For a first-order reaction, rate = k[A], so the unit of k is s⁻¹.
For a second-order reaction, such as rate = k[A]2, the unit of k is mol⁻¹ dm³ s⁻¹.
For rate = k[A]n, the units of k depend on n.
In nA → products, if n in the rate equation is 2, the reaction is second order with respect to A.
A larger rate constant generally indicates a faster reaction under the same conditions, but comparison must be made for reactions described by compatible rate laws.
The value of k is not the same as the reaction rate because the rate also depends on reactant concentrations.
Temperature affects k, and the Arrhenius relationship shows that k increases as temperature increases.

Key terms

Reaction kinetics: The branch of chemistry that studies the rates and mechanisms of chemical reactions.
Rate of reaction: The change in concentration of a reactant or product per unit time.
Average rate: The change in concentration divided by the time interval over which the change occurs.
Instantaneous rate: The rate of reaction at a particular instant of time.
Effective collision: A collision with suitable orientation and enough energy to produce products.
Activation energy: The minimum extra energy required by reacting particles to form the activated complex.
Activated complex: The short-lived, unstable, high-energy arrangement formed during an effective collision.
Rate law: An experimentally determined equation relating reaction rate to reactant concentrations.
Order of reaction: The sum of the powers of concentration terms in the experimentally determined rate law.
Molecularity: The number of reacting species involved in one elementary reaction step.
Zero-order reaction: A reaction whose rate is independent of the concentration of the reactant.
First-order reaction: A reaction whose rate is directly proportional to the concentration of one reactant.
Second-order reaction: A reaction whose rate law has a total power of two for the concentration terms.
Half-life: The time required for the concentration of a reactant to decrease to half of its initial value.
Rate constant: The proportionality constant in a rate equation at a specified temperature and condition.
Pseudo-unimolecular reaction: A reaction that appears first order because one reactant is present in large excess.
Catalyst: A substance that increases reaction rate by providing a pathway with lower activation energy without being consumed overall.
Irreversible process: A process that cannot be reversed to its original state by simply reversing the controlling conditions.

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Chemistry shortcuts

Finding the limiting reactant and percentage composition

Convert every given mass or volume into moles first. The reactant that produces the least amount of the required product is the limiting reactant.

Write the balanced equation and calculate moles using n = mass/Mr.
Use the mole ratio to calculate the product. For percentage composition, use percentage = mass of element in one mole of compound divided by molar mass, multiplied by 100.
Example: Percentage of nitrogen in KNO3 = 14/101 × 100 = 13.86%.
Answer: 13.86% nitrogen.

Use gas volume at molar volume only when the gas conditions are stated or are standard conditions.

Using gas volume, pressure and temperature relations

At the same temperature and pressure, gas volume is directly proportional to the number of molecules. For changing conditions, use P1V1/T1 = P2V2/T2.

At constant temperature and pressure, divide or multiply the volume in the same ratio as the number of molecules.
Example: 10 mL H2 contains 2 × 10^3 molecules. Oxygen in 200 mL contains 20 × 2 × 10^3 = 4 × 10^4 molecules.
Answer: 4 × 10^4 molecules.
For a rigid container, increasing temperature increases molecular speed and mean free path if the gas remains in the same phase.

The direct volume to molecule ratio does not apply when temperature or pressure changes.

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