Kinetics HL

1. Kinetics HL Rate Expression-

2. 16.1 Rate Expression, Order of reaction & order wrt particular reactant- • Rate Expression, is a mathematical function expressing the dependence of a rate on the concentration of reactants, determined experimentally. • Consider; mA + nB→ cC + dD • Rate of reaction = - d[A]/dt = k[A]m [B]n • k is called as rate constant.

3. 16.1 Rate Expression, Order of reaction & order wrt particular reactant- • Characteristics of rate constant- • Independent of concentration • Varies with temperature • Varies with surface area

4. Order of reaction • Consider; mA + nB→ cC + dD • Order of reaction is ‘ m ’ with respect to A and is ‘n’ with respect to B. • Overall order of reaction is m+n. • If concentration of [A] is doubled, others are kept constant, initial rate of reaction is doubled, then order of reaction is one with respect to A. [21 = 2]

5. Order of reaction • Consider; mA + nB→ cC + dD • If concentration of [A] is doubled, others are kept constant, initial rate of reaction is increased four times, then order of reaction is two with respect to A. [ 22 = 4 ] • If concentration of [A] is doubled, others are kept constant, and if there is no effect on initial rate of reaction, then order of reaction is ZERO with respect to A. [ 20 = 1 ]

6. First Order Reaction- • A first-order reaction depends on the concentration of only • one reactant (a unimolecular reaction). Other reactants • can be present, but each will be zero-order. • The rate law for an elementary reaction that is first order • with respect to a reactant A is • Rate = - d[A]/dt = k[ A ] • k is the first order rate constant, which has units of • 1/time. • Half Life – Radio active decay, • The half life of a first-order reaction is independent of the • starting concentration and is • given by, t1/2 = ln(2)/k

7. Zero-order reactions • A 0-order reaction has a rate which is independent of the • concentration of the reactant(s). • Increasing the concentration of the reacting species will • not speed up the rate of the reaction. • Zero-order reactions are typically found when a material • that is required for the reaction to proceed, such as a • surface or a catalyst, is saturated by the reactants. The • rate law for a zero-order reaction is initial rate of reaction • is equal to rate constant.

8. Second-order reactions • A second-order reaction depends on the • concentrations of one second-order reactant, or • two first-order reactants. • For a second order reaction, its reaction rate is • given by; • Rate = k[A]2 or = k[A][B] or = k[B]2

9. Pseudo first order • Measuring a second order reaction rate can be • problematic: the concentrations of the two • reactants must be followed simultaneously, which • is more difficult; or measure one of them and • calculate the other as a difference, which is less • precise. A common solution for that problem is the • pseudo first order approximation • If either [A] or [B] remain constant as the reaction • proceeds, then the reaction can be considered • pseudo first order because in fact it only depends • on the concentration of one reactant. If for • example, [B] remains constant • then: Rate = k [A]

11. 16.2 Reaction Mechanism- • Many chemical reactions that have much simple • equations do not occur in simple manner. For a • chemical change two colliding particles must • have correct geometry and sufficient energy. So • chemical changes takes place in steps. Each step • involves in formation of unstable product or • species. These species are called as • intermediates. • Various reaction steps proceed at different • speed. The product can not be formed faster • than slowest step. So the slowest step is called • as rate determining step.

12. 16.2 Reaction Mechanism- • A reaction mechanism is the series of steps a given • chemical reaction takes in going from reactants to • products. • aA + bB------------------------> products • e.g. NO2 (g) + CO (g) --------------------------> NO (g) + CO2 (g) • Proposed reaction mechanism : • NO2 (g) + NO2 (g)--------------------------> NO3 (g) + NO (g) • NO3 (g) + CO (g) -----------------------------> NO2 (g) + CO2 (g) • Overall Reaction: NO2 (g) + CO (g) = NO (g) + CO2 (g)

13. 16.3 Activation Energy • Activation energy is defined as the energy that must be overcome in • order for a chemical reaction to occur. • Activation energy may also be defined as the minimum energy • required to start a chemical reaction. • The activation energy of a reaction is usually denoted by Ea, and • given in units of kilojoules per mole. • Activation energy can be thought of as the height of the potential • barrier (sometimes called the energy barrier) separating two • minima of potential energy (of the reactants and products of a • reaction). • For a chemical reaction to proceed at a reasonable rate, there • should exist an appreciable number of molecules with energy equal • to or greater than the activation energy.

14. Temperature independence and the relation to the Arrhenius equation • The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the rate at which a reaction proceeds. • From the Arrhenius equation, the activation energy can be expressed as; Ea = - RT ln ( k/A ) where A is the frequency factor for the reaction, R is the universal gas constant, T is the temperature (in kelvins), and k is the reaction rate coefficient. • While this equation suggests that the activation energy is dependent on • temperature, in regimes in which the Arrhenius equation is valid this is cancelled • by the temperature dependence of k. Thus Ea can be evaluated from the reaction • rate coefficient at any temperature (within the validity of the Arrhenius • equation). K = Ae[-Ea/RT] • After processing mathematically, the equation can be ln k = ln A – ( Ea/R ).1/T • If a graph of ln k is plotted against 1/T a straight line with slope – Ea/R and • intercept ln A. Ea can be calculated.