Kinetics and Rate Law

RATE OF A REACTION The speed with which the reactants disappear and the products form is called the rate of the reaction

May be expressed in terms of: speed at which products appear or speed at which reactants disappear. Expressed as:(change in concentration)/time Units are mol/L/s The rate at any given moment is given by the slope of a tangent in concentration-time graph.

There are five principle factors that influence reaction rates: Chemical nature of the reactants Ability of the reactants to come in contact with each other Concentration of the reactants Temperature Availability of of rate-accelerating agents called catalysts

Reaction Mechanism A reaction mechanism is a series of steps by which a reaction takes place. Each step involves the collision of two particles. Each step is called an elementary process. The slowest step in the reaction mechanism is called the rate -- determining step. Mechanisms are determined experimentally

Reaction Mechanism The rate law for elementary processes can be predicted. The exponents for the rate law for elementary processes are the coefficients of the reactants in the chemical equation for the elementary process Intermediate -- a substance that is produced in one step and is used up in a later step.

Reaction Mechanisms 2NO2 + F2 2NO2F Rate = k[NO2][F2] The proposed mechanism is NO2 + F2 NO2F + F (slow) F + NO2 NO2F (fast) F is called an intermediate It is formed then consumed in the reaction

Reaction Mechanisms Each of the two reactions is called an elementary step . The rate for a reaction can be written from its molecularity . Molecularity is the number of pieces that must come together. Elementary steps add up to the balanced equation

How to get rid of intermediates They can’t appear in the rate law. Slow step determines the rate and the rate law Use the reactions that form them If the reactions are fast and irreversible the concentration of the intermediate is based on stoichiometry. If it is formed by a reversible reaction set the rates equal to each other.

Rate Laws Reactions are reversible. As products accumulate they can begin to turn back into reactants. Early on the rate will depend on only the amount of reactants present. We want to measure the reactants as soon as they are mixed. This is called the Initial rate method.

Rate Laws Two key points The concentration of the products do not appear in the rate law because this is an initial rate. The order (exponent) must be determined experimentally, can’t be obtained from the equation

Rate Law The rate of a homogeneous reaction at any instant is proportional to the product of the molar concentrations of the reactants raised to a power determined from experiment

Rate Law Expresses the relationship between rate and concentration. Order of the reaction -- can be positive, negative, zero, or a fraction. Order with respect to a reactant -- its exponent in the rate law; determined experimentally Overall order-- sum of exponents in rate law

The differential rate law is usually just called “the rate law.” Rate Laws Differential rate laws express (reveal) the relationship between the concentration of reactants and the rate of the reaction. The differential rate law is usually just called “the rate law.” Integrated rate laws express (reveal) the relationship between concentration of reactants and time

Suppose the experimental concentration-rate data for five experiments is:

The relationship between concentration and time can be derived from the rate law and calculus Integration of the rate laws gives the integrated rate laws Integrate laws give concentration as a function of time Integrated laws can get very complicated, so only a few simple forms will be considered

Integrated Rate Law Expresses the reaction concentration as a function of time. Form of the equation depends on the order of the rate law (differential). Changes Rate = D[A]n Dt We will only work with n= 0, 1, and 2

Determining Order with Concentration vs. Time data (the Integrated Rate Law) Zero Order: First Order: Second Order:

First order reactions Rate law is: rate = k [A] The integrate rate law can be expressed as: [A]0 is [A] at t (time) = 0 [A]t is [A] at t = t e = base of natural logarithms = 2.71828…

Graphical methods can be used to determine the first-order rate constant, note

A plot of ln[A]t versus t gives a straight line with a slope of -k The decomposition of N2O5. (a) A graph of concentration versus time for the decomposition at 45oC. (b) A straight line is obtained from a logarithm versus time plot. The slope is negative the rate constant.

The simplest second-order rate law has the form The integrated form of this equation is

Graphical methods can also be applied to second-order reactions A plot of 1/[B]t versus t gives a straight line with a slope of k Second-order kinetics. A plot of 1/[HI] versus time (using the data in Table 15.1).

The amount of time required for half of a reactant to disappear is called the half-life, t1/2 The half-life of a first-order reaction is not affected by the initial concentration

The half-life of a second-order reactions does depend on the initial concentration

COLLISIONS Molecules must collide in order to react. The rate is determined by the number of effective collisions per second. In order for a collision to be effective, an activated complex must form.

Collision Theory Particles have to collide to react. Have to hit hard enough Things that increase this increase rate High temperature – faster reaction High concentration – faster reaction Small particles = greater surface area means faster reaction

Unsuccessful Collisions Collision Theory Particle Orientation Required Orientation Unsuccessful Collisions Successful Collision

In order for an activated complex to form, the molecules must have: the proper orientation and the proper amount of energy. If the molecules do not have both of the above, no reaction will occur. See graphs of endothermic and exothermic reactions.

The potential-energy diagram for an exothermic reaction The potential-energy diagram for an exothermic reaction. The extent of reaction is represented as the reaction coordinate.

Activation energies and heats of reactions can be determined from potential-energy diagrams Potential-energy diagram for an endothermic reaction. The heat of reaction and activation energy are labeled.

Collision Theory Activation Energy depends on reactants low Ea = fast reaction rate Ea

An activated complex is an intermediate state formed by the interpenetration of the electron clouds of the molecules.

FACTORS AFFECTING RATE 1) Nature of the reactants -- Some reactions are fast by their nature and some are slow. Bonds must be broken, so the number and strength of bonds is a factor. In some cases ions must form or be rearranged. 2. Ability of the reactants to meet. - Homogeneous system -- usually fast - Heterogeneous- reaction at surface-slower

3. Surface Area high SA = fast reaction rate more opportunities for collisions Increase surface area by… using smaller particles dissolving in water

4. Temperature high temperature = fast reaction rate Ten degree Celsius increase in temperature often doubles the rate high KE fast-moving particles give more collisions that result in the formation of an activated complex more likely to reach activation energy

5. Concentration (pressure for gases) high concentration or pressure = fast reaction rate more opportunities for collisions

There are two types of catalysts: 6) Catalyst -- A catalyst is a substance that changes the rate of a reaction without being permanently changed itself. A catalyst changes the activation energy and changes the pathway of the reaction. There are two types of catalysts: Homogeneous -- same physical state as the reactants. Heterogeneous -- reactants are adsorbed on surface; collisions can occur more easily.

Catalyst substance that increases reaction rate without being consumed in the reaction lowers the activation energy

The activation energy is related to the rate constant by the Arrhenius equation k = rate constant Ea = activation energy e = base of the natural logarithm R = gas constant = 8.314 J mol-1 K-1 T = Kelvin temperature A = frequency factor or pre-exponential factor

The Arrhenius equation can be put in standard slope-intercept form by taking the natural logarithm A plot of ln k versus (1/T) gives a straight line with slope = -Ea/RT