Kinetics The Study of Rates of Reaction

Rate of a Reaction The speed at which the reactants disappear and the products are formed determines the rate of the reaction. The reaction rate slows as the concentration of the reactants decrease and the concentration of the products increases. - Elephant toothpasteRelated Videos

Factors that Effect the Rate of a Reaction 1. Concentration 2. Temperature 3. Ability of the reactants to meet: heterogeneous vs. homogenous and particle size 4. Catalysts YouTube - "Glow in the Dark“ YouTube - Brainiac Thermite and Liquid Nitrogen

Measuring the Rate Rate with respect to x =  (concen of X)  t Units of rate = Molarity/ second = mol/L = mol L -1 s -1 s  Reaction rate is always given a positive value: the rate at which the concentration is increasing or decreasing is positive.

Rates and Coefficients The coefficients of the balanced equation may be used to find the rates with respect to the other species in the equation. 2 N 2 O 5  NO 2 + O 2 Rate = 8.31 x M/s What is the rates at which the oxygen concentration is increasing? 8.31 x N 2 O 5 x 1 mol O 2 2 mol N 2 O 5 =4.1 x O 2 M/s forming

Rates and Coefficients 2 N 2 O 5  NO 2 + O 2 Rate = 8.31 x M/s What is the rate at which N 2 O 5 is disappearing? 8.31 x M/s

Concentration and Rate Law A + B  products Rate Law: Rate = k [A] m [B] n K = rate constant [ ] = concentration (M) m,n = the order of the reactant determined experimentally

Determining the Order of a Reaction Measure how varying the concentration of the reactants effects the rate 1 st order if the rate increase by the same magnitude as the reactant. A doubles and the rate doubles A triples and the rate triples 2 nd order if the rate increases by a factor of 2 compared to the reactant.

A + B  products [A][B]products x 4x 2x 3x 9x

Determining the Rate Law A doubles  rate doubles A triples  rate triples n = 1 B doubles  rate 4x greater B triples  rate 9x greater m = 2 Rate = k[A] 1 [B] 2

Order of a Reaction The overall order of the reaction is the sum of the orders for each reactant m + n = overall order Zero order - the concentration of the reactant does not effect the rate and is not included in the rate law.

Concentration vs. Time I) Rate Law wrt Reactant A Zero order: rate = k, units of k (rate constant) are M/s First order: rate = k [A] units of k are sec -1 Second order: rate = k [A] 2 units of k are L mol -1 s -1

Zero Order Plots

First Order Plots

Second Order Plots

Concentration vs. Time Reaction Order Differential Rate Law Integrated Rate Law Kinetic Plot Slope Units of Rate Constant Zero [A] = [A] 0 - k t [A] vs t- kmole L -1 sec -1 First [A] = [A] 0 e - k t ln [A] vs t - ksec -1 Second 1/[A] vs t kL mole -1 sec -1 d [A] -d t = k -d t = k [A] -d t = k[A] 2 [A] = 1 + kt[A] 0

Collision Theory The rate of the reaction is proportional to the number of effective collisions. Not every collision between the reactants produces a product, or else all reactions would be explosions. Activation Energy (E A )  the minimum energy that must be supplied for an effective collision to occur.

The Maxwell-Boltzmann Distribution

Points to notice: No molecules at zero energy Few molecules at high energy No maximum energy value For the reaction to occur, the particles involved need a minimum amount of energy - the Activation energy. If a particle is not in the shaded area, then it will not have the required energy so it will not be able to participate in the reaction.

Collision Theory and Reaction Rates 1. Activation Energy: Particles must have the minimum energy (E a ) required for an effective collision. 2. Kinetic Energy: Increasing the temperature of the reaction increases the KE and number of particles with the required E a for an effective collision. 3. Molecular Orientation: Reactants must be oriented correctly for an effective collision to occur.

Transition State The activated complex has partially formed and partially broken bonds  H = E A (forward) – E’ A (reverse) Potential energy

Catalysts increase the reaction rate by lowering the activation energy required to form the products.

Measuring EA The Arrhenius Equation gives the relationship between the E A and temperature of the reaction K = rate constant A = frequency factor (combines collision frequency & orientation factors) T = Kelvin temperature R = gas constant Notice that a small increase in temperature causes a large increase in the rate constant App. a factor of 2 to 3 increase in rate for every 10 o C increase in temperature k = A e -Ea/RT

Measuring E A 1. Graphical Method Taking the natural log of both sides of the Arrhenius Equation gives the equation of a line Ln k = ln A + ln e –E A /RT Ln k = ln A – E A /RT Ln k = (-E A /R)(1/T) + ln A Y = m x + b -so the slop of this graph is the activation energy divided by the gas constant

Measuring E A 2. Temperature change method Using the Arrhenius equation and Determining the rate constant at different temperatures gives the activation energy ln k 2 = E A k 1 R T 1 T 2

Reaction Mechanism and Rate  If several steps are involved in an overall chemical reaction, the slowest step limits the rate of the reaction.  Thus, the slow step is called the rate determining step. (Slow) 2N 2 O 5  4NO 2 + O 2 Reverse this equation to get the overall

The high E a for the slow step limits the reaction rate  The reaction cannot be any faster than the slowest step

Example 1 If the reaction:2 NO 2 + F 2 = 2 NO 2 F follows the mechanism, (i) NO 2 + F 2 = NO 2 F + F (slow) (ii) NO 2 + F = NO 2 F (fast) What is the rate law? Since step (i) is the rate-determining step, the rate law is: Rate = k [NO 2 ] m [F 2 ] n

The Rate Law The rate law is not derived from the overall equation, but the rate determining step. The rate law should not contain any intermediate products that are not in the overall reactions. The exponents of the reaction is determined experimentally and does not depend on the stoichiometric coefficients.

Derive the rate law that is consistent with the proposed mechanism (i) Cl 2  2 Cl - (fast) (ii) Cl - + CO  ClCO (fast) (iii) ClCO + Cl 2  Cl 2 CO + Cl - (slow) The overall reaction is Cl 2 + CO  Cl 2 CO Example 2

What is the rate law for the overall reaction Cl 2 + CO = Cl 2 CO ? From the rate-determining (slow) step, the rate appears to be Rate = k 3 [ClCO] [Cl 2 ] But [ClCO] is an intermediate that is not part of the overall reaction. Put it in terms of Cl 2 and CO by substituting for ClCO. [ClCO] = k -2 [Cl] [CO] (express [Cl] in terms of [Cl 2 ] using step (i))

What is the rate law for the overall reaction Cl 2 + CO = Cl 2 CO ? [Cl] = k -1 [Cl 2 ] (1/2) (Substitute and combine the k’s) Rate = K [CO] [Cl 2 ] (3/2) where K = k -1 k -2 k 3, the observed rate constant. The overall order of the reaction is 5/2, strange but that is the observed rate law.

Catalysts Homogenous catalyst occurs in a homogeneous mixture Example: Decomposition of H 2 O 2 with KI Heterogeneous catalyst adsorbs the reactants onto a solid surface Example: Decomposition of H 2 O 2 with MnO 2  Neither catalyst appears in the overall reaction H 2 O 2  O 2 + H 2 O