CHEMICAL KINETICS

Acetominophen (Tylenol, 500 mg) Biological Half-life: 3 hours WHY DO WE CARE??? Acetominophen (Tylenol, 500 mg) Biological Half-life: 3 hours Recommended dosage: 2 pills every 6 hours Toxic if over 4,000 mg are ingested in 24 hours Construct a line graph relating time elapsed after ingestion to amount of Tylenol present in the bloodstream.

REACTION RATES  

Chemical Jargon Average rate of reaction = rate of reaction over total time elapsed (final – initial) Instantaneous rate of reaction = rate of reaction at specific instant in time

GENERAL EQUATION FOR A REACTION RATE For aA + bB → cC + dD…

Write the rate expressions for the following: Practice Write the rate expressions for the following: I-(aq) + OCl-(aq)  Cl-(aq) + OI-(aq) 4NH3(g) + 5 O2(g)  4NO(g) + 6H2O(g)

PRACTICE For the reaction A + 2B → C under a set of given conditions, the initial rate is 0.100 M/s. What is the change in concentration of B under the same conditions?

PRACTICE FOR RATE OF RXN Consider this reaction: H2O2(aq) + 3 I-(aq) + 2H+(aq) → I3-(aq) + 2H2O(l) In the first 10.0 s, the concentration of I- dropped from 1.000 M to 0.868 M . Calculate the average rate of this reaction in this time interval. Determine the rate of change in the concentration of H+ during this time interval.

MEASURING REACTION RATES UV/Vis Spectroscopy—measures intensity of light absorption to determine concentration (Beer’s Law) Absorbance: A = εbc Transmittance: T = I/I0 I = Intensity light—amount of light energy that made it through the sample. IO = Incident light—total amount of light energy you started with. Pressure Measurement—for gaseous reactants and products

RATE LAWS: EFFECT OF CONCENTRATION ON REACTION RATE Rate depends on concentration of one or more of the reactants As long as rate of reverse reaction is negligibly slow, we can express the relationship, or rate law, as follows: Rate = k[A]n k = rate constant (temperature dependent) Reaction order = relates concentrations of reactants and products to the rate of the reaction.

DETERMINING THE ORDER OF A REACTION Order of a reaction can only be determined by experiment. Differential rate law = rate of rxn as a function of change in concentration of reactants over time. Used to describe what is happening on molecular level. Most common method: measure initial reaction rates while varying concentration of reactants.

ZERO ORDER REACTIONS Rate is independent of concentration Rate = k[A]0 = k Example: Sublimation—number of particles available to sublime remains constant (theoretically) [A] (M) Initial Rate (M/s) 0.10 0.015 0.20 0.40

FIRST ORDER REACTIONS Rate of reaction is directly proportional to concentration of the reactant. Rate = k[A]1 [A] (M) Initial Rate (M/s) 0.10 0.015 0.20 0.030 0.40 0.060

SECOND ORDER REACTIONS Rate of reaction is proportional to square of the concentration of the reactant. Even more sensitive to reactant concentration than first-order Rate = k[A]2 [A] (M) Initial Rate (M/s) 0.10 0.015 0.20 0.060 0.40 0.240

PRACTICE The reaction A → B has been experimentally determined to be second order. The initial rate is 0.0100 M/s at an initial concentration of A of 0.100 M. What is the initial rate at [A] = 0.500 M?

REACTION ORDER WITH MULTIPLE REACTANTS For aA + bB → cC + dD Rate = k[A]x[B]y Overall order of reaction: sum of exponents Must be determined experimentally…

REACTION RATES WITH MULTIPLE REACTANTS Consider the reaction between nitrogen dioxide and carbon monoxide: NO2(g) + CO(g) → NO(g) + CO2(g) The initial rate of the reaction is measured at several different concentrations of reactants with the accompanied results. From the data determine: The rate law for the reaction The rate constant for the reaction with correct units. [NO2] (M) [CO] (M) Initial Rate (M/s) 0.10 0.0021 0.20 0.0082 0.0083 0.40 0.033

WHY INTEGRATED RATE LAWS? What are they? Relates concentrations of reactions and time. Found by integrating the differential rate laws Allows us to answer the following: How long does it take? What was the initial concentration? How much remains after a given amount of time?

ORDER OF REACTION DETERMINED GRAPHICALLY Each reaction order rate equation can be integrated to relate time and concentration. A plot of 1/[A] versus t yields a straight line with a slope of k for a second- order reaction. A plot of ln[A] versus t yields a straight line with a slope of -k for a first-order reaction. A plot of [A] versus t gives a straight line with a slope of -k for a zero-order reaction.

ZERO ORDER REACTIONS

FIRST ORDER REACTIONS

SECOND ORDER REACTIONS

INTEGRATED FIRST ORDER RATE LAWS  

PRACTICE The decomposition of a certain insecticide in water follows first order kinetics and has a rate constant of 1.45 yr-1 at 12oC. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0×10-7 g/cm3. What is the concentration of the insecticide on June 1 of the following year? Assume the average temperature of the lake is 12oC. How long will it take for the concentration of insecticide to drop to 3.0×10-7 g/cm3?

PRACTICE The decomposition of dimethyl ether (CH3)2O at 510oC is a first-order process with a rate constant of 6.8*10-4 s-1. (CH3)2O(g) → CH4(g) + H2(g) + CO(g) If the initial pressure of dimethyl ether is 135 torr, what is the partial pressure at 1420 s?

INTERGRATED SECOND AND ZERO ORDER RATE LAWS For Rate = k[A]2 1/[A]t = kt + 1/[A]0 For Rate = k[A]0 [A]t = -kt + [A]0

HALF LIFE FOR FIRST-ORDER REACTIONS Half-life = time required for concentrations of a reactant to fall to one half of its initial value. For zero-order reaction half-life: t1/2 = [A]0/2k For first-order reaction half-life: ln([A]t/[A]0) = -kt t1/2 = 0.693/k For second-order reaction half-life: t1/2 = 1/k[A]0

ZERO-ORDER HALF-LIFE

FIRST-ORDER HALF-LIFE

SECOND-ORDER HALF-LIFE

PRACTICE Molecular iodine dissociates at 625 K with a first-order rate constant of 0.271 s-1. What is the half-life of this reaction? A first-order reaction has a half-life of 26.4 seconds How long does it take for the concentration of the reactant in the reaction to fall to one- eighth of its initial value?

CONCEPT CHECK A decomposition reaction, with a rate that is observed to slow down as the reaction proceeds, is found to have a half-life that is dependent on the initial concentration of the reactant. Which statement is most likely true for the reaction? A. A plot of the natural log of the concentration of the reactant as a function of time is linear. B. The half-life of the reaction increases as the initial concentration increases. C. A doubling of the initial concentration of the reactant results in a quadrupling of the rate.

SUMMARY FOR REACTION ORDER AND RATES Order and rate law have to be determined experimentally Rate law relates the rate of the reaction to the concentration of the reactants Integrated rate law (derived from differential rate law) relates concentration of reactants to time. Half-life for a first-order reaction is independent of initial concentration. Half-lives for zero- and second-order reaction depend on the initial concentration.

FACTORS THAT AFFECT THE RATE OF A REACTION surface area of a solid reactant concentration or pressure of a reactant temperature nature of the reactants (state of matter, molecular size, bond type, bond strength.) presence/absence of a catalyst

Activation Energy and Temperature Dependence

Catalysts Lower activation energy of reactions by putting the reactants into the proper orientation for more effective collisions 2 types: Heterogeneous Homogenous

Heterogeneous Catalyst

The Arrhenius Equation k = Ae-Ea/RT ln k = ln A – 𝐸𝑎 𝑅𝑇 Rearranging gives graphical method of determining the activation energy of a reaction. Read example 13.8 on page 591 in book.

Practice 1. Consider the decomposition of NO2. 2NO2(g) → 2NO(g) + O2(g) At 650K, the rate constant is 1.66 sec-1. At 700K, the constant is 7.39 sec-1. Calculate the activation energy.

Practice The activation energy for the isomerization of cyclopropane to propene is 274 kJ/mol. By what factor does the rate of reaction increase as the temperature rises from 500°C to 550°C?