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Chapter 14
Chemical Kinetics
Chemical kinetics: the area of chemistry dealing with the speeds or rates at which reactions occur. Rates are affected by several factors:
- The concentrations of the reactants : Most chemical reactions proceed faster if the concentration of one or more of the reactants is increased.
- The temperature at which a reaction occurs : The rates of chemical reactions increase as temperature is increased. Why do we refrigerate milk?
- The presence of a catalyst : A catalyst is a substance added to a reaction to increase its rate without being consumed in the reaction. The most common catalyst is enzymes.
- The surface area of solid or liquid reactants or catalysts: Reactions that involve solids often proceed faster as the surface area of the solid is increased. For example, a crushed aspirin will enter the bloodstream quicker. I. Reaction rates A. Speed of any event is measured by the change that occurs in any interval of time. The speed of a reaction (reaction rate) is expressed as the change in concentration of a reactant or product over a certain amount of time. B. Units are usually Molarity / second (M/s) C. Example: prepare a 0.100M solution butyl chloride in water and then measure the concentration at various intervals when it is involved in the following reaction: C 4 H 9 Cl (l) + H 2 O (l) → C 4 H 9 OH (aq) + HCl (aq) average rate = (decrease in concentration butyl chloride)/ (change in time) Since concentration of the reactant decreases over time, final concentration minus the initial will give a negative value. To account for this: Δ [C 4 H 9 Cl] Average Rate = - -------------- Δ t D. Reaction Rates and Stoichiometry We could also look at the rate of appearance of a product. As a product appears, its concentration increases. The rate of appearance is a positive quantity. We can also say the rate of appearance of a product is equal to the rate of disappearance of a reactant.
Rate = Δ [C 4 H 9 Cl] Δ [C 4 H 9 OH]
- - ------------- = + ---------------- Δ t Δ t What happens when the stoichiometric relationships are not 1:1 in a reaction? 2HI(g) → H 2 (g) + I 2 (g) The rate of disappearance of HI is twice that than the rate of appearance of H 2. Rate = Δ[HI] Δ[H 2 ] - --------- = ------- 2 ΔT ΔT Example 1: How is the rate of disappearance of ozone related to the rate of appearance of oxygen in the following equation? 2O 3 (g) → 3 O 2 (g) Rate = Δ[O 3 ] Δ[O 2 ] - --------- = ------- 2 ΔT 3 ΔT If the rate of appearance of O 2 , Δ [O 2 ] / Δ T, is 60. x 10-^5 M/s at a particular instant, what is the value of the rate of disappearance of O3 , Δ [O 3 ] / Δ T, at this same time? Δ[O 3 ] 2 Δ[O 2 ] - --------- = ------- = 2/3 (6.0 x 10-^5 M/s) = 4.0 x 10-^5 M/s ΔT 3 ΔT
Example 2: IF ONE REACTANT IS INVOLVED (usually a decomposition reaction) The initial rate of decomposition of acetaldehyde, CH 3 CHO, CH 3 CHO (g) → CH 4 (g) + CO (g) was measured at a series of different concentrations with the following results: Concentration CH 3 CHO (mol/L) 0.10 0.20 0.30 0. Rate (mol/L-s) 0.085 0.34 0.76 1. Using this data, determine the order of the reaction; that is, determine the value of m in the equation rate = k(conc. CH 3 CHO)m solution: Write down the rate expression at two different concentrations: rate 2 = k(conc 2 )m rate 1 = k(conc 1 )m Dividing the first equation by the second : rate 2 (conc 2 )m --------- = ------------- rate 1 (conc 1 )m substituting data: 0.34 (0.20)m ---- = ------ 0.085 (0.10)m Simplifying: 4 = 2m^ Clearly, m=2.
Example 3: TWO REACTANTS 2H 2 (g) + 2NO (g) → N 2 (g) + 2H 2 O (g) SERIES 1 SERIES 2 [H 2 ] [NO] Rate [H 2 ] [NO] Rate Exp 1 0.10 0.10 0.10 0.10 0.10 0. Exp 2 0.20 0.10 0.20 0.10 0.20 0. Exp 3 0.30 0.10 0.30 0.10 0.30 0. Exp 4 0.40 0.10 0.40 0.10 0.40 1. In the first series of experiments, we hold the initial concentration of NO constant and vary H 2. If you look at the data, it is clear the rate is directly proportional to the concentration of H 2. (When the concentration of H 2 doubles, the rate doubles). This means in the general expression: rate = k[H 2 ]m^ [NO]n^ m must equal 1. In the second series, [H 2 ]is held constant, while [NO] varies. It is apparent the rate is proportional to the square of [NO]. When [NO] is doubled (from 0.10 to 0.20) the rate increases by a factor of 2^2 = 4 ( from 0.10 to 0.40). Therefore n = 2.
III. The Change in Concentration with Time In reactions, most likely, one would be interested in knowing how much reactant is left after a certain period of time. The mathematics to do this involves calculus and is quite complex. We will look at first and second order reactions as well as half-life. A. First Order Reaction For the reaction A→ products, the rate is as follows: Δ[A] Rate = - -------- = k [A] Δt using calculus, this equation can be transformed into an equation that relates the conc. A at the start of the reaction, [Ao], to its concentration at any other time t , [At]: ln[At] - ln [Ao] = - kt or ln( [At]/[Ao]) = - kt (1) ln [At] = - kt + ln[Ao] (2) This equation has the form for the general equation of a straight line, y=mx+b. Thus, for a first order reaction, a graph of ln[At] vs time gives a straight line with the slope of - k and a y- intercept of ln[Ao] For a first order reaction, equation (1) or (2) can be used to determine a. the concentration of a reactant at any time after the reaction has started b. the time required for a given fraction of a sample to react c. the time required for a certain reactant to reach a certain level. Example4: The first-order rate constant for the decomposition of a certain insecticide in water at 12 ° C is 1.45 per year. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 x 10-^7 g/cm^3 of water. Assume the effective temperature of the lake is 12 ° C. (a) What is the concentration of the insecticide June 1 of the following year? (b) How long will it take for the concentration of the insecticide to drop to 3.0 x 10 -^7 g/cm^3_?_
B. Half-Life The half-life of a reaction (t (^) 1/2) is the amount of time required for the concentration of the reactant to drop to one-half its initial value. [At1/2] = 1/2 [A 0 ] We can determine the half- life of a first order reaction by substituting [At1/2] into equation (1). ln (1/2[A 0 ]/[A 0 ] = - kt1/ ln 1/2 = - kt1/ t1/2 = - (ln 1/2 / k) = 0.693/k Notice that half-life is independent of the initial concentration. For example, pick any point in a reaction, one half life from that point is where the concentration of the reactant in 1/2. In a first-order reaction, the concentration of the reactant decreases by 1\2 in each series of regularly spaced time intervals, namely t1/
IV. Temperature and Rate A. Collision Model The collision model of chemical kinetics state: molecules must collide to react. The greater the number of collisions occurring per second, the greater the reaction rate. Increasing concentration as well as temperature will increase the number of collisions. For most reactions, though, only a small fraction of collisions lead to a reaction. What keeps a reaction from happening more quickly? B. Activation Energy Arrhenius: suggested molecules must possess a certain minimum amount of energy in order to react. According to the collision model, this energy must come from the kinetic energy of collisions. the minimum energy required is called activation energy, Ea.
- For reactions to occur, not only do we need sufficient energy to overcome the activation energy, but the atoms must be suitably oriented.
- In general, for any process, ΔH = Ea - Ea’
- Activated Complex: Intermediate step. Bonds are breaking and new bonds are forming.
- Exothermic vs Endothermic reaction: If the forward reaction is exothermic (ΔH <0), Ea is smaller than Ea’. If the forward reaction is endothermic (ΔH>0), the activation energy for the forward reaction, Ea, is larger than the reverse reaction, Ea’. C. Catalyst Catalyst increases reaction rate without being consumed in a reaction. This happens because a catalyst provides an alternative path for the reaction with lower activation energy. Even though the activation energy is lowered, ΔH remains the same.
D. Effect of Temperature on Reaction Rate. In general increase in temperature increases rate. Rate is approximately doubled when T increases by 10°C. Since increasing temperature does not affect concentration that much, rate expressions must reflect temperature increases through the rate constant. Therefore, the rate constants we’ve used previously, are very temperature dependent. Energy increases Relation between K and T Arrhenius: found that most reaction-rate data obeyed the equation: k= Ae(-Ea/RT) where k is the rate constant, Ea, the activation energy, R the gas constant (8.314 J/mol- K), T is the temperature and A is constant as temp varies. A, called the frequency factor , is related to the frequency of collisions and the probability that the collisions are favorably oriented for the reaction. The equation can also be rearranged as follows: lnk = - Ea + lnA RT Graphing this equation, ln k vs 1/T should yield a straight line. The activation energy can be obtained from the slope of the line. (-Ea/R) We can use a variation of the Arrhenius equation to obtain a relation between rate constants k 2 and k 1 at two different temperatures, T 2 and T 1. The “two point” equation we use is as follows: K 1 at T 1 ln k 1 = - Ea + lnA RT 1 K 2 at T 2 ln k 2 = - Ea + lnA RT 2 Subtracting ln k 2 from lnk 1 for change in temperature
V. Reaction Mechanisms A reaction mechanism is a description of the path, or sequence of steps by which a reaction occurs. A single step reaction mechanism: The reaction between CO and NO 2 at high temperatures (above 600 K) CO(g) + NO 2 (g) → NO (g) + CO 2 (g) Research shows that at low temperatures, this reaction occurs in two steps: Step 1: NO 2 (g) + NO 2 (g) → NO 3 (g) + NO(g) Step 2: NO 3 (g) + CO(g) → NO 2 (g) + CO 2 (g)
CO(g) + NO 2 (g) → NO(g) + CO 2 (g) Net equation: Simplifying by eliminating substances that are on both sides of the equation. The substances eliminated (in this case NO 3 ) is the intermediate. Rate Laws in Reaction Mechanisms We stressed that rate laws must be determined experimentally. They cannot be derived from the balanced equations. The reason: Every reaction is actually made of one or more steps and the rate laws and relative speed of these steps will determine the overall rate law. the overall rate law cannot exceed the rate of the slowest elementary step. ( rate determining step) We can therefore determine the rate law from the reaction mechanism. Before we do this, we need to understand the types of elementary steps: The number of molecules that participate as reactants in an elementary step defines the molecularity of the step. Unimolecular : a single molecule is involved as a reactant: A → products Rate = k[A] Bimolecular : elementary step involving collision of two reactant molecules H 2 + Br 2 → 2HBr(g) or NO 2 + NO 2 → NO + NO 3
rate = k[A][B] rate = k[A]^2 Termolecular: elementary step involving simultaneous collision of three molecules. These are rarely encountered A + A + A → products OR A + A + B →products OR A + B + C→ products Rate = k[A]^3 Rate = k[A]^2 [B] Rate = k[A][B][C] To Determine the overall rate law based on the reaction mechanism:
1. Locate the slow step in the mechanism. The rate of the overall reaction will be the rate of that step. Step 1: NO 2 (g) + NO 2 (g) → NO 3 (g) + NO(g) (slow) Step 2: NO 3 (g) + CO(g) → NO 2 (g) + CO 2 (g) (fast)
Overall (Net): CO(g) + NO 2 (g) → NO(g) + CO 2 (g) Step 2 is much faster than step 1, that is k 2 >>k 1 if you were given rate constants 2. Write the rate expression for the slow step. To do this, note the exponent of a reactant in the rate expression for a step is its coefficient in the equation for that step. NOTE THIS IS A DIFFERENT PROCEDURE THAN WE USED TRYING TO FIND THE RATE EXPRESSION STRAIGHT FROM THE OVERALL EQUATION. Rate = k 1 [NO 2 ]^2 (notice it is bimolecular) This is the rate law that is observed experimentally. If we had attempted to derive a rate law from the overall Net equation, the rate law would be Rate = k[NO 2 ][CO] however, this does not agree with experimental observations.
