Chapter 12 Chemical Kinetics Honors Chemistry 2

How fast or slow is a reaction? Let’s look at the reaction CO(g) + NO2 (g) → CO2 (g) + NO (g) At the start, there are only reactants and no products. As times goes on, there are less reactants and more products. In the end, only product remains. OK, but how fast did the reaction occur?

Factors that affect reaction rate. Spontaneity isn’t one of them, don’t confuse spontaneous and instantaneous. The nature of reactants. Concentration Surface Area Temperature Presence of a catalyst.

Reaction Rate The average rate of a reaction is  quantity = mol/L =  concentration  time s  time We use brackets [ ] to denote concentration in mol/L or M. Average reaction rate = [NO]t2 - [NO]t1 t2 - t1

Reaction Rate Laws The equation that represents the relationship between the rate and the concentration of reactants is called the rate law. For the reaction A → B, the rate law is: Rate = k [A], where k is the specific rate constant for that reaction. k is unique for each reaction. This is the differential rate law (rate law) – rate of a reaction depends on concentration.

Reaction order. Rate = k [A] is a first order reaction because [A] = [A]1. This means that the concentration and the rate are a direct relationship. For the reaction a A + b B → products, the general rate law is: Rate = k [A]m [B]n, where m and n are the reaction orders of A and B. Rarely does m=a or n=b. The rate order is m + n.

Determining the rate order. Rate laws are determined experimentally, one method uses initial rates. This is done by comparing the initial rates of a reaction with varying reactant concentration. See page 535. You can graph them.

Determining the Reaction Order For Experiment 1: Rate = 5.4 x 10-7 mol/L*s = k(0.0100 mol/L)n (0.200 mol/L)m For Experiment 2: Rate = 10.8 x 10-7 mol/L*s = k (0.0200 mol/L)n (0.200 mol/L)m Rate 2 = 10.8 x 10-7 mol/L*s = k(0.0200 mol/L)n (0.200 mol/L)m Rate 1 5.4 x 10-7 mol/L*s k(0.0100 mol/L)n (0.200 mol/L)m = (0.0200 mol/L) = (2.0)n (0.0100 mol/L) Rate 2 = 2.00 = (2.0) Rate 1 n = 1

Determining the Reaction Order, cont'd Similarly, Rate 5 = 10.8 x 10-7 mol/L*s = k(0.200mol/L)n (0.0202mol/L)m Rate 6 21.6 x 10-7 mol/L*s = k(0.200mol/L)n (0.0404mol/L)m =0.0202 mol/L = (0.50)m 0.0404 mol/L Rate 5 = 0.500 = (0.50)m Rate 6 m = 1 Rate = k[NH4+ ] [NO2- ] 5.4 x 10-7 mol/L*s = k(0.0100 mol/L) (0.200 mol/L) k = 2.7 x 10-4 L/mol*s

The Integrated Rate Law The integrated rate law shows the concentration of species in the reaction depend on time. For a chemical reaction aA products where the kinetics are first order in [A] In[A] = -kt + ln[A]º or ln([A]º) = kt y = mx + b ([A]) The reaction is first order in A if a plot of ln[A] is a straight line.

Half-Life Half-life of a reactant is the time it takes for a reactant to reach half its original concentration. For a first-order reaction, t1/2 = 0.693 k

Second-Order Rate Laws For a reaction aA → products That is second order in A, the integrated second-order rate law is 1 = kt + 1 [A] [A]º y = mx + b t1/2 = 1 k[A]º

Zero-Order Rate Laws A reaction is said to be zero-order if the rate is constant. The integrated rate law for a zero-order reaction is [A] = -kt + [A]º t1/2 = [A]º 2k

Instantaneous Reaction Rates. It sometimes is necessary to know the rate at any given moment, this is the instantaneous rate. One way is to determine the slope of the tangent to the curve of the reaction at the given time. Another way is to use the rate law and determine the rate at the given concentration of interest.

Graph ln[ ] Graph 1/[ ] 1st order 2nd order

Temperature In general, increasing temperature increases the rate of reaction. The molecules are moving faster and the number of collisions increases. In general, increasing the temperature by 10 K approximately doubles the rate of reaction.

Collision Theory In order for a reactants to come together to form products, collisions under the right conditions have to occur. If the orientation of the collision is correct an activated complex or intermediate will form. If the collision has sufficient energy (activation energy) then the product is formed.

Arrhenius Equation For reactants to collide successfully: The collision must involve enough energy to produce the reaction; the collision energy must equal or exceed the activation energy. The relative orientation of the reactants must allow formation of any new bonds necessary to produce products. ln(k) = -Ea (1/T) + ln(A) R y = m x + b k = rate constant; E = activation energy; R = gas law constant, 8.3145 J/K*mol; T = temperature; A = frequency factor

Arrhenius Equation The graph of Arrhenius equation yields a straight line of slope= -Ea /R and intercept = ln(A) To find Ea , plot ln(k) vs 1/T and calculate the slope. See example page 555 Ea can also be calculated from the values of k at only two temperatures by ln (k2/k1 ) = Ea (1/T1 – 1/T2) R

Reaction energy diagram. activated complex activation Energy Energy reactants energy released by reaction products Reaction Progress

Nature of the Reactants Some substances, like halogens and group 1 and 2 elements, are more reactive than others. The more reactive a substance, the faster the reaction occurs.

Concentration In order for a reaction to occur collisions must happen. Obviously, more particles mean more collisions and this means that the reaction occurs faster. However, too many particles of one kind tend to get in the way of each other and the reaction slows.

Surface Area Increasing the surface area allows the number of collisions between reactants to increase. As with dissolving rates, by grinding, pulverizing, or vaporizing the reactants increases the rate of reaction.

Reaction Mechanisms Most reactions consist of a sequence of steps. Each of these is called an elementary step. Several elementary steps make a complex reaction. The complete sequence of steps in a complex reaction is a reaction mechanism. The product of the first elementary step of a complex reaction is an intermediate, like catalysts, these don’t appear in the balanced equation.

Rate determining step. In a complex reaction the elementary step that is the slowest determines the rate of the overall reaction. This is the rate determining step. The slowest step always determines the rate.

Catalyst or Inhibitor A catalyst is a substance that increases the rate of reaction without actually taking part in the reaction (it remains unchanged). It does this by lowering the activation energy and thus speeds the formation of intermediate products. An inhibitor raises the activation energy and slows the reaction down.

The effect of a catalyst. Catalysts don’t change equilibrium since they only lower the activation energy. This speeds up the reaction rate equally in both directions and doesn’t provide a stress to either reactants or products.