Chemical Kinetics – Chapter 12- Part 1 - the Area of Chemistry Concerned with the Study of the Rates of Chemical Reactions

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Chemical kinetics – Chapter 12- Part 1 - the area of chemistry concerned with the study of the rates of chemical reactions. The purposes of kinetic studies are to find the factors that affect reaction rates and determine the reaction mechanism. Knowledge of the factors that affect reaction rates enables chemists to control rates. Finding the reaction mechanism means we can identify the intermediate steps by which reactants are converted into products.

What is rate or speed? - rate is change in some quantity with time. The symbol for "the change " is Δ. What is rate of reaction or speed of reaction? -change in concentration of a reactant or a product with time.

Change in concentration = (concentration) = concentrationfinal – concentrationinitial change in time = t = tfinal – tinitial For instance, as the reaction A + B C progresses, the concentration of C increases. The rate is expressed as the change in the molar concentration of C, [C], during the time interval t. Concentration of C = [C ]

For a specific reaction we need to take into account the stoichiometry; that is, we need the balanced equation. For example, let's express the rate of the following reaction in terms of the concentrations of the individual reactants and products.

2NO(g) + O2(g) 2NO2(g) These concentrations can be monitored experimentally as a function of time. Notice from the balanced equation, that 2 mol NO reacts with 1 mol O2; therefore, the concentration of NO will decrease twice as fast as that of O2.

Since the rates of change of individual reactants and products may differ the convention is to make the reaction rate come out to be the same no matter which reactant or product is used to calculate it. First we divide each concentration change by the coefficient from the balanced equation

Second, a negative sign is inserted before terms involving reactants. The change in NO concentration, [NO], is negative because the concentration of NO decreases with time. Inserting a negative sign in the expression makes the rate of reaction a positive quantity. For a general equation: aA + bB cC the rate can be expressed in terms of any individual reactant or product.

No matter which reactant or product we use, the reaction rate will be positive and have the same value.

1. Write expressions for the rate of the following reaction in terms of each of the reactants and products.

2N2O5(g) 4NO2(g) + O2(g)

Rate of reaction =

2. In the reaction 2NO(g) O2(g) + N2(g) If the rate of formation of O2 is 0.054 M/s, what is the rate of change of NO concentration?

Average Rate. The average rate of reaction over any time interval is equal to the change in the concentration of a reactant [A], or of a product [C] divided by the time interval, t, during which the change occurred.

Instantaneous Rate: The slope of the tangent to the curve at any given time or instant when you plot or graph [reactant] vs. time.

Initial Rate: The instantaneous rate at time Zero

Three types of reaction rates for the reaction of O3 and C2H4.

3. Calculation of the Average Rate Experimental data for the hypothetical reaction are listed in the following table: A 2B Time (s) [A] (mol/L) 0.00 1.000 10.0 0.891 20.0 0.794 30.0 0.707 40.0 0.630 a. Calculate the average rates of change of [A], and the average reaction rates for the two time intervals from 0 to 10 s and from 30 to 40 s. 0 to 10 s 30 to 40 s

average rate of change mol/L·s mol/L·s

average reaction rate mol/L·s mol/L·s b. Why does the rate decrease from one time interval to the next?

4. Write expressions for the rate of reaction in terms of each of the reactants and products.

N2(g) + 3H2(g) 2NH3(g)

5. Thiosulfate ion is oxidized by iodine in aqueous solution according to the equation 2– 2– – 2S2O3 (aq) + I2(aq) S4O6 (aq) + 2I (aq) If 0.025 mol of is consumed in 0.50 L solution per minute: 2– i. Calculate the rate of removal of S2O3 in M/s = ii. What is the rate of removal of I2 in M/s =

6. N2O5 is an unstable compound that decomposes according to the following equation.

2N2O5 4NO2 + O2 The following data was obtained at 50°C.

[N2O5] (M) Time (s) 1.00 0 0.88 200 0.78 400 0.69 600 0.61 800 0.54 1000 0.48 1200

0.43 1400 a. What is the average rate of N2O5 disappearance in the time interval 200-400 s = ______b. What is the average rate of N2O5 disappearance in the time interval 800-1000 s = ______c. What is the rate of O2 production in the time interval 800-1000 s? = ______

Answers for 4-6

5. a.

6. a. 5.0 x 10-4 M/s b. 3.5 x 10-4 M/s c. 1.8 x 10-4 M/s

RATE LAWS: Part 2

Factors that Affect Reaction Rate 1. Concentrations of reactants in solution or Pressure of gaseous reactants 2. Temperature 3. Catalysts 4. Surface area of a solid reactant 5. Extent of mixing 6. Nature of reactants

Effect of Concentration. The rate of a reaction is proportional to the reactant concentrations. For the reaction NO + O2 NO2 , the rate is proportional to the concentrations of NO and O2.

x y The rate law (or rate equation) for the reaction is: rate = k[NO] [O2]

The proportionality constant k is called the rate constant. The value of k depends on the reaction and the temperature. x and y are exponents which could be integers, fraction or negative.

The exponents x and y determine how strongly the concentration affects the rate. The exponent x is called the order with respect to NO, and y is the order with respect to O2. The sum x + y is the overall order. The values of x and y must be determined from experiment, and cannot be derived by any other means. We will discuss how to determine the order of reaction in the next section. For now we will just use the results. For the NO reaction with O2 experiments show that x = 2 and y = 1. Therefore, the rate law for this reaction is:

2 rate = k[NO] [O2]

This reaction is second order in nitric oxide, and first order in oxygen. It is third order overall.

The fact that the reaction is first order in O2 means that the rate is directly proportional to the O2 concentration. If [O2] doubles or triples, the rate will double or triple also. We can show this mathematically. Consider two experiments. In expt 1 the concentration of O2 is c. In expt 2 the concentration of O2 is doubled from c to 2c. If the concentration of NO is the same in both experiments, it will have no effect on the rate. Use of the rate law allows us to write the ratio of the two rates:

As discussed, we see that doubling the concentration of a reactant that is first order will cause the rate to double. If the concentration of O2 is held constant in two experiments and the concentration of NO doubles (from c to 2c), the rate law predicts that the rate will quadruple.

The fact that the reaction is second order in NO means that the rate is proportional to the square of the concentration of NO. Doubling or tripling of [NO] causes the rate to increase four- or nine-fold, respectively.

In general, if the concentration of one reactant is doubled while the other reactant concentration is unchanged, and the rate is:

1. unchanged, the order of the reaction is zero order with respect to the changing reactant. 2. doubled, the order of the reaction is first order with respect to the changing reactant. 3. quadrupled, the order of the reaction is second order with respect to the changing reactant.

1. Concentration Effect on the Rate

The reaction A + 2B products was found to have the rate law: rate = k[A][B]3. By what factor will the rate of reaction increase if the concentration of B is increased from x to 3x, while the concentration of A is held constant? ______

The Isolation Method. One procedure used to determine the rate law for a reaction involves the isolation method. In this method the concentration of all but one reactant is fixed, and the rate of reaction is measured as a function of the concentration of the one reactant whose concentration is varied. Any variation in the rate is due to the variation of this reactant's concentration. In practice the experimenter observes the dependence of the initial rate on the concentration of the reactant.

To determine the order with respect to A in the following chemical reaction

2A + B à C the initial rate would be measured in several experiments in which the concentration of A is varied and the concentration of B is held constant. To determine the order with respect to B, the concentration of A must be held constant and the concentration of B is varied in several experiments.

2. Finding the Rate Law

The following rate data were collected for the reaction: 2NO + 2H2 à N2 + 2H2O

Experiment [NO]0 [H2]0 Δ[N2]/ Δt (M) (M) (M/h)

1 0.60 0.15 0.076 2 0.60 0.30 0.15 3 1.20 0.60 1.21 4 0.60 0.60 ???

a. Determine the rate law.

rate =

b. Calculate the rate constant and its units.

k =

c. rate of appearance of N2 & rate of disappearance of H2 in exp. 4 are = ______& ______respectively. 3.The rate law for the reaction 2A + B C was found to be rate = k[A][B]2. If the concentration of B is tripled and the concentration of A is unchanged, by how many times will the reaction rate increase?

4. Use the following data to determine (a) the rate law and (b) the rate constant for the reaction 2A + B C

Experiment [A]0 [B]0 Rate (M/s)

1 0.25 0.10 0.012 2 0.25 0.20 0.048 3 0.50 0.30 0.216

rate law: rate constant: ______; its units = ______