Chapter 5 Rates of Chemical Reaction

5-1 Rates and Mechanisms of Chemical Reactions 5-2 Theories of Reaction Rate 5-3 Reaction Rates and Concentrations 5-4 Effect of Temperature on Reaction Rates 5-5 Effect of Catalyst on Reaction Rates

5-1 Rates and Mechanisms of Chemical Reactions The Rate of Chemical Reaction reaction rates: the change in the concentration of a reactant or a product with time. The rate is defined to be a positive number.

A+3B → 2D (5-1) (5-2) or

△ [A] 1 △ [B] 1 △ [D] Rate = - = － = + △ t 3 △ t 2 △ t The units of the rate are usually mol·L -1 ·s -1 ; mol·L -1 ·min -1 ; mol·L -1 ·h -1

average reaction rate is obtained by dividing the change in concentration of a reactant or product by the time interval over which the change occurs. v refers to average reaction rate, Δc refers to change in concentration and Δt refers to change in time.

Instantaneous rate: the average rate over an arbitrary short period of time

5-1.2 The Mechanisms of Chemical Reactions Reaction Mechanisms is a description of the path that a reaction takes. Elementary reaction: A reaction can complete directly by only one step or reactants can convert into products.

termolecular Types of Elementary Reactions unimolecular bimolecular Overall reaction : A reaction was completed through several elementary reactions.

5-2 Theories of Reaction Rate Collision Theory and Activation Energy ● Contents of Collision Theory ⑴ reacting molecules must come so close that they collide. ⑵ not every collision between molecules creates products, only few collisions between reactant molecules will react.

2NOCl ─→ 2NO + Cl 2 ⑶ enough energy; proper orientation ineffective collision: the collisions unable to result in reactions effective collision: a collision that leads to a reaction

● activation energy (E a ) : The minimum energy of a collision that leads to a reaction. It has the symbol E a and is expressed in kilojoules.

5-2.2 The Transition StateTheory Transition state theory (TST) is also called activated complex theory. reactants pass through high-energy transition states before forming products, they are associated in an unstable entity called an activated complex, then change into products.

Example 1: HI + HI → IH H I → H 2 + I 2 activated complex Absorb energy Give off energy Activated process Activation energy

5-3 Reaction Rates and Concentrations

The rate of a reaction is proportional to the product of the concentrations of the reactants raised to some power The Rate Law v ∝ [A] m [B] n Consider the reaction: a A+b B → c C+d D v = k[A] m [B] n

where k is the rate constant; [A], [B] are the concentration of A and B; m and n are themselves constants for a given reaction Notice: ① when [A]=[B]=1mol·L -1, v=k ② the greater the k, the faster the rate ③ m and n must be determined experimentally, in general, m and n are not equal to the stoichiometric coefficients a and b

The order of a reaction with respect to one of the reactants is equal to the power to which the concentration of that reactant is raised in the rate equation Order of A Reaction The sum of the powers to which all reactant concentrations appearing in the rate law are raised is called the overall reaction order.

m is the order of the reaction with respect to A, n is the order of the reaction with respect to B. The overall order of the reaction is the sum of m and n. For equation v = k[A] m [B] n the exponents m and n are not necessarily related to the stoichiometric coefficients in the balanced equation, that is, in general it is not true that for a A + b B → c C + d D, a = m and b = n

The follow example illustrates the procedure for determining the rate law of a reaction. 2NO(g) + 2H 2 (g) Example 5-1: The reaction of nitric oxide with hydrogen at 1280 ℃ is N 2 (g) + 2H 2 O(g) From the following data collected at this temperature, determine the rate law and calculate the rate constant.

Experiment [NO] [H 2 ] Initial Rate (mol/L s) × × × × × × × × × Reasoning and Solution: We assume that the rate law takes the form v = k[NO] m [H 2 ] n

Experiments 1 and 2 shows that when we double the concentration of NO at constant concentration of H 2, the rate quadruples. Thus the reaction is second order in NO. Experiments 2 and 3 indicate that doubling [H 2 ] at constant [NO] doubles the rate; the reaction is first order in H 2. The rate law is given by v = k[NO] 2 [H 2 ] which shows that it is a (1 + 2) or third-order reaction overall. The rate constant k can be calculated using the data from any one of the experiments. Since

v k= [NO] 2 [H 2 ] data from experiment 2 gives us 5×10 -5 k= (10 ×10 -3 ) 2 (2 ×10 -3 ) =2.5 ×10 2 /(mol/L) 2 ·s

First-order reactions A first-order reaction is a reaction whose rate depends on the reactant concentration raised to the first power. A → product the rate is

Integrate the left side from c = c 0 to c and the right from t = 0 to t. Also, from the rate law we know that Thus

The characteristics of first-order reactions ： 1. A plot of logc versus t (time) gives a straight line with a slope of -k/2.303.

2. The rate constant, k, has units of [time] half-life (t 1/2 ) : is the time it takes for the concentration of a reactant A to fall to one half of its original value. By definition, when t = t 1/2, c = c 0 /2, so

Second - order reactions A second-order reaction is a reaction whose rate depends on reactant concentration raised to the second power or on the concentrations of two different reactants, each raised to the first power. v=k[A][B] v=k[A] 2

The characteristics of second- order reactions ： 1. A graph of 1/c against time is a straight line, the slope of which gives the rate constant for the reaction ；

2. The rate constant, k, has units of [c] -1 [t] -1 ； 3. The half-life of 2th-order reactions

Zero - order reactions A zero-order reaction is one where the rate does not depend on the concentration of the species.

c = - k t + c 0 1. A graph of c against t is a straight line The characteristics of zero-order reactions ： 2. The rate constant, k, has units of [c] [t] -1 ； 3. The half-life of a zero-order reaction is t 1/2 =0.5c 0 /k.

5-4 Effect of Temperature on Reaction Rates

5-4.2 The Arrhenius Equation Where E a is the activation energy of the reaction (in kJ/mol), R is the gas constant (8.314 JK -1 mol -1 ), T is the absolute temperature, and e is the base of the natural logarithm scale. The quantity A represents the collision frequency, and is called the frequency factor.

Thus, a plot of log k versus 1/T gives a straight line whose slope is equal to -E a /2.303R and whose intercept with the ordinate is log A.

5-4.3 Application of Arrhenius Equation T 1 → k 1 According to this equation, we can calculate E a and k T 2 → k 2

Example 5-6 The rate constant of a first-order reaction is 3.46×10 -2 /s at 298 K. What is the rate constant at 350 K if the activation energy for the reaction is 50.2 KJ/mol? Answer:

5-5 Reaction Rates and Catalyst Catalyst: is a substance that increase the rate of a chemical reaction without itself being consumed (changed). MnO 2

The features of catalysts No change of mass and composition Selective Small amount can have big action Not only speed forward reaction but also speed reverse reaction ( effect velocity, not effect equilibrium constant )

Enzyme Catalysis Enzymes are biological catalysts. An average living cell may contain some 3000 different enzymes Three features Gentle High efficient High selective ( special)