Chapter 14 Chemical Kinetics Chemical Kinetics CH 141

2 Factors affecting chemical reaction Rate of reaction Average rate, Instantaneous rate Rate law Order of reaction First order reaction Second order reaction Half - life time

Chemical Kinetics CH 143 Chemical Kinetics: How fast is the chemical reaction, (i.e. studying of rates of chemical processes).

Factors That Affect Reaction Rates 1. Reactant concentration: As the concentration of reactants increases, so does that reactant molecules will collide and rate of reaction increases. 2. Temperature: As temperature increases, the reaction rate increases, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy. 3. Catalysts: catalyst increases chemical reactions by changing mechanism. Chemical Kinetics CH 144

Speed of a reaction is measured by: the change in concentration with time. For a reaction A  B Reaction Rates Chemical Kinetics CH 145

Reaction Rates Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time.  [A] /  t Chemical Kinetics CH 146 A  B

 At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present = zero.  At t = 20 min, there is 0.54 mol A and 0.46 mol B.  At t = 40 min, there is 0.30 mol A and 0.70 mol B.  Calculating average rate: Reaction Rates Chemical Kinetics CH 147

For the reaction: A  B There are two ways of measuring rate: 1.The speed at which the products appear (i.e. change in moles of B per unit time), or 2.The speed at which the reactants disappear (i.e. the change in moles of A per unit time). Reaction Rates Chemical Kinetics CH 148

9 Example: Reaction of butyl chloride to give butanol. Average rate decreases as the reaction goes on.

The average rate of the reaction over each interval = the change in concentration divided by the change in time: Average Rate, M/s C 4 H 9 Cl (aq) + H 2 O (l)  C 4 H 9 OH (aq) + HCl (aq) Chemical Kinetics CH 1410

Instantaneous rate defines as The rate at any instant in time and it is the slope of the tangent to the curve. Average rate: is the change in reactant or product concentration to the change of time. Chemical Kinetics CH 1411 Instantaneous Rate & Average Rate

Example: C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) –If We plot [C 4 H 9 Cl] with respect to t. –The units for average rate are mol/L·s or M/s. Chemical Kinetics CH 1412 Instantaneous Rate & Average Rate

Chemical Kinetics CH 1413 Calculate: 1. average rate ? 2. instantaneous rate at Z point ? Average rate= Y 2 -Y 1 X 2 -X 1 Z

Reaction Rates and Stoichiometry What if the ratio is not 1:1? H 2 (g) + I 2 (g)  2 HI (g) Only 1/2 HI is made for each H 2 used. Chemical Kinetics CH 1414

In General, for the reaction aA + bBcC + dD (-) sign because Reactants (decrease) with time (+) sign because Products (increase) with time Chemical Kinetics CH 1415 Reaction Rates and Stoichiometry

For Example C 4 H 9 Cl(aq) + H 2 O(l)  C 4 H 9 OH(aq) + HCl(aq) Chemical Kinetics CH 1416

Chemical Kinetics CH 1417 For Example

In general rates increase as concentrations increase. NH 4 + (aq) + NO 2 - (aq)  N 2 (g) + 2H 2 O(l) Concentration and Rate Chemical Kinetics CH 1418 Constant increases

From previous table, for the reaction NH 4 + (aq) + NO 2 - (aq)  N 2 (g) + 2H 2 O(l) we note:  as [NH 4 + ] doubles with [NO 2 - ] constant the rate doubles,  as [NO 2 - ] doubles with [NH 4 + ] constant, the rate doubles Concentration and Rate Chemical Kinetics CH 1419

Chemical Kinetics CH 1420 Concentration and Rates The above equation is called the rate law, and k is the rate constant. For the reaction

For a general reaction w i th rate law m: order in reactant 1 and n: order in reactant 2. The total order of reaction = (m + n + ….) The total order of reaction = zero, if m = 0, n = 0. Rate Law Chemical Kinetics CH 1421

Chemical Kinetics CH 1422 Concentration and Rate This reaction is First-order in [NH 4 + ] First-order in [NO 2 − ] The overall reaction order: is the sum of the exponents on the reactants in the rate law. The overall order of this reaction= 1+1= 2 ( i.e. second-order).

Chemical Kinetics CH 1423 ABAB Differential Rate Law

Chemical Kinetics CH 1424 [A] 0 : the initial concentration at t = 0. [A] t : the concentration after time, t >0.

Chemical Kinetics CH 1425 When [A] t is plotted as a function of time, a curve results. Slope = - k First Order Reactions

Straight Line Equation y = mx + b Slope= + m intercept = b Chemical Kinetics CH 1426 First Order Reactions

A plot of ln[A] t vs t is a straight line. slope = -k intercept = ln[A] 0 Chemical Kinetics CH 1427 First Order Reactions ln[A] t

Half-life t 1/2 : is the time taken for the concentration of a reactant to drop to half its original value. For a first order process, when t = t ½, so [A] t = ½[A] 0. Chemical Kinetics CH 1428 First Order Reactions  Half- life time doesn’t depend on concentration of reactant

For a second order reaction with just one reactant. Second Order Reactions Chemical Kinetics CH 1429 [A] = [A] 0, t=0 Differential Equation

Second Order Reactions The Change of Concentration with Time y = mx + b A plot of 1/[A] vs. t is a straight line with a slope of k. Intercept= 1/[A] 0 Chemical Kinetics CH 1430

Chemical Kinetics CH 1431 For a second-order process, set [A] t =0.5 [A] 0. Half-Life of Second Order

Chemical Kinetics CH 1432 The decomposition of NO 2 at 300°C is described by the equation NO 2 (g) NO (g) + 1/2 O 2 (g) and yields these data: Time (s)[NO 2 ], M Determining the order of chemical reaction Example

Chemical Kinetics CH 1433 Graphing ln [NO 2 ] vs. t yields: Time (s)[NO 2 ], Mln [NO 2 ] The plot is not a straight line, so the process is not first- order in [A]. Does not fit: Determining the order of chemical reaction

Chemical Kinetics CH 1434 A graph of 1/[NO 2 ] vs. t gives this plot. Time (s)[NO 2 ], M1/[NO 2 ] This is a straight line. Therefore, the process is second-order in [NO 2 ]. Determining the order of chemical reaction

Chemical Kinetics CH 1435 Practice Problems CH.14 in the book