CHEM 3310 Chemical Kinetics The Zeroth Order Integrated

CHEM 3310 Chemical Kinetics The Zeroth Order Integrated Rate Equation

The Rate Law for a general reaction a X + b Y products is k, m, and n are numbers that are determined experimentally!! This is the differential Rate Law. • The differential rate law relates the rate of reaction to the concentrations of the various species in the system. • In this form, it isn't useful for predicting how much reactant remains in solution or how much product has been formed in a given amount of time. CHEM 3310 2

We use the integrated form of the rate law for: • Testing to see whether a set of data follows 0 th, 1 st, or 2 nd order. • Predicting how much reactant remains in solution or how much product has been formed in a given amount of time. Let’s see what the integrated form of the rate law looks like for: Zeroth, First, and Second Order Rate Laws. CHEM 3310 3

Zeroth Order Rate Law CHEM 3310 4

Zero Order (m+n=0) For a general reaction a X + b Y products that obeys zero order rate law. This is the zero order differential rate law. • The rate of a zero order reaction is independent of the concentration of the reactant. • Increasing the concentration of the reacting species will not speed up the rate of the reaction. (i. e. Doubling concentration has no effect on rate. ) CHEM 3310 5

Zero Order (m+n=0) For a general reaction a X + b Y products that obeys zero order rate law. This is the zero order differential rate law. • The reaction is experimentally determined to proceed at a constant rate. CHEM 3310 6

Zero Order For a general reaction a X + b Y products that obeys zero order rate law. This is the zero order differential rate law. • When this equation is rearranged and both sides are integrated we get the following result. CHEM 3310 7

Zero Order For a general reaction a X + b Y products that obeys zero order rate law. This is the zero order differential rate law. Separate the variables Integrate CHEM 3310 This is the zero order integrated rate law. 8

Zero Order For a general reaction a X + b Y products that obeys zero order rate law. This is the zero order integrated rate law. • [X]0 is the concentration of X at time=0 [X]t is the concentration of X at time=t • Rearrange, [X]t = -ak 0 t + [X]0 • A reaction is zeroth order if concentration data is plotted against time and the result yields straight line. • The slope of this resulting line is -ak 0 • The unit of k 0 is M s-1 CHEM 3310 9

Zero Order For a general reaction a X + b Y products that obeys zero order rate law. Differential rate law Integrated rate law • Rearrange, [X]t = -ak 0 t + [X]0 Slope = -ak 0 CHEM 3310 10

Zero Order Example: A catalyzed reaction Oxygen atom CO Catalyst (Pt, Pd or Rh) CHEM 3310 CO 2 11

Zero Order For a general reaction a X + b Y products that obeys zero order rate law. Integrated rate law Half-life, The half-life, , of a reaction is the time required for the concentration of the reactant to decrease by half. When t= , Half-life of a zero-order reaction is proportional to the initial concentration of X, [X]0. CHEM 3310 12

For a general reaction a X + b Y products that obeys zero order rate law. Half-life,

Rate Equations For a general reaction, a X + b Y products Zeroth Order Differential Rate Law Integrated Rate Law Units of k M s-1 Linear Plot [X] vs. t Half-life CHEM 3310 14

Determine the rate constant in M s-1 for a zero order reaction, X products The initial concentration is 2. 0 M. After one minute, the concentration is 1. 0 M. What is the initial half-live? [X]t = 1. 0 M and [X]0= 2. 0 M, a = 1 t = (1 min) (60. sec/1 min) = 60. s 2. 0 M - 1. 0 M = k (60. sec) k = rate constant = 0. 017 M s-1 Note: Since it took 1 min for the initial concentration to drop to half its value. The half-life for this reaction is 1 min.

Rate Equations For a general reaction, a X + b Y products Zeroth Order First Order Second Order Units of k M s-1 M-1 s-1 Linear Plot [X] vs. t ln([X]) vs. t Differential Rate Law Integrated Rate Law Half-life CHEM 3310 16