Measuring Reaction Rates

• Continuous monitoringpolarimetry spectrophotometry total pressure

• Taking aliquotsgas chromatography titration for one of the componentsgravimetric analysis

The Rate Law• The Rate Law of a reaction is the mathematical relationship

between the rate of the reaction and the concentrations of the reactants

• The rate of a reaction is directly proportional to the concentration of each reactant raised to a power

• For the reaction aA + bB products the rate law would have the form given belown and m are called the orders for each reactantk is called the rate constant

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Rate = k[A]n[B]m

• The exponent on each reactant in the rate law is called the order with respect to that reactant

• The sum of the exponents on the reactants is called the order of the reaction

• The rate law for the reaction:

2 NO(g) + O2(g) 2 NO2(g) is

Rate = k[NO]2[O2] • The reaction is second order with respect to [NO], first

order with respect to [O2], and third order overall.

Reaction Order

Sample Rate Laws

Important: The rate laws can only be determined by experiment. The stoichiometry of the reaction

does not tell us what the rate law is.

Reaction Rate Law

CH3CN CH3NC Rate = k[CH3CN]

CH3CHO CH4 + CO Rate = k[CH3CHO]3/2

2 N2O5 4 NO2 + O2 Rate = k[N2O5]

H2 + I2 2 HI Rate = k[H2][I2]

Tl+3 + Hg2+2 Tl+1 + 2 Hg+2 Rate = k[Tl+3][Hg2

+2][Hg+2]-1

Why is the Rate Law Important?

• The concentrations of reactants and products can be predicted for any time throughout the reaction

• It can be used to propose reaction mechanisms that give insights into what is happening in the reaction on the molecular level.

Determining the Rate Law: Method of Initial Rates

• Most common method

• Rates are measured at the beginning of the reaction when products don’t interfere

• Several experiments are done, varying the concentration of one reactant at a time and measuring the initial rate each time.

For the following reaction run at 800˚CH2(g) + 2NO (g) --> N2O (g) +H2O (g)

initial rates are measured as the concentration of the reactants are varied:

Exp [H2] (mol/L) [NO] (mol/L) initial rate (mol/L-sec) 1 0.10 0.10 0.12 2 0.20 0.10 0.24 3 0.20 0.20 0.96

•What is the rate law for this reaction?•Calculate the rate constant for the reaction at 800˚C.

For the following reaction --BrO3

-(aq) + 5 Br- (aq) + 6 H+ (aq) --> 3 Br2 (l) + 3H2O (l)initial rates are measured as the concentration of the reactants are varied:

Exp [BrO3-] (mol/L) [Br-] (mol/L) [H+ ] (mol/L) initial rate

(mol/L-sec) 1 0.10 0.10 0.10 8.0 x 10 -4

2 0.20 0.10 0.10 1.6 x 10 -3

3 0.20 0.20 0.10 3.2 x 10 -3

4 0.10 0.10 0.20 3.2 x 10 -3

•What is the rate law for this reaction?•Calculate the rate constant for the reaction.

Integrated Rate Laws: Predicting Concentrations as a Function of Time

• We are going to discuss integrated rate laws for reactions that are zero, first and second order in one reactant only.Rate = k[A]0 “zeroth” orderRate = k[A] first orderRate = k[A]2 second order

• Other rate laws are too complicated mathematically

Reactant Concentration vs. TimeA Products

ln[A]0

ln[A]

time

slope = −k

First Order Reaction

The decomposition of N2O5 is first order in [N2O5] at 65˚, at which temperature the rate constant is 5.2 x 10-3 s-1.

If the initial concentration of N2O5 is 4.0 x 10-3 M, what is the concentration of N2O5 600s after the reaction begins?

Half-Life• The half-life, t1/2, of a

reaction is the length of time it takes for the concentration of the reactants to fall to ½ its initial value.

• The half-life of the reaction depends on the order of the reaction

Half-Life of a First-Order ReactionIs Constant

Half-life for a First Order Reaction

In the N2O5 decomposition, after what time will half of the reactants decompose at 65˚C?

A certain first order reaction has a half life of 20.0 minutes.

1. Calculate the rate constant for this reaction.2. How much time is required for this reaction to be 75%

complete?

Summary: First Order Reactions• Rate law: rate = k[A]

• Integrated rate law: ln[A] = -kt + ln[A]0 • Graph: ln[A] vs. time gives straight line

slope = -k and y-intercept = ln[A]0

used to determine the rate constant

• Half-lifet½ = 0.693/kThe half-life of a first order reaction is constant

• Units for k: sec-1

Second Order Reaction

l/[A]0

1/[A]

time

slope = k

The reaction HI (g) --> 1/2 I2 (g) + 1/2 H2 (g)

Is second order with respect to HI. At 700˚C, the rate constant is 1.8 x 10-3 M-1s-1. If the initial concentration of HI is 1.0 M, what will be the concentration after 5.0 x 103 s.

The half-life of a second order reaction depends on the concentration of the reactant or reactants.

Summary: Second Order Reactions

• Rate law: rate = k[A]2

• Integrated rate law: 1/[A] = kt + 1/[A]0

• oooo 1/[A] vs. time gives straight line slope = k and y-intercept = 1/[A]0

used to determine the rate constant

• Half life: t½ = 1/(k[A0])

• Units for k: k = M-1∙sec-1

Zero Order Reactions• Rate law: rate = k[A]0 = k

constant rate reactions

• Integrated rate law: [A] = -kt + [A]0

• Graph: [A] vs. time is straight line with slope = -k and y-intercept = [A]0

• t ½ = [A0]/2k• Units: if Rate = M/sec, k = M/sec

[A]0

[A]

time

slope = - k