Reaction Rates: Reaction Rates. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Rate Laws The rate of a reaction depends

Reaction Rates:

Reaction Rates

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Rate Laws

•The rate of a reaction depends in part on the concentrations of the reactants.


Rate Laws

•The rate of a reaction depends in part on the concentrations of the reactants.

• Suppose there were a reaction with only one reactant and one product.

A B• The rate at which A forms B can be

expressed as the change in A (ΔA) with time.

rate = ΔAΔt


Rate Laws

• The rate of disappearance of A is proportional to the concentration of A.

ΔAΔt [A]

• The proportionality can be expressed as the concentration of A, [A], multiplied by a constant, k.

rate = = k × [A] ΔAΔt


Rate Laws

• This equation is a rate law, an expression for the rate of a reaction in terms of the concentration of the reactants.



Rate Laws

• This equation is a rate law, an expression for the rate of a reaction in terms of the concentration of the reactants.

• The specific rate constant (k) for a reaction is a proportionality constant relating the concentrations of reactants to the rate of the reaction.



Rate Laws

•The value of the specific rate constant, k, in a rate law is large if the products form quickly; the value is small if the products form slowly.



Rate Laws

First-Order Reactions

•The order of a reaction is the power to which the concentration of a reactant must be raised to match the experimental data on concentration and rate.


Rate Laws

First-Order Reactions

•The order of a reaction is the power to which the concentration of a reactant must be raised to match the experimental data on concentration and rate.• In a first-order reaction, the rate is directly

proportional to the concentration of only one reactant.


•Over time, the rate of reaction decreases because the concentration of the reactant is decreasing.

• The reaction A B is a first-order reaction.

• If [A] is reduced by one half, the reaction rate is reduced by one half.

• The rate (ΔA/Δt) at any point on the graph equals the slope of the tangent to the curve at that point.


Rate Laws

Higher-Order Reactions

•For the reaction of A with B, the rate of reaction is dependent on the concentrations of both A and B.

aA + bB cC + dD

rate = k[A]x[B]y

In some reactions, two substances react to produce products.

• In the general equation for a double-replacement reaction below, the coefficients are represented by lowercase letters.


Rate Laws


•When each exponent in the rate law equals 1 (that is, x = y = 1) the reaction is said to be first order in A and first order in B.

rate = k[A]x[B]y


Rate Laws


•The overall order of a reaction is the sum of the exponents for the individual reactants.


Rate Laws


•The overall order of a reaction is the sum of the exponents for the individual reactants.• A reaction that is first order in A and first order

in B is thus second order overall.


Rate Laws


•The overall order of a reaction is the sum of the exponents for the individual reactants.• A reaction that is first order in A and first order

in B is thus second order overall.• The actual order of a reaction must be

determined by experiment.


Finding the Order of a Reaction from Experimental Data

Consider the reaction aA B. The rate law for this reaction is Rate = k[A]x. From the data in the table, find the order of the reaction with respect to A and the overall order of the reaction.

Trial Initial concentration of A (mol/L)

Initial rate (mol/(L·s))

1 0.050 3.0 10–4

2 0.10 12 10–4

3 0.20 48 10–4


KNOWNS[A]1 = 0.050 mol/L

[A]2 = 0.10 mol/L

Rate1 = 3.0 10–4 mol/(L·s)

Rate2 = 12 10–4 mol/(L·s)

UNKNOWNOrder of reaction with respect to A = ?

Overall order of the reaction = ?

Analyze List the knowns and the unknowns.1

Use the first two trials to calculate the order and the third to evaluate your answer.


• Start with the rate law for each initial concentration of A. The rate law of the

reaction and the specific rate constant, k, is the same for any initial concentration of A.

• Divide the second expression by the first expression.

Rate1 = k [A1]x

Rate2 = k [A2]x

= = ( )Rate1 k [A1]x

Rate2 k [A2]x [A2]

[A1]

x

Calculate Solve for the unknowns.2


• Substitute the known quantities into the equation.

Calculate Solve for the unknowns.2

• Determine the value of x.

= ( )3.0 10–4 mol/(L·s)

12 10–4 mol/(L·s) 0.10 mol/L

0.050 mol/L

x

4.0 = 2.0x

x = 2

The reaction is second order in A.

Since A is the only reactant, the reaction must be second order overall.


• If the reaction was first order in A, doubling the concentration would double the rate.

• However, Rate2 is four times Rate1.

• So, the reaction is second order for A and second order overall because A is the only reactant.

• As a further test, look at what happens to the rate when the concentration doubles again from 0.10 mol/L to 0.20 mol/L.

Evaluate Does this result make sense?3


•The following reaction is a second-order reaction.

aA bB + cCIf the initial concentration of A is 2.0 mol/L and the initial rate is 9.6 10–7 mol/(L·s), what is the concentration when the rate is 1.2 10–7 mol/(L·s)?


•The following reaction is a second-order reaction.

aA bB + cCIf the initial concentration of A is 2.0 mol/L and the initial rate is 9.6 10–7 mol/(L·s), what is the concentration when the rate is 1.2 10–7 mol/(L·s)?

1.2 10–7 mol/(L·s)

9.6 10–7 mol/(L·s) = ( )[A2]

2.0 mol/L

2

[A2] = 0.71 mol/L


Reaction Mechanisms

Reaction Mechanisms

•How do most reactions progress from start to finish?


•A balanced equation does not tell you how a reaction occurred. • Plants use photosynthesis to capture and

store light energy. • The process can be summarized by stating

that carbon dioxide and water yield simple sugars and oxygen.

• However, the process of photosynthesis is not as simple as this summary implies.

Reaction Mechanisms


One-Step and Multistep Reactions

•An elementary reaction is a reaction in which reactants are converted to products in a single step.• This type of reaction has only one activation-

energy peak and one activated complex.

Reaction Mechanisms


One-Step and Multistep Reactions•Most chemical reactions consist of two or more elementary reactions.

Reaction Mechanisms


One-Step and Multistep Reactions•Most chemical reactions consist of two or more elementary reactions.

• The series of elementary reactions or steps that take place during the course of a complex reaction is called a reaction mechanism.

Reaction Mechanisms


One-Step and Multistep Reactions

•An intermediate is a product of one step in a reaction mechanism and a reactant in the next step.• An intermediate has a more stable structure

and longer lifetime than an activated complex.

• Intermediates do not appear in the overall chemical equation for a reaction.

Reaction Mechanisms


•The figure below shows a reaction progress curve for a complex chemical reaction.

• A reaction progress curve shows all the energy changes that occur as reactants are converted to products.

• The graph has a peak for each activated complex and a valley for each intermediate.


Rate-Determining Steps

•In a multistep chemical reaction, the steps do not all progress at the same rate.

• One step will be slower than the others.• The slowest step will determine, or limit, the

rate of the overall reaction.

Reaction Mechanisms


•Consider the reaction mechanism for the decomposition of nitrous oxide (N2O). Experiments have shown that the mechanism consists of the two steps shown below.

N2O(g) N2(g) +O(g)

N2O(g) + O(g) N2(g) + O2(g)

2N2O (g) 2N2(g) + O2(g)


Reaction Mechanisms


•In the first step, nitrous oxide decomposes into nitrogen gas and oxygen atoms.

N2O(g) N2(g) +O(g)

N2O(g) + O(g) N2(g) + O2(g)

2N2O (g) 2N2(g) + O2(g)

• The oxygen atoms are an intermediate.


Reaction Mechanisms


•For the decomposition of nitrous oxide, the first step is the rate-determining step.

N2O(g) N2(g) +O(g)

N2O(g) + O(g) N2(g) + O2(g)

2N2O (g) 2N2(g) + O2(g)

• To increase the rate of the overall reaction, you would need to increase the rate of the first step.


Reaction Mechanisms


•In the following reaction mechanism, which is an intermediate?

A. A2 C. A

B. B2 D. AB

A2 2A

2A + B2 2AB

A2 + B2 2AB


•In the following reaction mechanism, which is an intermediate?

A. A2 C. A

B. B2 D. AB

A2 2A

2A + B2 2AB

A2 + B2 2AB


Key Concepts and Key Equations

•The value of the specific rate constant, k, in a rate law is large if the products form quickly; the value is small if the products form slowly.

Most chemical reactions consist of two or more elementary reactions.

Rate = = k [A]DADt

Rate = k[A]x[B]y


Glossary Terms

• rate law: an expression relating the rate of a reaction to the concentration of the reactants

• specific rate constant: a proportionality constant relating the concentrations of reactants to the rate of the reaction

• first-order reaction: a reaction in which the reaction rate is proportional to the concentration of only one reactant


• elementary reaction: a reaction in which reactants are converted to products in a single step

• reaction mechanism: a series of elementary reactions that take place during the course of a complex reaction

• intermediate: a product of one of the steps in a reaction mechanism; it becomes a reactant in the next step

Glossary Terms

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Reaction Rates: Reaction Rates. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Rate Laws The rate of a reaction depends