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7-3-2011

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Reaction Rates and Stoichiometry

In general, for the reaction

aA + bB → cC + dD

Rate = - (1/a)Δ[A]/Δt = - (1/b)Δ[B]/Δt

= (1/c) Δ[C] /Δt = (1/d) Δ[D] /Δt

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Write the rate expression for the following reaction:

CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (g)

rate = -[CH4]

t= -

[O2]t

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=[CO2]

t=

[H2O]t

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Depending on the time interval between measurements, the rates are called :

1. average rate: rate measured between long time interval2. instantaneous rate: rate measured between very short interval (at specific time and conc)3. initial rate: instantaneous rate at the beginning of an experiment

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slope oftangent

slope oftangent

slope oftangent

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Reaction Rates

Example: How is the rate of disappearance of N2O5 related to the rate of appearance of NO2 in the following reaction?

2 N2O5 (g) 4 NO2 (g) + O2 (g)

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Reaction Rates

Example: If the rate of decomposition of N2O5 in the previous example at a particular instant is 4.2 x 10-7M /s, what is the rate of appearance of NO2?

2 N2O5 (g) 4 NO2 (g) + O2 (g)

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2 N2O5 (g) 4 NO2 (g) + O2 (g)

Rate = - 1 [N2O5] = 1 [NO2]

2 t 4 t

[NO2] = - 4 [N2O5]

t 2 t= 2 x 4.2 x 10-7 M /s = 8.4 x 10-7 M/s

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How do we measure Rate of a Reaction experimentally?

1. For reactions in solution:Changes in concentration can be

measured spectroscopically2. For reactions involving gases:

Changes in pressure can be measured3. For reactions in solution with ions

present:Change in concentrations can be

measured through electrical conductance

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Rate of a Reaction

So if we have an aqueous solution of molecular bromine and formic acid, how do we determine the reaction rate?

Br2(aq)+HCOOH(aq) → 2Br–(aq)+2H+(aq)+CO2 (g)

time

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Rate Calculations

• How do we calculate the rate of a reaction?

– We first need this information:

• Time (s)

• [reactant]

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Rate CalculationsBrBr2(aq)2(aq) + HCOOH + HCOOH(aq)(aq) → 2Br → 2Br––

(aq)(aq) + 2H + 2H++(aq)(aq) + CO + CO2(g)2(g)

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Using this information, calculate the average rate of the bromine reaction over the first 50s of the reaction.

Average Rate =

-Δ[Br2]/Δt = -[Br2]final – [Br2]initial/[t]final – [t]initial

Instantaneous Rate =

rate for specific instance in time [Br2] / t

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Rate Calculations

Average Rate = - [Br2]final – [Br2]initial / [t]final – [t]initial

Average Rate = - (0.0101- 0.0120)M / (50s – 0s)

Average Rate = 0.002M / 50s

Average Rate = 3.80 x 10-5 M/s

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Rate LawsIn the reaction:

A BWe may write:Rate [A]x where x is called the order of the

reaction.

When x = 1 the reaction is called a first order reaction; when x = 2 the reaction is called a second order reaction, and so on. X can be an integer, a fraction or zero (a zero order reaction has a rate independent on concentration).

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For more complex reactions, we may have:

A + B ProductsRate [A]x[B]y

Rate = k[A]x[B]y

Where k is the rate constant.

The reaction is said to be of the xth order with respect to A and yth order with respect to B. the overall reaction order is equal to x+y.

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It should be clear that the order of the reaction with respect to some reactant is not the number of moles in a stoichiometric reaction (it is not the molecularity). For instance, in the reaction:

NO2(g) + CO(g) CO2(g) + NO(g)

The rate below 225 oC was found to be independent on [CO] and the rate law is given by the relation:

Rate = k[NO2]2

Which means that the reaction is second order with respect to NO2 and zero order with respect to CO.

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Another example can be presented by considering the following reaction:

2 ICl(g) + H2(g) I2(g) + 2 HCl(g)

The rate law for this reaction was experimentally determined at 230 oC to be:

Rate = 0.163 mol L-1s-1[ICl][H2]

This means that the reaction is first order with respect to both ICl and H2 and the overall order is two (second order).

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Rate laws are always determined experimentally

Reaction order is always defined in terms of reactants

Reactant order is not related to the stoichiomteric coefficient in the overall reaction.

F2 (g) + 2ClO2 (g) 2FClO2 (g)

rate = k [F2][ClO2]

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Determining the Rate Law

Rate laws (and reaction orders) must be determined experimentally

The key is to calculate the initial rate of reaction for different concentrations of reactants

1. If a reaction is zero order for a particular reactant, then changing its concentration will have no effect upon the reaction rate

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2. If a reaction is first order for a particular reactant, then changing its concentration will cause a direct, proportional change in the reaction rate. In other words, doubling the concentration will double the reaction rate, etc.

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3. If a reaction is second order for a particular reactant, then changing its concentration will cause an exponential change in the reaction rate.

In other words, doubling the concentration will result in a four-fold increase (22) in reaction rate; tripling the concentration will result in a nine-fold increase (32) in reaction rate.

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Example

Find the rate law and the rate constant for the reaction:

NH4+

(aq) + NO2-(aq) N2(g) + 2H2O(l)

The following data were collected, keeping [NO2

-] constant

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From the first table we can observe that the initial rate is directly proportional to [NH4

+] which suggests that the rate is first order with respect NH4

+. The same conclusion can be reached from the second table where as the concentration of NO2

- was doubled, the rate was also doubled which means that the reaction is first order with respect to NO2

- as well.

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The overall order of the reaction is thus 2 (a second order reaction) and the rate law is:

Rate = k [NH4+][NO2

-]

To fully determine the rate law we need to determine k. This is done by substitution using concentrations of [NH4

+] and [NO2-] with

the corresponding reaction rate:

10.8 x 10-7 = k*(0.20*0.20)

k = 2.7x10-4 mol L-1s-1

Therefore, the rate law will be:

Rate = 2.7x10-4 mol L-1s-1 [NH4+][NO2

-]

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It is clear from the first two experiments that when the concentration of O3 was doubled, the rate was doubled as well. Therefore, the reaction is first order with respect to O3

From experiments 2 and 3 keeping the concentration of O3 constant at 2.0x10-5 M, decreasing the concentration of NO2 by one-half results in a decrease of the initial rate by the same value. The reaction is therefore first order with respect to NO2

The rate law can be written as:

Rate = k [NO2][O3]

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The rate constant can be calculated by substitution for the concentrations of reactants and corresponding rate value, taking the first experiment, for instance, will give:

0.022 mol L-1s-1 = k * 5.0x10-5 (mol L-1)* 1.0x10-5 (mol L-1)

k = 4.4x107 L mol-1 s-1