How to determine the order of a reaction by the initial rates method?

 

A rate law is an expression which shows how the rate of a reaction depends on the concentrations of reactants. For the decomposition of NO₂ we can write:

2NO₂(g) → 2NO(g) + O₂(g)

 Rate = k [NO₂]ⁿ     (Rate Law)

k is the rate constant

and n is the order of reaction (n can be positive or negative, integer or fraction)

Both k and n must be determined experimentally.

For the general reaction:

aA + bB → cC + dD   (1)

the rate law is given by:   Rate = k. [A]^m [B]ⁿ    (2)

 

There are two types of rate laws:

The differential rate law shows how the rate of a reaction depends on concentrations
The integrated rate law shows how the concentrations of species in the reaction depend on time

The first step in understanding how a given chemical reaction occurs is to determine the form of the rate law. In this post we will show ways to obtain the differential rate law of a reaction.

The rate law - in its general form - for most reactions is given by equation 1. Therefore, the task of determining the rate law becomes one of determining the reaction order m and n.

In most cases the reaction orders are:

Reaction order 0 in a reactant A (zero order reaction)  ⇒ we write [A]⁰ ⇒changing the concentration of [A]  the reaction rate R₁ is not affected
Reaction order 1 in a reactant A (first order reaction) ⇒ we write [A]¹ ⇒changing the concentration of [A]  the reaction rate R₁ is  affected proportionally (doubling [A] will double the rate R₂ = 2* R₁)
Reaction order 2 in a reactant A (second order reaction) ⇒ we write [A]² ⇒ doubling the concentration of [A]  the reaction rate R₁ is  affected by a factor 22 (doubling [A] will affect the rate R₂ = 4* R₁) – tripling [A] the reaction rate R₁ is  affected by a factor 32 and becomes  R₃ = 9* R₁)

N.B. Reaction rate depend on concentration but the rate constant k does not. The rate constant k is mainly affected by temperature and by the presence of a catalyst.

 

 

Example I.1

The initial rate of a chemical reaction A + B → C + D was measured for several different initial concentrations of A and B and the results are shown in Table I.1:

Experiment #	[A] (M)	[B] (M)	Initial Rate (M/s)
1	0.100	0.100	2.0*10-5
2	0.100	0.200	2.0*10-5
3	0.200	0.100	8.0*10-5

Using the data in Table I.1 determine: a) the rate law for the reaction  b) the rate constant

a) The general form of the rate law for the reaction given is the following:

R = Rate = k * [A]^m * [B]ⁿ

We must determine the reaction orders m and n using the experimental data given in Table I.1.

 

By comparing experiments #1 and #2 we see that while the concentration of [A] remains constant the concentration of [B] is doubled but the reaction rate remains constant. Therefore, [B] does not affect the rate of reaction and that means n=0.

By comparing experiments #1 and #3 we see that while the concentration of [B] remains constant the concentration of [A] is doubled and the reaction rate increases fourfold. This indicates that the rate is proportional to [A]².

From the above two observations the rate law for the reaction is given by the expression:

R = Rate = k * [A]² * [B]⁰ = = k * [A]²    (3)

b) Using data from Experiment #1 (or from #2 or #3) and from equation (3):

k = R / [A]²  =   2.0*10^-5 / (10^-1)² = 2.0*10^-3 M^-1s^-1

 

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Relevant Posts - Relevant Videos

Rate of a Chemical Reaction - Chemical Kinetics

Rates of Chemical Reactions and the Collision Model

 

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References

1. David W. Oxtoby, H.P. Gillis, Alan Campion, “Principles of Modern Chemistry”, Sixth Edition, Thomson Brooks/Cole, 2008
2. Steven S. Zumdahl, “Chemical Principles”  6th Edition, Houghton Mifflin Company, 2009
3. Ralph H. Petrucci, “General Chemistry”, 3rd Edition, Macmillan Publishing Co., 1982

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Key Terms

reaction rate, chemical kinetics, rate law, method of initial rates, reaction order, ,, reactant concentrations, ,

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