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

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

How to determine the order of a reaction? Determining the form of the Rate Law (Order of Reaction) by the method of Initial Rates

# 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

Relevant Posts - Relevant Videos

Rate of a Chemical Reaction - Chemical Kinetics

Rates of Chemical Reactions and the Collision Model

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

Key Terms

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