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# Order of a Reaction -Definition, Characteristics, Determination, Examples, Applications, Practice Problems and FAQs

You might have crossed toll gates on the highway while travelling. Consider a toll gate which has four ways. One for containers, one for buses and one for cars exclusively. Fourth one for all, containers, buses and cars. If you are to count the rate of vehicles crossing, can you guess the different rates?

Due to their length, the rate of vehicle crossing will be lowest for containers and highest for cars. All in some multiples or powers of them. For the fourth lane, the rate will be some multiple or power of all containers, buses and cars.

Rate of crossing in container lane 𝞪 [container]x

Rate of crossing in bus lane 𝞪 [bus]y

Rate of crossing in car lane 𝞪 [car]z

Rate of crossing in the general lane 𝞪 [container]A[bus]B[car]C

Rate of the general lane is more general rate law, in the sense, that rate of other lanes can be obtained by placing the powers as zero. When B and C are zero the rate is for the container and so on.

Similarly. Chemical reaction rates are also dependent on the concentration of all reactants in terms of some powers, the sum of which is called the order of the reaction.

Let us understand the nature of the order of reaction and its applications in the following description.

Table of Content

• Order of Reaction
• Characteristics of Order of Reaction
• Determination of Order of Reaction
• Examples of Differently Ordered Reactions
• Applications of Order of Reaction
• Practice Problems

## Order of Reaction

The Order of reaction refers to the dependence of the rate of a chemical reaction on the concentration of the reactants. undergoing reaction. Consider a stoichiometric equation of general chemical reaction,

aA + bB +....→ cC +dD +...

Law of mass action, predicts the rate of the reaction as dependent on the concentration of the reactants.

But in practice, the rate of reaction need not depend on all reactants and also need not be in the same proportionality to concentrations of all of them.

In general, the rate of the reaction can be written as

Rate of a reaction ∝ [A]x[B]y.......;

where [A] and [B] are the molar concentration of reactants A and B.

x, y…. are some integers called the partial order of reaction with respect to A, B…. respectively. The sum of all the partial orders is the total order of the reaction.

Adding a proportionality constant, ‘k’, called the rate constant, to the rate equation,

Rate of a reaction ……….(i)

The equation (i) is termed as a differential rate equation.

## Characteristics of Order of Reaction

Some characteristics of the reaction order for a chemical reaction are listed below.

• The reaction order of a chemical reaction is mostly expressed in terms of reactant concentration.
• In complex and chain reactions, the product concentration also may influence the rate of reaction and hence have a partial order of the reaction.
• The power of the reactant concentration in a rate equation is the partial order of the reactant for the reaction
• Positive partial reaction order represents the reactant species whose concentration directly affects the rate of reaction.
• Sum of the partial order of reactants gives the total order of the reaction.
• Partial order of reactant and overall order of reaction, can have any value of zero, fractions and whole numbers.
• The actual dependence of the rate of reaction on reactants will be exactly known only by experimentally determining the values x,y,..
• Order of reaction is an experimental quantity.
• In a single elementary step reaction only, the partial order of the reaction will be the same as the stoichiometric coefficients of the reaction. In multistep or complex reactions, the order of the reaction stems from the concentrations of species involved in the rate-determining slowest elementary reaction step.

## Determination of Order of Reaction

Order of the reaction is determined from the general rate of a reaction.

1. Initial Rates Method

Initial rate of reactions is measured for several combinations of reactants concentration, where all concentrations except one are taken in excess such that their concentration can be considered as constant and the rate will show the dependence on the lesser concentrated reactant.

Let us conduct the following two experiments and determine the initial rate of the reaction. Both experiments have 2 moles each of all reactants other than A and 1 mole of A in one experiment and two moles of A in the second experiment.

Rate of first reaction= r1 = k [1]x [2]y…(i)

Rate of second reaction= r2 = k [2]x [2]y…(ii)

Dividing the two initial rates. , from which the partial order ‘x’ can be determined.

The experiment can be repeated for each reactant to determine its partial order.

The sum of the partial order will give the order of the reaction.

2. Integral Method

Rate of a reaction ……

On integrating this differential rate law, we get, : ln r = ln k + x.ln[A] + y.ln[B] + ….

For different orders of reaction, different integrated rate equations can be written as follows.

Rate equation of zero order reaction of reactant A, [A] = -kt + C

A straight line in a plot of [A] vs time, indicates a zero-order reaction.

The rate equation of the first-order reaction of reactant A, ln [A] = -kt + ln [A0]

A straight in a plot of ln[A] vs time, indicates a first-order reaction.

Rate equation of second order reaction of reactant A, 1[At] = kt + 1[A0]

A straight in a plot of 1[At] vs time, indicates a second order reaction.

From the plots that give, a straight line the overall order of the reaction can be determined.

3. Half-life Method

The time taken to half the initial concentration differs for different ordered reactions. Hence, measuring the time taken to get reduce 50% of its initial reactant concentration and comparing it with the expected theoretical values order can be easily predicted.

 Order of Reaction Half-life formula Zero order First order ${t}_{1/2}$ $\frac{0.693}{k}$ Second order ${t}_{1/2}$ $1k\left[A0\right]$

## Examples of Differently Ordered Reactions

1. Zero Order Reactions

• The rate of reaction is constant and immaterial of the initial concentration of the reactant.
• Example: Enzyme-catalyzed oxidation of CH3CH2OH (ethanol) to CH3CHO (acetaldehyde).
1. First-Order Reactions

• The rates of these reactions change with only one of the reactant and is independent of the presence of other reactants.
• In multiple reactant reactions, the partial and hence the overall order of the reaction of one reactant will be one and the partial order of all other reactants will be zero.
• Example: Decomposition of hydrogen peroxide to water and oxygen, 2H2O2 → 2H2O + O2

c) Pseudo-First Order Reactions

• This is a multiple reactant reaction, where the concentration of only one reactant undergoes changes with the progress of the reaction. All other reactant concentrations are either regenerated or in so much excess their relative change compared to one reactant is negligible.
• Example: CH3COOCH3 + H2O → CH3COOH + CH3OH
• Hydrolysis of ester in the presence of an acid catalyst is pseudo-first order with respect to the reactant ester.

d) Second-Order Reaction

These are reactions where the order of the reaction is proportional to twice the concentrations, which can be of either the same molecules or of two different molecules. The rate of these reactions can be

i) For a single reactant, the rate equation corresponds to r = k[A]2

Example: Second-order reaction of the same reactant: 2NO2 → 2 NO + O2

The rate of decomposition is proportional to the square of nitrogen dioxide concentration or pressure.

ii) For a multiple reactants reaction, the rate equation corresponds to r = k[A][B]

Example: The rate of reaction of a base hydrolysed ester changes with the concentration changes of both ester and the base.

CH3COOC2H5 + NaOH → CH3COONa + C2H5OH

It can be noted that when the order of the reaction is a fraction, the reaction is generally a chain reaction or follows some other complex mechanism. An example of a chemical reaction with a fractional reaction order is the pyrolysis of acetaldehyde. This reaction has an order of 1.5.

Applications of Order of Reaction

Order of the reaction can be used to

1. Identify the reactant whose concentration affects the rate of the reaction
2. Quantify the concentration effect of reactants on the rate of reaction,
3. Decide on the mechanism of the reaction

## Practice Problems

Q1. The order and molecularity of a reaction can be the same when the reaction is-

a. Single step reaction
b. Multiple-step reaction
c. Complex reaction
d. Stoichhiometric and the slowest step of the reaction is the same

Solution: Molecularity is related to the stoichiometric coefficients. A single-step reaction can be in zero order but cannot be of zero molecularity. The order of the reaction is decided by the reactants involved in the slowest step of multi-molecular and complex reactions. If the slowest step also involves the same number of molecules shown in the stochiometric equation then only they can be the same.

Q2. Order and molecularity of the reactions are determined by

a. Theoretically, theoretically
b. Theoretically, experimentally
c. Experimentally, theoretically,
d. Experimentally, theoretically

Solution: Order of the reaction is determined only from experiments by varying reactant concentration and hence an experimental quantity. Molecularly is the stoichiometric coefficients and is obtained from the stochiometric coefficients of a balanced equation. So molecularity is a theoretical quantity.

Q3. Hydrolysis of an ester in the presence of hydrochloric acid is a ----- order reaction.

a. Zero order
b. First order
c. Pseudo first order
d. Second order

Solution: In the hydrolysis of ester, the acid is a catalyst in very small amounts. Though it takes part in the reaction, it is regenerated and not consumed. So it is not a reactant.

The reactants are the ester and water, of which water will be in excess concentration, such that the variation of concentration is so small it can be considered constant. So, only the ester concentration varies much during the reaction. Though the reaction is bimolecular, it is of first order on ester concentration. Hence it is called a pseudo-first-order reaction.

CH3COOCH3 + H2O (excess) → CH3COOH + CH3OH

Q4. Hydrolysis of an ester in the presence of a base sodium hydroxide is a ----- order reaction.

a. Zero order
b. First order
c. Pseudo first order
d. Second order

Solution: Both are reactants and are needed for the products. So this is a second-order reaction.

CH3COOC2H5 + NaOH → CH3COONa + C2H5OH

Q1. Give an example of a fractional-order reaction
Answer: Decomposition of phosgene is a fractional-order reaction. First order with respect to phosgene and half order with respect to chlorine. The total order of the reaction is 1.5

COCl2 → CO + Cl2: rate of reaction = k [COCl2]1 [Cl2]0.5

Q2. Can the reaction rate involve the concentration of the product also?
Answer: Yes in complex or chain reactions where products are also involved in the rate-determining step, they may also affect the rate of reaction.

Q3. Give an example of a natural first-order reaction.
Answer: All natural processes are first-order reactions. Radioactive decay is an example of a first-order reaction.

Q4. In what way the molecularity and order of the reactions are useful to a chemical reaction?
Answer: Molecularity is useful in quantitative measurements of chemical reactions while the order of the reaction helps in the understanding of the mechanism of the reaction.

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