ORDER OF REACTION

What is an order of reaction?

The number of reacting molecules whose concentration changes due to chemical change is called reaction order.

There are four reaction orders: first-order reaction, second-order reaction, third-order reaction, and zero-order reaction.

What is First order reaction?

During a reaction, a one-molecule concentration change in a number of reacting molecules is called a first-order reaction.

\[\displaystyle {{N}_{2}}{{O}_{5}}\to {{N}_{2}}{{O}_{4}}+\frac{1}{2}{{O}_{2}}\]

What is Second order reaction?

During a reaction, two-molecule concentration change a number of reacting molecules is called second order reaction.

\[\displaystyle 2HI\to {{H}_{2}}+{{I}_{2}}\]

What is the Third order of reaction?

During a reaction, a three-molecule concentration change in a number of reacting molecules is called a third-order reaction.

\[\displaystyle 2NO+{{O}_{2}}\to 2N{{O}_{2}}\]

METHOD FOR DETERMINING THE ORDER OF REACTION

The majority of reactions are of the first or the second order reaction. The following methods are used to determine the order of a reaction.

USE OF DIFFERENTIAL RATE EXPRESSION

In this method devised by van’t Hoff, the rate of an nth order reaction is,

\[\displaystyle r={{k}_{n}}{{c}^{n}}---(1)\]

Taking log both sides in the above equation,

\[\displaystyle \ln r=\ln {{k}_{n}}+n\ln c---(2)\]

Plot a graph with a double logarithmic rate against concentration; it gives a straight line. Slop gives the value of n, and intercept gives lnkn seen in the figure.

lnr vs. lnc_for_anth_order

lnr → lnc_for_an nth order

If r1 and r2 are the rates at two different reactant concentrations, c1 and c2, then

\[\displaystyle \frac{{{{r}_{1}}}}{{{{r}_{2}}}}=\frac{{-\frac{{d{{c}_{1}}}}{{dt}}}}{{-\frac{{d{{c}_{2}}}}{{dt}}}}=\frac{{{{k}_{n}}c_{1}^{n}}}{{{{k}_{n}}c_{1}^{n}}}={{\left( {\frac{{{{c}_{1}}}}{{{{c}_{2}}}}} \right)}^{n}}\]

Taking log both sides,

\[\displaystyle \ln \frac{{{{r}_{1}}}}{{{{r}_{2}}}}=n\ln \frac{{{{c}_{1}}}}{{{{c}_{2}}}}\]
\[\displaystyle n=\frac{{\ln \left( {\frac{{{{r}_{1}}}}{{{{r}_{2}}}}} \right)}}{{\ln \left( {\frac{{{{c}_{1}}}}{{{{c}_{2}}}}} \right)}}----(3)\]

USE OF INTEGRAL RATE EXPRESSION

This method can be used in two ways, either analytically or graphically. The analytical method assumes a specific order for the reaction and calculates the rate constant from the given data.

If the value of k is not constant, we assume a different order for the reaction. Again, calculate the k value using a new rate expression and see if k is constant.

In the graphical method, the plot of lnc against t is give a straight line, and the reaction is of the first order reaction. Similarly, the integrated expression for the second order reaction graphically and so on.

HALF-LIFE METHOD

All reactants are present in the same molar concentration; the half-life t1/2 of an nth order All reactants are present in the same molar concentration; the half-life t1/2 of an nth order reaction is,

\[\displaystyle \frac{{{{{\left( {{{t}_{{\frac{1}{2}}}}} \right)}}_{1}}}}{{{{{\left( {{{t}_{{\frac{1}{2}}}}} \right)}}_{2}}}}={{\left( {\frac{{{{a}_{2}}}}{{{{a}_{1}}}}} \right)}^{{n-1}}}\]

Different initial molar concentration, if two experiments are carried out, then

\[\displaystyle \ln \frac{{{{{\left( {{{t}_{{\frac{1}{2}}}}} \right)}}_{1}}}}{{{{{\left( {{{t}_{{\frac{1}{2}}}}} \right)}}_{2}}}}=(n-1)\ln \frac{{{{a}_{2}}}}{{{{a}_{1}}}}\]
\[\displaystyle n=1+\frac{{\ln {{{\left( {{{t}_{{\frac{1}{2}}}}} \right)}}_{1}}\ln {{{\left( {{{t}_{{\frac{1}{2}}}}} \right)}}_{2}}}}{{\ln \frac{{{{a}_{2}}}}{{{{a}_{1}}}}}}----(2)\]

Determining the half-life of a reaction at two different initial concentrations leads to the determination of n, and Ostwald suggested this method.

ISOLATION METHOD

Kinetics of reaction is studied in many experiments by concentration constant of all but one reactant is large excess so, the result gives the order concerning the reactant whose concentration is changing significantly.

Share post on

About the author

Bhoomika Sheladiya

BSc. (CHEMISTRY) 2014- Gujarat University
MSc. (PHYSICAL CHEMISTRY) 2016 - School of Science, Gujarat University

Junior Research Fellow (JRF)- 2019
AD_HOC Assistant Professor-(July 2016 to November 2021)

View all posts

Leave a Reply

Your email address will not be published. Required fields are marked *