Method of determination of order of reaction - Rate law in chemical kinetics-Chem Article

This differential rate expression is first time found by van’t Hoff. He considered the n-th order reaction. Therefore the rate equation is

Introduction

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Method of determination of order of reaction| chemarticle.com

Hello everyone, today we will discuss the chemical kinetics-3 chem article. We have already finished our two classes, class note , previous question answer solutions. Now today we will briefly discuss chemical kinetics reaction mechanisms. And we see in this class what is a steady state approximation for a chemical reaction. What is the method for determining reaction order?

What is a steady state approximation in chemical kinetics?

The determination of reaction order

How to determine order of reaction?
Or how to determine reaction order?

Firstly we are considering a reaction which is of unknown reaction order. That means the reaction order does not know which is first order or second order. We can use this type of method for determining the order of the reaction. We are following this type of method for order determination of a reaction.

Using the differential rate expression method
Using the integral rate expression method
Using Half Life time method
Using the isolation method

These types of techniques are mainly used in laboratory conditions only. when reaction Rate having half life time of several minutes or hours. This method useful for primary steps measure the concentration of reactant or measure the concentration of of product. When direct concentration is not possible Then we can easily use these types of methods.

For these types of methodology you can consider similar types of physical property for a certain time.

For sugar kinetics we can easily measure the optical rotation with time. On the other hand, the potentiometric titration we can measure the EMF value correlates with concentration through Nernst equation.

For the pH metric titration and conductometric titration we can easily measure the pH and conductance of the sample respectively.

1.The differential rate expression

This differential rate expression is first time found by van’t Hoff. He considered the n-th order reaction. Therefore the rate equation is constantly given below..

r = kncn …….(1)

Take a log on both sides, then we can get..

ln r = ln kn + n ln c ………..(2)

Where k_n is the rate constant of this reaction. And c is the concentration of the reactant.

Now, consider two different rates for two different reactants. Let us r₁ and r₂ are two different rates for two different reactants corresponding Their concentrations are C₁ and C₂ respectively.

In case the rate constant is equal for different types of reaction. Then we get the rate equation...

$\begin{array}{l} \frac{{{r_1}}}{{{r_2}}} = \frac{{{k_n}c_{_1}^n}}{{{k_n}c_2^n}}\\ \frac{{{r_1}}}{{{r_2}}} = {\left( {\frac{{{c_1}}}{{{c_2}}}} \right)^n} \end{array}$

Now, we take log on both sides,

$\begin{array}{l} \ln \frac{{{r_1}}}{{{r_2}}} = n\ln \frac{{{c_1}}}{{{c_2}}}.......(3)\\ n = \ln \frac{{{r_1}{c_2}}}{{{r_2}{c_1}}} \end{array}$

$n = \frac{{\ln \left( {\frac{{{c_1}}}{{{c_2}}}} \right)}}{{\ln \left( {\frac{{{r_1}}}{{{r_2}}}} \right)}}$

The experimental data for determination of order of a reaction

Determination of order of reaction by graphical method

We get the experimental data of reaction rate (r) and concentration of reactant (c). Then draw a graph lnr vs lnc for an unknown reaction order. We collected the value of lnr and lnc from grave. Then putting the value in equation no-3, we are Easily get n value. Which is the order of this reaction. This is the method for reaction order determination.

Experimental data for determination of order of a reaction

ln c	ln r
ln 1	-8.294
ln 2	-7.60085
ln 3	-7.195
ln 4	-6.907
ln 6	-6.5022
ln 8	-6.2146
ln 10	-5.99146
ln12	-5.8091

Plot of lnc vs lnr for First order reaction:

Chart

We can see this graphical image plot of lnr vs lnc for n-th order reaction. Putting the value of lnr and lnc in rate equation (3). we get the value of reaction order (n). Where Intercept is lnk_n this value we will get lnk_n=-8.294. And slope of this curve is n, which is the order of the reaction. Where we consider the rate constant k_n =0.00025.

Concentration of reactant c₁= 1. Then ln1 =0, we get the value of lnr₁ =-8.294 or r₁ =0.00025 =k_n which is the rate constant of this reaction.

When c₂= 2, then lnc₂ =ln2, we get the value of lnr₂ = -7.60085 or r₂ =0.00050. Put the value of Concentration of reactant and Rate of the reaction. Then we can easily get a Reaction order.

$\begin{array}{l} n = \frac{{\ln \left( {\frac{1}{2}} \right)}}{{\ln \left( {\frac{{2.5 \times {{10}^{ - 4}}}}{{5 \times {{10}^{ - 4}}}}} \right)}}\\ n = 1 \end{array}$

The value of n=1, this is the first order reaction. Graph straight lines help to detect this reaction as a first order reaction.

2.Using the integral rate expression

Already demonstrated this type of method solving for various orders of the reaction. This method is more powerful used for graphical or analytical parts. This method determines the Order of reaction given certain Data from experiment. Where k is the constant value Then we called them to have a reaction in only one order. But in case k is not constant that means Experiment not correct. This reaction varies in different types of order. The method of integration rate expression was first used in 1850 by scientist Wilhelmy. First of all consider the n-th order reaction where one reactant is involved.

A → P

In case a is initial concentration of the reactant A and (a-x) is concentration of reactant at time t. Then integrated rate expression for a reaction.

For zero order reaction we get integrated rate expression is..

$K = \frac{x}{t}$

For first order reaction we get integrated rate expression is..

$k = \frac{1}{t}\ln \frac{a}{{a - x}}$

For second order reaction we get integrated rate expression is...

$k = \frac{1}{t}\frac{x}{{a\left( {a - x} \right)}}$

For given initial concentration is to measure reactant or produce any one at a different time. Then we put the value in the integrated rate expression of the given order. This value satisfies the given reaction order when k value is constant then calls that this is the order of the reaction. Otherwise this k value does not exist as a constant value then again choose the other order. This type of method is called trial method or error method.

Exercise.1

The decomposition of NH₄NO₃ In the Aqueous solution. Find out the reaction order using the following data.

Time in min.	10	15	20	25	Infinite
Volume of N₂O	6.25	9.00	11.40	13.65	35.05

Ans:

The decomposition of NH₄NO₃ Reaction is

NH₄NO₃ → 2H₂O + N₂O

We can clearly see that the N₂O of a product of a volume is directly proportional to molar concentration of the product. We are considered the first order reaction..

$k = \frac{1}{t}\ln \frac{a}{{a - x}} = \frac{1}{t}\ln \frac{{{V_ \propto }}}{{{V_ \propto } - {V_t}}}$

Therefore we can write ,Put in the given data in this rate expression and we get..

${k_1} = \frac{1}{{10}}\ln \frac{{35.05}}{{\left( {35.05 - 6.25} \right)}} = 0.019639$

${k_2} = \frac{1}{{15}}\ln \frac{{35.05}}{{\left( {35.05 - 9.00} \right)}} = 0.01978$

${k_3} = \frac{1}{{20}}\ln \frac{{35.05}}{{\left( {35.05 - 11.40} \right)}} = 0.0196$

From the given data see that k value is almost the same , that mains k is constant. Therefore the rate expansion is satisfied. Hence , the order of this reaction is 1.

Plot the ln c vs t graph. In graphical data showing the graph will be straight line then we will easily call this reaction a first order. Similarly we are determined by the second order reaction and so on.

3.Half Life Time method

How to determine the order of reaction from the Half Life Time method?

We show the n-th order of the reaction formula discussed in the previous note. Today how to experiment on the half lifetime method for determination of reaction order. Already we have to show the end order reaction and their half life time period formula. Now remind me of this and get the formula ..

First of all we are considering the two different types of initial molar concentration. Two different initial molar concentrations are a1 and a2. These types of molar concentration correspond to half life time of the reaction is (t_1/2)₁ and (t_1/2)₂ Respectively.

$\frac{{{{\left( {{t_{\frac{1}{2}}}} \right)}_1}}}{{{{\left( {{t_{\frac{1}{2}}}} \right)}_2}}} = {\left( {\frac{{{a_2}}}{{{a_1}}}} \right)^{n - 1}}$

$or\ln \frac{{{{\left( {{t_{\frac{1}{2}}}} \right)}_1}}}{{{{\left( {{t_{\frac{1}{2}}}} \right)}_2}}} = (n - 1)\ln \left( {\frac{{{a_1}}}{{{a_2}}}} \right)$

$n = 1 + \frac{{\ln {{\left( {{t_{1/2}}} \right)}_1}/\ln {{\left( {{t_{1/2}}} \right)}_2}}}{{\ln \frac{{{a_2}}}{{{a_1}}}}}...........(4)$

Use this type of equation For the determination of order of the reaction. Where different types of half life time For different types of molar concentration of reactant. We can easily calculate n value using the experimental data. What is the order of reaction we can easily calculate? Yes, easily calculate the order of reaction using the half life time method.

4. The method of isolation

In chemical kinetics reaction studies the expression of concentration are different types of amount. incase the reactant concentration all are same but one concentration reactant is Greater or larger than other. Therefore the concentration of reactants is significantly changed.

We can see this synthesis of HI from hydrogen gas (H₂) and I₂. pseudo first order reaction . H₂ when the large access concentration with respect to I₂ this is the first order reaction similarly I₂ to large or excess concentration of reactant then respect to H₂ This is first order reaction. Total two types of exercise concentrate a reactant have formation of second order reaction.

This reaction is called Pseudo-monomolecular reaction.

Conclusion

Today we are discussing how to determine the reaction order using the experimental value. Titration for given data we will use the differentiate rest expression, integral rate expression, and methods of isolation. This is the brief introduction in chemical kinetics for experiment in laboratory thought. The reaction mechanism will be easy to solve their order with a certain time variation. Therefore we conclude that Specialization of chemical kinetics is easy to determine their reaction order. Thank you for reading. You have any query you can index me.