Question

what do we do if the orders of reaction are criss crossing and why? this question is for my reactor design course.

Answer 1

The Order of reaction refers to the relationship between the rate of a chemical reaction and the concentration of the species taking part in it. In order to obtain the reaction order, the rate expression (or the rate equation) of the reaction in question must be obtained. Once the rate equation is obtained, the entire composition of the mixture of all the species in the reaction can be understood.

Reaction Order

The order of reaction can be defined as the power dependence of rate on the concentration of all reactants. For example, the rate of a first-order reaction is dependent solely on the concentration of one species in the reaction. Some characteristics of the reaction order for a chemical reaction are listed below.

• Reaction order represents the number of species whose concentration directly affects the rate of reaction.
• It can be obtained by adding all the exponents of the concentration terms in the rate expression.
• The order of reaction does not depend on the stoichiometric coefficients corresponding to each species in the balanced reaction.
• The reaction order of a chemical reaction is always defined with the help of reactant concentrations and not with product concentrations.
• The value of the order of reaction can be in the form of an integer or a fraction. It can even have a value of zero.

In order to determine the reaction order, the power-law form of the rate equation is generally used. The expression of this form of the rate law is given by r = k[A]x[B]y.

In the expression described above, ‘r’ refers to the rate of reaction, ‘k’ is the rate constant of the reaction, [A] and [B] are the concentrations of the reactants. The exponents of the reactant concentrations x and y are referred to as partial orders of the reaction. Therefore, the sum of all the partial orders of the reaction yields the overall order of the reaction.

How to Determine Reaction Order

There are several different methods which can be followed in order to determine the reaction order. Some of these methods are described in this subsection.

(a) Initial Rates Method

• First, the natural logarithm form of the power-law expression is obtained. It is given by: ln r = ln k + x.ln[A] + y.ln[B] + ….
• The partial order corresponding to each reactant is now calculated by conducting the reaction with varying concentrations of the reactant in question and the concentration of the other reactants kept constant.
• If the partial order of A is being determined, the power-law expression of the rate equation now becomes ln r = x.ln[A] + C, where C is a constant.
• A graph is now plotted by taking ‘ln r’ as a function of ln[A], the corresponding slope is the partial order, given by x.

(b) Integral Method

• The order of reaction obtained from the initial rates method is usually verified using this method.
• The measured concentrations of the reactants are compared with the integral form of the rate law.
• For example, the rate law for a first-order reaction is verified if the value for ln[A] corresponds to a linear function of time (integrated rate equation of a first-order reaction: ln[A] = -kt + ln[A]0).

(c) Differential Method

• This method is the easiest way to obtain the order of reaction
• First, the rate expression of the reaction is written (r = k[A]x[B]y..)
• The sum of the exponents x+y+… gives the final value of the reaction order.

Apart from these methods, there exist other ways to obtain the reaction order, such as the method of flooding in which the concentration of a single reactant is measured when all the other reactants are present in huge excess.

Different Values of Reaction Order

As discussed earlier, the value of the order of reaction may be in the form of an integer, zero, or a fraction. A graph detailing the reaction rates for different reaction orders can be found below.

Chemical reactions can be classified into the following types based on the dependence of the rate on the concentration.

Zero Order Reactions

• The rate of reaction is independent of the concentration of the reactants in these reactions.
• A change in the concentration of the reactants has no effect on the speed of the reaction
• Examples of these types of reactions include the enzyme-catalyzed oxidation of CH3CH2OH (ethanol) to CH3CHO (acetaldehyde).

First-Order Reactions

• The rates of these reactions depend on the concentration of only one reactant, i.e. the order of reaction is 1.
• In these reactions, there may be multiple reactants present, but only one reactant will be of first-order concentration while the rest of the reactants would be of zero-order concentration.
• Example of a first-order reaction: 2H2O2 → 2H2O + O2

Pseudo-First Order Reactions

• In a pseudo-first order reaction, the concentration of one reactant remains constant and is therefore included in the rate constant in the rate expression.
• The concentration of the reactant may be constant because it is present in excess when compared to the concentration of other reactants, or because it is a catalyst.
• Example of a pseudo-first order reaction: CH3COOCH3 + H2O → CH3COOH + CH3OH (this reaction follows pseudo-first order kinetics because water is present in excess).

Second-Order Reaction

• When the order of a reaction is 2, the reaction is said to be a second-order reaction.
• The rate of these reactions can be obtained either from the concentration of one reactant squared or from the concentration of two separate reactants.
• The rate equation can correspond to r = k[A]2 or r = k[A][B]
• Example of a second-order reaction: NO2 + CO → NO + CO2

A Pseudo first order reaction can be defined as a second order or bimolecular reaction that is made to behave like a first order reaction. This reaction occurs when one reacting material is present in great excess or is maintained at a constant concentration compared with the other substance. Reactions that appear to be second order in nature but are approximated as a first-order of reaction on close analysis. For example, a second – order of the reaction is given by the equation,

A + B —-> C + D

This reaction is dependent upon the concentrations of both A and B but one of the components is present in large excess and thus its concentration hardly changes as the reaction proceeds.

So, if component B is in large excess and the concentration of B is very high as compared to that of A, the reaction is considered to be pseudo-first order reaction with respect to A and if component A is in large excess and the concentration of A is very high as compared to that of B, the reaction is considered to be pseudo first order with respect to B.

When you say that the order of reactions are criss crossing, I believe that it is about pseudo phase reactions. In that case, we can consider the design eqautions of a first order reaction for a reactor. Also other the type of the reactor and other required conditions are to be considered. For additional details you can go through Coulson and Richardson's Chemical Engineering Book Volume 6 for design purpose.