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# Third Order Reaction

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## What is a Third Order Reaction?

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A reaction is said to be of third order if the rate is determined by the three terms of concentration variation. To put it another way, the minimum number of molecules required for the reaction is three.

3rd Order Reaction Derivation

Only equations of the 1st order have the exponential decay that leads to a constant of natural time.

A third-order reaction has time dependence expressed as:

Third-order reaction equation:

d[A]/dt = -k[A]3.

This integrates up, to give: T = 1/( 2k[A]2) this is evaluated at the two times in question.

You can see that the time to go to half the concentration depends on the concentration, unlike the case of first order where the time to half the concentration is independent of that.

If the 3rd order reaction has time dependence given by:

d[A]/dt = -k[A] * [B]2

or d[A]/dt = -k[A][B][C]

And[ B] and[ C] are altered only marginally, so you have a pseudo-1st-order reaction which then has a definable half-life.

The reason the 1st order reaction gives a half-life is that when the equation integrates it produces a logarithmic function that produces a quotient when subtracted and the starting quantities cancel by division.

### Different Cases in  3rd Order Kinetics

Three different cases may occur in the third-order reaction.

1. Equal concentrations: The concentrations of all three species are equivalent.

A + A + A → Products

1. There are two species of equal concentrations, and one with specific.

A + A + B → Products

-dx/dt = k[A]2[B]

1. Both three species have dissimilar amounts.

A + B + C → Products

-dx/dt = k[A][B][C]

### Some Facts About Third Order Rate Law

• The reaction order is determined from the slowest reaction step.

• It is an experimental value

• Below are some examples of fractional order:

(i) COCl2 → CO + Cl2

rate = k[COCl]3/2

Therefore Order = 3/2 = 1.5

(ii) H2 + Br2 → 2H Br

Rate = k[H2]1[Br2]1/2

Therefore Order = 1.5

(iii) CH3CHO → CH4 + CO

Rate = k[CH3CHO]3/2

Therefore Order = 3/2 = 1.5

• Higher - order reactions [ > 3] are very unusual because many molecules have very little chance of experiencing effective collisions.

• 2O3 → 3O2

Rate = k[O3]2 ⋅ [O2]-1

Third Order Reaction Examples

• Let us understand the nitric oxide-chloride reaction

2 NO +Cl2 → 2 NOCl

Then Rate, R= k[NO]2 [Cl2]

Order of above reaction is equal to addition of exponent of nitric oxide and chloride Order = 2 + 1 = 3.

• Let us consider the nitric oxide-oxygen reaction

2 NO + O2 → 2 NO2 R= k[NO]2 [O2]

Therefore Order = 2 + 1 = 3.

FAQ (Frequently Asked Questions)

1. What is the Rate Law for a Third-Order Reaction?

Ans. Reaction Order and Rate Constant Units

 Reaction Order Units of k Zero mol/L/s First s-1 Second L/mol/s Third mol-1 L2 s-1

2. Why are Third-Order Reactions Unlikely?

Ans. This type of reaction is very unusual because to create a reaction, all three reactants have to collide with each other simultaneously, with sufficient energy and proper orientation. There are three ways to react to termolecular reactions, and they all come in the third order.

3. How Many Orders of Reaction are There?

Ans. Reaction orders which define their kinetics may be allocated to chemical reactions. Order types are zero-, first-order, second-order, or mixed-order. At a constant rate a zero-order reaction proceeds. A reaction rate at first order depends on the concentration of one of the reactants.