```Third Order Reactions
A reaction is said to be of third order if its rate is determined by the variation of three concentration terms.
When the concentration of all the three reactants is same or three molecules of the same reactant are involved, the rate expression is given as
3A  →  products
A + B + C  →  products
dx/dt = k(a-x)3
On solving this equation,
k = 1/t.x(2a-x)/(2a2 (a-x)2)
Characteristic of third order reaction
1.   Half life period
= 1/k.0.5a(2a-0.5a)/(2a2 (0.5a)2) = 1/k(0.5a × 1.5a)/(2a2×0.5×0.5a)
= 3/(2a2 K)
Thus, half life is inversely proportional to the square of initial concentration.
2.   The change in the unit of concentration changes the numerical value of k.
3.   The unit of k is expressed as (mol/litre)-2 time-1 or litre2 mol-2 litre-1.
Examples of third order reacting
1.   Reacting between nitric oxide and oxygen
2NO + O2  →  2NO2

2.   Reaction between nitric oxide and chlorine.
2NO + Cl2 → 2NOCl

3.   Reduction of FeCl3 by SnCl2
2F2Cl3 + SnCl2  →  SnCl4 + 2FeCl2

Expressions for the constant for reactions of different orders:

Reaction

Order

Rate law eqn.

Expression for rate const.

A → Products

A → Products

2A → Products

A + B → Products

3A → Products

0

1

2

2

3

Rate = k

Rate = k[A]

Rate = k[A]2

Rate = k[A][B]

Rate = k[A]3

k = 1/t[[A]0-[A]]

k = 2.303/t log [A]0/[A]

k = 1/t [1/([A])-1/[A]0]

k = 2.303/t([A]0-[B]0) log([B]0 [A])/([A]0[B])

k = 1/2t [1/[A]2-1/([A]_02)]

```
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