Zero order kinetics, the rate of these reactions does not depend on the concentration of the reactants.
Mathematical derivation of zero order kinetics

Let us take a reaction represented as

A → Product

Let the initial concentration of the reactant a and product is zero. After the time interval t, the concentration of the reactant is (ax) and concentration of the product is x.
Thus x is decreases of concentration in zero order reaction.
 Mathematical derivation of zero order kinetics in terms of product.

Thus the mathematical equation of zero order kinetics in terms of product,

dx/dt = k₀
Where k₀ is the rate constant of zero order reaction.
or, dx = k₀dt

Integrating the above reaction,
∫dx = k₀ ∫dt
or, x = k₀t + c
where c is the integration constant of the reaction.

When t = o, x is also zero thus, C = o
Thus the above equation is,
x = k₀ t 

This is the relationship between decreases of concentration of the reactant(x) within time(t).
 Mathematical derivation of zero order kinetics in terms of reactant.

Rate equation in terms of reactant,
d[A]/dt = k₀ [A]⁰ = k₀
Where [A] is the concentration of thereactant at the time t.
or,  d[A] = k₀dt

Integrating the above equation,
We have  ∫d[A] = k₀ ∫ dt
or,  [A] = k₀t + c
where c is the integration constant of the reaction.

If initial at the time t = 0 concentration of the reactant [A]₀
Then from the above equation,
 [A]₀ = 0 + c
or, c = [A]₀

Putting the value on the above equation,
 [A] = kt  [A]₀ 

This is another form of the rate equation in zero order kinetics.
The halflife of zero order kinetics

The time required for half of the reaction to be completed is known as the halflife of the zero order reaction. It means 50% of reactants disappear in that time interval.
Halflife in zero order kinetics

If in a chemical reaction initial concentration is [A]₀ and after t time interval the concentration of the reactant is [A].

Then, [A]₀  [A] = kt

Thus when t = t_{½}, that is the halflife of the reaction, the concentration of the reactant [A] = [A]₀/2. Putting the value on the above equation,

We have [A]₀  [A]₀/2 = k t_{½}
or, k t_{½} = [A]₀/2
t_{½} = [A]₀/2k 

Thus for the zero order kinetics the halflife of the reaction proportional to its initial concentration.
Examples of the zero order kinetics

The only heterogeneous catalyzed reactions may have zero order kinetics.
Examples of zero order kinetics 
Characteristics of zero order kinetics
 The rate of the reaction is independent of concentration.
 Halflife is proportional to the initial concentration of the reactant.
 The rate of the reaction is always equal to the rate constant of the reaction at all concentration.
Unit of the rate constant in zero order kinetics

The rate equation in terms of product for the nthorder reaction is,

d[A]/dt = k [A]^{n}
or k = (d[A]/dt) × (1/[A]^{n})

Thus the unit of rate constant(k)
= (unit of concentration)/{unit of time × (unit of concentration)^{n}}

= (unit of concentration)^{1n}/unit of time

Thus if zero order kinetics the concentration is expressed in lit mole⁻¹ and time in sec

Then the rate constant = (lit mol⁻¹)/sec
= mol lit⁻¹sec⁻¹
Questions and Answers of zero order kinetics
 Question

The rate constant of a chemical reaction is 5 × 10⁻⁸ mol lit⁻¹sec⁻¹. What is the order of this reaction? How long does it take to change concentration from 4 × 10⁻⁴ moles lit⁻¹ to 2 × 10⁻² moles lit⁻¹?
 Answer

The reaction is zero order reaction and 3.92 × 10⁵ Sec take to change concentration from 4 × 10⁻⁴ moles lit⁻¹ to 2 × 10⁻² moles lit⁻¹.
 Questions

The halflife of a zeroorder reaction is x and the reaction is completed on t₁ time. What is the relation between x and t₁?
 Answer

2x = t₁
 Question

If the rate of the reaction is equal to the rate constant. What is the order of the reaction?
 Answer

Zeroorder reaction.
 Question

For a reaction, N₂ + 3 H₂ → 2NH₃, if d[NH₃]/dt = 2 × 10⁻⁴mol lit⁻¹sec⁻¹, What is the order and the value of  d[H₂]/dt of this reaction?
 Answer

Zeroorder reaction and the value of d[H₂]/dt = 3 × 10⁻⁴ mol lit⁻¹sec⁻¹.
 Question

For the reaction N₂O₅ → 2NO₂ + ½ O₂, the rate of disappearance of N₂O₅ is 6.25 × 10⁻³ mol lit⁻¹sec⁻¹, what is the rate of formation of NO₂ and O₂ respectively?
 Answer

1.25 × 10⁻² and 3.125 × 10⁻³ mol lit⁻¹sec⁻¹
 Question

For the reaction H₂ + Cl₂ → 2HCl on sunlight and taking place on the water. What is the order of the reaction?
 Answer

This is a zero order reaction.

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