# Zero order kinetics

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
Product
Let the initial concentration of the reactant a and product is zero. After the time interval t, the concentration of the reactant is (a-x) 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 the 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 the reactant 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 half-life of zero-order kinetics

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

#### Half-life 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 = t½, that is the half-life 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 t½
or, k t½ = [A]₀/2
 t½ = [A]₀/2k
Thus for the zero-order kinetics the half-life 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

1. The rate of the reaction is independent of concentration.
2. Half-life is proportional to the initial concentration of the reactant.
3. 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 nth-order 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)1-n/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?
The reaction is a 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 half-life of a zero-order reaction is x and the reaction is completed on t₁ time. What is the relation between x and t₁?
2x = t₁
• Question
If the rate of the reaction is equal to the rate constant. What is the order of the reaction?
Zero-order 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?
Zero-order 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?
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?
This is a zero-order reaction.

Zero order kinetics in terms of reactant or product and half-life, examples, characteristics, and unit of the rate constant with related questions answers

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