Zero order kinetics

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

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 (a-x) and the concentration of the product is x. Thus x is decreased concentration in zero-order reaction.

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).

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.

Zero-order kinetics reactions examples

    The only heterogeneous catalyzed reactions may have zero-order kinetics.
Zero-order kinetics reaction
Zero-order kinetics reaction


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 concentrations.

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?
Answer
    The reaction is a zero-order reaction and 3.92 × 10⁵ sec takes 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?
Answer
    2x = t₁
Question
    If the rate of the reaction is equal to the rate constant. What is the order of the reaction?
Answer
    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?
Answer
    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?
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.

Zero-order kinetics in terms of reactant and product, half-life and unit of the rate constant of a chemical reaction with questions answers

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