### What is the zero-order kinetics reactions?

- Chemical kinetics is the branch of physical chemistry that deals with a study of the speed of chemical reaction. Such studies also enable us to understand the mechanism by which the reaction occurs.

- Study of chemical equilibrium only initial and final states was considered, the energy relation between reactants and product is governed by thermodynamics where the time or the intermediate states were of no concern.

- The velocity of a reaction is the amount of chemical change occurring per unit time. The rate is generally expressed as the decrease in the concentration of the reactant or increase in concentration per unit time.

- Some surface reactions the rate has been found to be independent of concentration. These are

**zero-order kinetic reactions**.

####
**The concentration of zero-order reactions**

- 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.

- If the rate of the reaction is equal to the rate constant. What is the

**order**of the reaction?

- Zero-order reaction.

#### The zero-order reaction in terms of product

- The mathematical equation of zero-order kinetics in terms of product,

dx/dt = k₀

Where k₀ is the rate constant of the

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,

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 reactions 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

-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.

###
**Half-life and zero-order kinetics reactions**

- 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.

- 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 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 t

or, k t

_{½}or, k t

_{½}= [A]₀/2t_{½} = [A]₀/2k |

- Thus for the

**zero-order kinetics**the half-life of the reaction proportional to its initial concentration.

### Examples of zero-order of reactions

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

Zero-order kinetics reaction |

- 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

- 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.

###
**Unit of the rate constant in a chemical reaction**

- The rate equation in terms of product for the nth-order reaction is,

d[A]/dt = k [A]

or, k = (d[A]/dt) × (1/[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

- Zero-order kinetics reaction the concentration is expressed in lit mole⁻¹ and time in sec

Then the rate constant = (lit mol⁻¹)/sec

= mol lit⁻¹sec⁻¹

Question= mol lit⁻¹sec⁻¹

- 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

- 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 takes to change concentration from 4 × 10⁻⁴ moles lit⁻¹ to 2 × 10⁻² moles lit⁻¹.

- 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

###
**Characteristics of zero-order kinetics**

- The rate of the reaction is independent of concentration.
- Half-life 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 concentrations.