## Zero order Reaction in Chemical Kinetics

Zero order kinetics define the rate of zero order chemical reaction in terms of reactant and product per unit time and rate of reactions independent with the decrease or increase the concentration of reacting species. Therefore the zero order kinetics are rare in reality, the enzyme catalyzed reaction is an example of zero order kinetic with respect to the substrate.

Two most important for study the zero-order or kinetics reactions in chemical science.

- The first is the practical importance to predict how quickly a reaction mixture moves to the equilibrium state.
- The second reason is the theoretical importance of formulating the mechanism of a chemical reaction.

### Kinetic Reaction in terms of Reactant and Product

In kinetics, the rate of a chemical reaction generally expressed in terms of reactant and product. Therefore the concentration of reactant decrease and reactant increase. When this decrease or increase concentration expressed per unit time, we find the rate laws in kinetics.

A → Product

Rate of reaction = – d[A]/dt = k [A]^{n}

Some surface reactions the rate has been found to be independent of concentration. These reactions are known as the zero order kinetics reaction.

### Define Zero-order Kinetics Reaction

To define rate laws for zero order chemical kinetics show the dependence of the concentration of the reacting species. Whereas the integrated law provides the increase or decreases the concentration of reacting species at any time from the start of the reactions.

Let us take a chemical reaction with the initial concentration of reactant = a and product = 0.

A → Product

After time t concentration of reactant = (a – x) and product = x. Therefore concentration decrease after t time = x.

Question

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

Answer

Zero order reaction.

### Rate of Reaction in terms of product

The rate in terms of product,

dx/dt = k_{0
}where k₀ = rate constant.

or, dx = k_{0}dt

When we integrating the above equation within limits, produce the rate equation for the reactions.

∴ x = k_{0}t + c

where c = integration constant.

When t = 0, that is the initial state of the reaction, x = 0. Therefore the integration constant of this rate equation also zero.

∴ x = k_{0}t

This is the relationship between decreases of concentration of the reactant within the time for zero order kinetic.

### Rate of Reaction in terms of Reactant

Let the initial concentration of reactant = [A]_{0} and after t time = [A], thus the rate equation in terms of reactant,

– d[A]/dt = k_{0} × [A]^{0} = k_{0}

Negative sign because the concentration decreases with time and initial concentration reactant [A]_{0} = 0.

or, – d[A] = k_{0}dt

Integrating the above equation

∫d[A] = k_{0} ∫dt

∴ – [A] = k_{0}t + c

where c = integration constant.

If the initial concentration of the reactant = [A]_{0} when time = 0, that is the initial time.

– [A]_{0 }= 0 + c

∴ [A] = – [A]_{0}

Therefore the integrated rate equation for the zero order kinetic

– [A] = k_{0}t – [A]_{0}

or, [A]_{0} – [A] = k_{0}t

This is another form of the rate equation of the zero order kinetic reaction.

### Unit of the Rate Constant in Kinetics

The rate equation in terms of chemical product

– d[A]/dt = k_{0} × [A]^{n}

∴ Unit of k_{n} = unit of conc/(unit of conc)n × unit of time

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

Unit molar concentration = mol lit^{-1} and time = sec.

Thus the unit rate constant for the zero order kinetics

(mol lit^{ -1})^{1 -0}/ sec

= mol lit^{-1} sec^{-1}

### Half-life of Zero Order Reaction

Half-life means 50% of reactants disappear in that time interval.

The rate equation for zero order kinetics reactions

[A]_{0} – [A] = k_{0}t

But when t = t_{½}, that is the half-life of the reaction completed, the concentration of the reactant

[A] = [A]/2

∴ t_{½} = [A]/2k

Therefore, the half-life of the zero order kinetics depends on the initial concentration of the reactant.

Question

The half-life of zero order = x. If the reaction completed on t_{1} time, what is the relation between x and t_{1}?

Answer

t_{½} = x = a/2k and completion time t_{1} = a/k

∴ x/t_{1} = (a/2k) × (k/a)

or, t_{1} = 2x

### Order of Enzyme-Catalyzed Kinetic Reaction

Although the reactions which have an overall order of zero are rare. The enzyme-catalyzed reaction is the example of zero order kinetics with respect to the substrate.

[Substrate] ⇒ [Product]

Heterogeneous catalyzed reactions are also the zero order kinetics.

### Examples of Zero Order Kinetic Reaction

- Dissociation of hydrogen iodide in gold surface with high pressure.

2HI(gas) → H_{2}(gas) + I_{2} (gas)

Rate of reaction = k × [HI]^{0} = k

- Dissociation of N
_{2}O in the platinum surface at high pressure.

2N_{2}O (gas) → 2N_{2}(gas) + O_{2}(gas)

Rate of reaction = k [N_{2}O]^{0} = k

### Concentration and Zero order Kinetics

- The rate of the reactions is independent of concentration.
- Half-life is proportional to the initial concentration of the reactant.
- The rate is always equal to the rate constant at all concentrations.