### The Differential form of a zero order reaction can be written as:

Zero-order reaction is a chemical reaction wherein the rate does not vary with the increase or decrease in the concentration of the reactants. Therefore, the rate of these reactions is always equal to the rate constant of the specific reactions (since the rate of these reactions is proportional to the zeroth power of reactants concentration).

The Differential form of a zero order reaction can be written as:

Rate = (frac{-dA}{dt} = k[A]^{0} = k)

Where ‘Rate’ refers to the rate of the reaction and ‘k’ is the rate constant of the reaction.

This differential form can be rearranged and integrated on both sides to get the required Integral form as shown below.

Multiplying both sides with ‘-dt’, we get:

(int_{[A]_{0}}^{[A]}d[A] = -int_{0}^{t}kdt)

Where [A] 0 is the initial concentration of the reactant [A] at time t=0. Solving for [A], we get:

Which is the required integral form. This form enables us to calculate the population of the reactant at any given time post the start of the reaction.

The integral form of zero order reactions can be rewritten as

Comparing this equation with that of a straight line (y = mx + c), an [A] against t graph can be plotted to get a straight line with slope equal to ‘-k’ and intercept equal to [A] 0 as shown below.

The timescale in which there is a 50% reduction in the initial population is referred to as half-life. Half-life is denoted by the symbol ‘t 1/2 ’.

From the integral form, we have the following equation

Replacing t with half-life t 1/2 we get:

(frac{1}{2}[A] = [A_{0}] – kt_{1/2})

Therefore, t 1/2 can be written as:

It can be noted from the equation given above that the half-life is dependent on the rate constant as well as the reactant’s initial concentration.

The following reactions are examples of zero order reactions that are not dependent on the concentration of the reactants.

(H_{2}(g) + Cl_{2} (g)overset{hv}{rightarrow} 2HCl (g))

(2N_{2}O overset{Pt(hot)}{rightarrow} 2N_{2} + O_{2})

(CH_{3}COCH_{3} + I_{2} overset{H^{+}}{rightarrow} ICH_{2}COCH_{3} + HI)

Reactions wherein a catalyst is required (and is saturated by reactants) are generally zero order reactions. The unit of the rate constant in a zero order reaction is given by concentration/time or M/s where ‘M’ is the molarity and ‘s’ refers to one second.

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