# Zero-order Reaction

A chemical reaction in which the rate is independent of the reactants’ concentrations is called a zero-order reaction. The reaction rate does not change as the reaction proceeds with time [1-4].

A zero-order reaction is due to any of the following two conditions:

1. A small portion of the reactant from a large “pool” is available for the reaction. Once that portion is used, it is immediately refilled from the pool.
2. One of the reactants is present in a vast concentration or is a heterogeneous catalyst.

## Formula

Since the rate is independent of concentration, it can be written as proportional to the zeroth power of the concentration [1-4].

Rate = k [A]0

=> R = k

The unit for the reaction rate is moles per liter per second or mol L-1 s-1. Hence, the unit for the reaction coefficient is also mol L-1 s-1.

### Differential Form

The reaction rate is the decrease in reactants’ concentration per time. Therefore, the differential form of the zero-order rate equation is given by

-d[A]/dt = k

### Integrated Form

Rearranging the above equation and integrating it on both sides gives the integrated rate equation.

∫d[A] = -k ∫dt

=> [A] = [A]o – kt

Where [A]o is the concentration at t = 0 and [A] is the concentration at time t.

## Graphs

We have seen that the rate remains constant in a zero-order reaction, and the concentration is linear with time. Therefore, the plot of [A] vs. t will yield a straight line, as shown below [1-4].

## Half-life

The half-life of a reaction is the time frame in which a reactant’s concentration is reduced to one-half of its initial concentration. It can be calculated as follows [1-4]:

At half-life, t = t1/2 and [A] = [A]o/2. Plugging these in the equation for concentration, we get

[A]o/2 = [A]o – kt1/2

=> t1/2 = [A]o/2k

Therefore, the half-life of a zero-order reaction depends on the initial concentration and the rate constant.

## Examples

Reactions catalyzed by enzymes and solid surfaces (heterogeneous catalysis) are typically zero-order reactions. Let us look at a few examples [1-4].

1. Hydrogen (H2) reacts with chlorine (Cl2) in the presence of ultraviolet light to give hydrogen chloride (HCl).

H2 (g) + Cl2 (g) → 2 HCl (g)

Such a type of reaction is known as a photochemical reaction.

1. Nitrous oxide (N2O) decomposes over a hot platinum surface that is at a temperature of 200 to 400 ˚C to give nitrogen (N2) and oxygen (O2).

2 N2O (g) → 2 N2 (g) + O2 (g)

1. Decomposition of ammonia (NH3) in the presence of a molybdenum (Mo) catalyst to give nitrogen (N2) and hydrogen (H2).

2 NH3 (g) → N2 (g) + 3 H2 (g)

This reaction is the inverse of Haber’s process.

Besides, enzyme-catalyzed reactions common in the human body are zero-order reactions. For example, yeast contains enzymes. One of them, zymase, converts glucose into alcohol.