Zero-Order Reaction: Graph, Equation, Example and Derivation

Zero Order of reaction explains the relationship between the rate of a chemical reaction and the concentration of the elements present in the reaction. Hence, this order of reaction can be said as the rate of reaction which is independent of the concentration of all the reactants. The power-law form of the rate equation is generally used to identify the reaction order.

Key Terms: Zero order reaction, Half life, Equatation and of zero rate reaction, Concentration of the reactant, Kinetics

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Zero-Order Reaction Definition

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“A zero-order reaction is a chemical reaction in which the rate does not change as the reactants’ concentration increases or decreases.” As the rate of these reactions is proportional to the 0th power of the concentration of reactants, the rate of the reactions is always equal to the rate constant of the specific reactions.

A zero-order reaction is an artefact (created by humans) of the conditions under which the reaction occurs. Due to this reason, the reactions that follow the zero-order reactions are also named as pseudo-zero-order reactions at times.

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Equation of Zero-Order Reaction

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The differential rate equation is an equation that represents the dependence of the rate of reaction on the reacting species concentration. The slope of the tangent at any point of time in the concentration-time graph represents the instantaneous rate of reaction. The concentration-time graph makes determining the rate of reaction difficult.

Zero-order reaction is defined as the process in which the rate of the reaction is proportional to the 0^th power of the concentration of reactants. Consider the reaction

R → P

Rate = - d[R] / dt = k[R]⁰

Any quantity raised to power zero is unity therefore R⁰ will be 1,

Rate = - d[R] / dt = k × 1

d[R] = - k dt

On integrating both sides

[R] = - kt + I         Eq.(1)

where I is the constant of integration.

At t = 0, the concentration of the reactant R = [R]₀, where [R]₀ is referred to as initial concentration of the reactant.

Substituting in equation (1)

[R]₀ = - k × 0 + I

[R]₀ = I

After substituting the value of I in the equation (1)

[R] = - kt + [R]₀         Eq.(2)

While comparing equation (2) with the equation of a straight line, y = mx + c, if we plot [R] against t, we get a straight line with slope (Fig. 1) = -k and intercept equal to [R]₀

Variation in concentration v/s time plot

After simplifying equation (2), we get the rate constant (k) as:

K = R₀ – R / t

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Graph of Zero Order Reaction

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After rewriting the integral form of zero-order reactions, you will get;

[R]=–kt + [R₀][R] = -kt + [R₀]

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

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Relationship between Half-Life & Zero-Order Reactions

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The half-life of a reaction defines the amount of time required for half of the reactants to be depleted, which is the same as the half-life involved in nuclear decay (first-order reaction). The half-life of the reaction is denoted by ‘t_1/2’ and is expressed in seconds. Remember the half-life of a reaction changes with the order of the reaction. Given below is the half-life of a zero-order reaction:

[A] = [A₀] - kt

Replace t with half-life t_1/2

½[A] = [A₀] – kt_1/2

Therefore, we can write t_1/2 as:

kt1/2 = ½ [A]₀

And,

t_1/2 = 1/2k [A]₀

• t_1/2 stands for the half-life of a reaction
• [A]₀ stands for initial concentration (mol. L^-1 or M)
• k stands for the zero-order rate constant.

It is clearly visible from the above equation that the half-life of the reaction is dependent on the rate constant as well as the initial concentration of the reactant.

For the 1^st order reaction, the half-life is; t_1/2 = 0.693/k

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Examples of a Zero-Order Reaction

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Here are a few examples of zero-order reaction:

Example 1: Haber Process

The Haber process is defined as the process that produces ammonia from hydrogen and nitrogen gas. The exact opposite of this process (form nitrogen and hydrogen by the decomposition of ammonia) is known as the reverse Haber process which is an example of a zero-order reaction.

2NH₃ (g) → 3H₂ (g) + N₂ (g)

Example 2: Photochemical Reaction

The Photochemical reaction is defined as the reaction of hydrogen with chlorine.

H₂ + Cl₂ → 2HCl

Rate = k (H₂)⁰ (Cl₂)⁰

Rate = k

Example 3

Decomposition of nitrous oxide on a hot platinum surface.

N₂O → N₂ + 1/2 O₂

Rate [N₂O]⁰ = k[N₂O]⁰ = k

d[N₂O] / dt = k

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Things to Remember

• Zero-order reaction is a part of CBSE class 12 Chemistry syllabus under unit 4 Chemical Kinetics. 
• It carries a total of 5 periods and 3 to 5 marks.
• The expression for the rate law in zero order reaction is r = kA^xB^y
• Here ‘r’ stands for “rate of reaction”, ‘k’ stands for “rate constant”.
• ‘A’ and ‘B’ stand for “concentrations of the reactants” and exponents ‘x’ and ‘y’ are “partial orders of the reaction”.
• The overall order of the reaction is equal to the sum of its partial orders in the zero order reaction.

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Previous Year Questions​

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