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# Rate of Reaction : Definition with Solved Examples

Nov 25, 2022

Chemistry is mostly about the chemical reaction rate of reaction. Some reactions complete slowly, while others are fast. For instance, iron combines with oxygen in the presence of moist air. It gets rust, and it is a slow reaction. When a piece of phosphorus is exposed to air, it bursts into flame. It is a spontaneous or fast reaction.

Therefore, chemical reactions are said to proceed at different rates. Various factors and causes lead to the change in the rate of every reaction.

## What is the Rate of Reaction?

Just like automobiles run at different speeds, chemical reactions occur at different speeds. The speed of an automobile is expressed in terms of change in the position or distance covered by it in a certain duration. Similarly, the speed or the rate of a reaction can be defined as the change in concentration of a reactant or product in a unit of time.

It defines how fast the reaction is going. It is calculated by finding the change in a measurable property of a reactant or a product, directly or indirectly, with time.

For several reactants and products in a reaction, the rate related to each compound is calculated using the coefficients in a balanced chemical equation. Once the rate is determined for different concentrations of reactants and temperatures, the rate law lets us evaluate the reaction order, rate constant, activation energy, etc., factors.

### Definition for Rate of Reaction

During a chemical reaction, reactants are reshaped into products. The rate of reaction defines how fast or slow the reaction occurs by indicating how much of a reactant is consumed or how much of a product is formed in a given time.

Simply put, the rate of reaction definition is the speed with which the reaction takes place. Therefore, it is defined as the change in concentration (number of moles per litre) of product or reactant per unit of time.

Mathematically,

Rate of chemical reaction = Change in concentration of a reactant or product / Time taken for the change

When a reaction commences, the concentration of reactant(s) starts decreasing while the concentration of product(s) starts appearing or increasing.

Thus, for a hypothetical reaction,

1. R → P, Rate of chemical reaction = Decrease in concentration of a reactant, R / Time interval

or Rate of chemical reaction = Increase in concentration of a product, P / Time interval

Thus, for time t1, if [P1] and [R1] represent the molar concentrations of the P and R, respectively, and for time t2, [P2] and [R2] are their concentrations, then,

time interval, Δt = t2 – t

Δ[R] = [R2] – [R1]

Δ[P] = [P2] – [P1]

The rate of reaction in terms of reactant or product will be,

Rate of reaction = – Δ[R]/Δt = + Δ[P]/Δt

1. For a reaction,

A + B → C + D

The rate of reaction in terms of reactants will be,

Rate of reaction = – Δ[A]/Δt = – Δ[B]/Δt

And in terms of products will be,

Rate of reaction = + Δ[C]/Δt = + Δ[D]/Δt

### Rate of Reaction Formula

d[Z]/dt, –d[A]/dt, –d[B]/dt, dz/dt, −da/dt, −db/dt

where t is the current time, [A], [B], and [Z] are the substance concentrations, and [a], [b], and [z] are the substance quantities.

### Solved Examples of the Rate of Reaction

Let’s understand how to calculate the rate of reaction for different reactions with the help of some solved examples.

Example 1: Write the expression for the rate of reaction in terms of products and reactants for the following reaction:

PCl5 → PCl3 + Cl2

Answer: Here, the reactant is PCl5, and the products are PCl3 and Cl2.

Hence, the expressions for the rate of reaction are,

Rate of reaction = – Δ[PCl₅]/Δt = + Δ[PCl₃]/Δt = + Δ[Cl₂]/Δt

Example 2: Write the expression for the rate of reaction in terms of products and reactants for the following reaction:

H₂ + I₂ ⇌ 2HI

Answer: Here, the reactants are H₂and I₂, and the product is 2HI.

Therefore, the rate of reaction = – d[H₂]/dt = – d[I₂]/dt = + 1/2 d[HI]/dt

Example 3: For the reaction,

4NH3 + 5O2 → 4NO + 6H2O,

suppose the rate expression in terms of disappearance of NH3 is – d[NH₃]/dt. Write the rate expression in terms of concentrations of O₂ and H₂O.

Answer: According to the rate of reaction,

d[NH₃]/dt = – d[O₂]dt = + d[H₂O]dt

Now, putting stoichiometry values of reactants and products,

14 d[NH₃]dt = – 1/5  d[O₂]/dt = + 1/6 d[H₂O]/dt

Hence,

Rate of reaction in terms of concentration of O₂ = – 4/5 d[O₂]/dt.

Rate of reaction in terms of concentration of H₂O = + 4/6 d[H₂O]/dt.

## What is the Rate of Reaction Unit?

As concentration is usually expressed as moles/ litre, and the time is taken in seconds or minutes,

The unit of the rate of reaction is moles litre-1 sec-1 or mol L-1 s-1.

In terms of minutes,

The unit of rate of reaction will be moles litre-1 minute-1 or mol L-1 min-1.

### Factors that Affect Rate

The rate of any specific reaction depends upon the factors given below:

#### Nature of the reactants:

The rate of reaction will differ for different reactions, whether the stoichiometry in two reactions is the same or different. It is because different amounts of energy are required to break different bonds. Similarly, different amounts of energy are required to form different bonds.

For example,

2NO + O2 → 2NO2

2CO + O2 → 2CO2

Both reactions have equal stoichiometry. But the rate of reaction is different for both of them.

#### The concentration of the reactants:

The reaction rate is directly equivalent to the concentrations of products or reactants. Therefore, the greater the concentrations of the reactants, the faster the reaction. Similarly, the slower the concentrations of the reactants, the slower the reaction rate.

#### Temperature:

As the reaction’s temperature increases, the collision between the reactant molecules increases. Thus, the rate of product formation increases. Hence, the rate of reaction increases with the increase in temperature.

Generally, the reaction rate becomes nearly double for a 10° rise in temperature. In some cases, reactions do not occur at room temperature but at a higher temperature.

#### Presence of catalyst:

Catalysts are those substances that adapt to the rate of chemical reactions without experiencing any gross chemical change. They are used to increase the rate of product formation in a chemical reaction. So, a catalyst generally increases the speed of a reaction itself being consumed in the reaction.

In reversible reactions, a catalyst aids in attaining equilibrium in the reaction quickly without deranging the state of equilibrium of the reaction.

#### The surface area of the reactants:

The larger the surface area for the reactants, the faster the reaction. It is because reactant molecules get scattered in a larger area, giving them more opportunities to collide, resulting in different product formations.

#### Presence of light:

Reactions like photosynthesis and photography both do not take place in the dark. Such reactions need sunlight to form the products. Hence, these reactions are termed ‘photochemical reactions.’

You have experienced in your daily life that when a coloured cloth is dried in sunlight, it gradually fades. It is because the cloth dyes undergo a chemical change and fade gradually. Similarly, plants prepare their food only in the presence of sunlight. These are all examples of light-sensitive reactions.

##### Summary

The reaction rate is the ratio of change in concentration to the time interval. It is expressed in terms of any reactant or product. When the attention of the reactant diminishes, a negative sign is used to convey the reaction rate concerning reactants. At the same time, a positive sign is used to convey the rate of reaction regarding products.

The rate expressions are divided by the stoichiometric coefficients present in the balanced chemical equation to make the different expressions for the rate to be equivalent.

### Q1. What is the average rate of reaction?

Answer: As per the Law of Mass Action, the reaction rate depends upon the molar concentrations of reactants, which keep decreasing with time. At the same time, it keeps on increasing in the case of products. Therefore, the rate of reaction does not remain constant throughout. It is defined as the ‘average rate of reaction’ during the time interval chosen.

Mathematically,

Average rate of reaction, rav = – Δ[R]/Δt = + Δ[P]/Δt

In general,

rav= Δx/Δt

### Q2. What is the instantaneous rate of reaction?

Answer: The rate of change in the concentration of any reactants or products at that particular time is known as an instantaneous rate of reaction.

If dc is the change in concentration in a very small time interval dt, then the rate of reaction at that instant is given by dc/dc. Thus,

Instantaneous rate, rinst = dc/dt

For example, for a reaction R → P,

rinst = – Δ[R]/Δt = + Δ[P]/Δt

In fact,

rinst = – Δ[R]/Δt = + Δ[P]/Δt, as Δt → 0

### Q3. What is the rate of reaction at any instant in time?

Answer: The rate of reaction at any instant in time is equal to the slope of the tangent to the curve between the concentration of any reactant or product versus time at that instant in time.

### Q4. What is the unit of rate of reaction when reactants are gaseous?

Answer: In the cases of gaseous reactants, pressures are used in place of concentrations. The unit of pressure is the atmosphere. Therefore, the units of the rate of reactions will be atm min-1 or atm s-1, etc.

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