# Instantaneous and Average Rate of Reaction: Definition, Mathematical and Graphical Representations, Practice Problems and FAQs

There are numerous reactions occurring around us but have you ever noticed that some are occurring at a rapid rate and others at a very slow rate. Have you ever given a thought, to why water cannot be made by simply combining atmospheric oxygen with hydrogen? Well, this is not possible, as this reaction takes infinite time to occur on its own. On the other hand, lighting a gas stove is rather an easy process and this reaction occurs at a pretty rapid rate.

Now, the question is how do we measure the rate of a reaction? So, let's study the types of reactions and how we can measure them.

• Average Rate of a Reaction
• Instantaneous Rate of a Reaction
• Practice Problems

## Average Rate of a Reaction

The average rate of reaction is defined as the change in concentration over an appreciable interval of time.

Mathematical Representation of Average Rate of a Reaction

Let’s consider a reaction,

Average rate of reaction

• Average rate of disappearance of

Average rate of disappearance of

During the reaction, , the concentration of reactant decreases.

• Average rate of appearance of

Average rate of appearance of

During the reaction, , the concentration of the product increases.

It can be said that;

Average rate of reaction Average rate of disappearance of Average rate of appearance of

I.e.,

Graphical Representation of Average Rate of a Reaction

We can determine the average rate of a reaction between any two intervals by calculating the slope of the line joining those two points in a concentration time plot.

Let’s consider a reaction,

Let or and or be the concentrations of reactant or product at any time and respectively, as taken from the graph.

Plot of time

Average rate of a reaction ( = Slope of the line joining two points 1 and 2

Plot of time

Average rate of a reaction ( = Slope of the line joining two points 1 and 2

## Instantaneous Rate of a Reaction

Instantaneous rate of a reaction is defined as the change in the concentration in an infinitesimally small time interval.

Mathematical Representation of Instantaneous Rate of a Reaction

Suppose the value of the term (time interval) is very small and tends to zero. Now, we have an infinitesimally small which can be considered a particular instant of time. So, mathematically instantaneous rate of a reaction can be expressed as:

Instantaneous rate of a reaction ==

Graphical Representation of Instantaneous Rate of a Reaction

Instantaneous rate of a reaction at any point can be measured by calculating the slope of the tangent at a particular instant of time on the curve in the concentration time graph.

Plot of time

Instantaneous rate of a reaction ( = Slope of the tangent at a particular instant of time on the curve

Plot of time

Instantaneous rate of a reaction ( = Slope of the tangent at a particular instant of time on the curve

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## Practice Problems

Q 1. Calculate the average rate of reaction from the given plot

Average rate of a reaction = = =

Q 2. Calculate the instantaneous rate of reaction at , from the given equation.

Answer: The instantaneous rate of reaction can be obtained by differentiating the equation mentioned in the question with respect to . So, by differentiating we will get a slope at on the curve of concentration time graph which is basically the instantaneous rate of a reaction at

Differentiating both sides;

Instantaneous rate of reaction at would be:

Q 3. For a chemical reaction, , the correct representation of the average rate of reaction would be:

(A)

(B)

(C)

(D)

For the given reaction:

Average rate of reaction (in terms of reactants):

Average rate of reaction (in terms of products):

So, average rate of the reaction would be:

Q 4. In a reaction, the concentration of a reactant (A) changes from 0.50 to 0.10 in 2 minutes. The average rate of a reaction during this interval is:

(A)

(B)

(C)

(D)

Average rate of reaction can be calculated using below mentioned formula;

Q 1. In what ways we can determine the instantaneous rate of reaction?
Answer: The instantaneous rate of reaction can be determined by using data from experiments and then plotting a curve between concentration-time. Then by calculating the slope of the tangent on the concentration-time curve at a particular instant of time.

Q 2. How the instantaneous rate of reaction can be calculated from an average rate of reaction?

Average rate of reaction = =

Taking limit such that

=

Q 3. Why do we use in average rate and instantaneous rate?
Answer: symbol used in case of appreciable change whereas is used in case of infinitesimally small change.

Q 4. Can the rate of reaction be negative?
Answer: No, the rate of reaction cannot be negative. Because if we calculate it mathematically, concentrations cannot be negative as according to rate law expression, the rate is proportional to the concentration of the reactants.

For a reaction;

Rate of a reaction

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