Rate of a Chemical Reaction: Meaning, and Calculations

The rate of chemical reaction refers to how quickly the products are generated from the reactants. It provides some insight into how quickly a reply can be performed. The reaction rate of cellulose combustion in fire, for example, is extremely high, and the reaction is finished in less than a second.

A vehicle’s speed is measured in terms of distance travelled per unit time. Some chemical reactions, like the reaction of sodium with water, are very fast. In contrast, some chemical reactions like rusting of iron are very slow. To express the speed of a chemical reaction, we use the term rate of a chemical reaction.

Rate of a Reaction

The rate of a chemical reaction means the speed with which the reactants change into products. The rate of reaction is the change in the concentration of any reactants or products per unit time. It can be expressed in terms of a decrease in the concentration of any of the reactants per unit time or an increase in the concentration of any products per unit time.

For a hypothetical reaction \({\rm{R}} \to {\rm{P}}\)
\({\rm{Rate}}\,{\rm{of}}\,{\rm{reaction}} = \frac{{{\rm{Decrease}}\,{\rm{in}}\,{\rm{the}}\,{\rm{concentration}}\,{\rm{of}}\,{\rm{a}}\,{\rm{reactant}}\,{\rm{R}}}}{{{\rm{Time}}\,{\rm{taken}}\,{\rm{for}}\,{\rm{the}}\,{\rm{change}}}} = – \frac{{\Delta \left[ {\rm{R}} \right]}}{{\Delta {\rm{t}}}}\)
Or \({\rm{Rate}}\,{\rm{of}}\,{\rm{reaction}} = \frac{{{\rm{Increase}}\,{\rm{in}}\,{\rm{the}}\,{\rm{concentration}}\,{\rm{of}}\,{\rm{a}}\,{\rm{product}}\,{\rm{P}}}}{{{\rm{Time}}\,{\rm{taken}}\,{\rm{for}}\,{\rm{the}}\,{\rm{change}}}} = + \frac{{\Delta \left[ {\rm{P}} \right]}}{{\Delta {\rm{t}}}}\)

Where \({\Delta \left[ {\rm{R}} \right]}\) is the change in the molar concentration of a reactant at time intervals \({{\rm{t}}_1}\) and \({{\rm{t}}_2}.\)
\(\Delta \left[ {\rm{R}} \right] = {{\rm{R}}_2} – {{\rm{R}}_1}\)
\(\Delta \left[ {\rm{P}} \right]\) is the change in the molar concentration of product at time intervals \({{\rm{t}}_1}\) and \({{\rm{t}}_2}.\)
\(\Delta \left[ {\rm{P}} \right] = {{\rm{P}}_2} – {{\rm{P}}_1}\)
And \(\Delta {\rm{t}}\) is the change in the time interval, \(\Delta {\rm{t}} = {{\rm{t}}_2} – {{\rm{t}}_1}\)

As the concentration of reactant decreases, a negative sign is used to express the rate of reaction in terms of reactant. As the concentration of the product increases, a positive sign is used in terms of products.
For example, \({\rm{PC}}{{\rm{l}}_5} \to {\rm{PC}}{{\rm{l}}_3} + {\rm{C}}{{\rm{l}}_2}\)
Rate of reaction \({\rm{ = }}\frac{{\Delta \left[ {{\rm{PC}}{{\rm{l}}_5}} \right]}}{{\Delta {\rm{t}}}}{\rm{ = + }}\frac{{\Delta \left[ {{\rm{PC}}{{\rm{l}}_3}} \right]}}{{\Delta {\rm{t}}}} = + \frac{{\Delta \left[ {{\rm{C}}{{\rm{l}}_2}} \right]}}{{\Delta {\rm{t}}}}\)

Average Rate of Reaction

The rate of reaction does not remain constant throughout the reaction. Hence, the rate of a reaction is defined in terms of the average rate of reaction during the time interval. The change in concentration of any of the reactants or any of the product per unit time over a specified interval of time is called the average rate of reaction.

Average rate of reaction \(\left( {{{\rm{r}}_{{\rm{av}}}}} \right) = – \frac{{\Delta \left[ {\rm{R}} \right]}}{{\Delta {\rm{t}}}} = + \frac{{\Delta \left[ {\rm{P}} \right]}}{{\Delta {\rm{t}}}}\)
In general, \({{\rm{r}}_{{\rm{av}}}} = \frac{{\Delta {\rm{x}}}}{{\Delta {\rm{t}}}}\)

Instantaneous Rate of Reaction

The rate of reaction at any instant of time during the reaction is defined in terms of the instantaneous rate of reaction. The rate of change of concentration of any one of the reactants or products at a particular instant of time is called the instantaneous rate of reaction.

Instantaneous rate of reaction, \({{\rm{r}}_{{\rm{inst}}}} = \frac{{{\rm{dx}}}}{{{\rm{dt}}}}\)
Where \({{\rm{dx}}}\) is the small change in the concentration and \({{\rm{dt}}}\) is the small interval of time.
Example: For the reaction \({{\rm{N}}_2} + 3\,{{\rm{H}}_2} \to 2\,{\rm{N}}{{\rm{H}}_3}\)
Rate of reaction \( = – \frac{{{\rm{d}}\left[ {{{\rm{N}}_2}} \right]}}{{{\rm{dt}}}} = – \frac{1}{3}\frac{{{\rm{d}}\left[ {{{\rm{H}}_2}} \right]}}{{{\rm{dt}}}} = + \frac{1}{2}\frac{{{\rm{d}}\left[ {{\rm{N}}{{\rm{H}}_3}} \right]}}{{{\rm{dt}}}}\)
To make the different expressions for the rate to be equivalent, the rate expressions are divided by the stoichiometric coefficient present in the balanced chemical equation.

Units of Rate of Reaction

Concentrations of reactants and products are usually expressed in moles per liter, and time is usually expressed in seconds or minutes. Therefore, the units of the rate of reactions are \({\rm{mol}}\,{{\rm{L}}^{ – 1}}{{\rm{S}}^{ – 1}}\) or \({\rm{mol}}\,{{\rm{L}}^{ – 1}}{\min ^{ – 1}}.\)

When the reactants and products are in the gaseous state, their concentrations are expressed in terms of their partial pressure in atmospheres. Then the unit of rate of reaction is \({\rm{atm}}\,{{\rm{S}}^{ – 1}}\) or \({\rm{atm}}\,{\min ^{ – 1}}.\)

Factors Affecting Rate of Chemical Reactions

The rate of a chemical reaction depends upon several factors like the nature of the reactant, the concentration of the reactants, temperature, presence of a catalyst, the surface area of the reactant, radiation, etc.

Nature of Reactant

The rate of a chemical reaction depends upon the amount of energy required to break different bonds, and different amounts of energy are released in the formation of different bonds.

The reactions involving ionic or polar substances are very fast because of the electrostatic force between the molecules and are easily broken in an aqueous solution.

Example: The oxidation of nitric oxide to nitrogen peroxide is very fast as compared to the oxidation of carbon monoxide to carbon dioxide, although the two reactions appear to be similar.
\(2\,{\rm{NO}}\left( {\rm{g}} \right) + {{\rm{O}}_2} \to 2\,{\rm{N}}{{\rm{O}}_2} – – – – > \left( {{\rm{fast}}} \right)\)
\(2\,{\rm{CO}}\left( {\rm{g}} \right) + {{\rm{O}}_2} \to 2\,{\rm{C}}{{\rm{O}}_2} – – – – > \left( {{\rm{slow}}} \right)\)

Concentration of Reactants

In general, the rate of a reaction increases by increasing the concentration of the reactants and vice versa. When the concentration of a reactant is increased, the possibility of molecular collisions increases. Therefore, the rate of reaction increases.

Temperature

The temperature has a significant effect on the rate of reaction. In most cases, the rate of reaction becomes nearly doubled for a \({10^{\rm{o}}}\) rise in temperature.

Catalyst

A catalyst is a substance that increases the rate of reaction and remains unchanged in amount and chemical composition at the end of a reaction. The catalyst forms an activated complex with the reactants at lower potential energy. Hence the activation energy of the reaction decreases, and the rate of reaction increases.

Surface Area

For a reaction involving a solid reactant or a catalyst, the smaller is the particle size, i.e., the greater is the surface area, the faster is the reaction. Finely divided solid reactants possess a large surface area as compared to massive reactants and react much faster.
Example: Powdered coal burns much faster as compared to a lump of coal.

Radiation

Some reactions take place only in the presence of light. Such reactions are called photochemical reactions. The absorption of quantum energy of light facilitates the breaking of bonds of the reactants. As the intensity of light increases, the rate of reaction also increases.

Solved Numerical

Q.1. The reaction, \(2\,{{\rm{N}}_2}{{\rm{O}}_5}\left( {\rm{g}} \right) \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\leftharpoonup\over {\smash{\rightharpoondown}}$}} 4\,{\rm{N}}{{\rm{O}}_2}\left( {\rm{g}} \right) + {{\rm{O}}_2}\left( {\rm{g}} \right)\) was studied in a closed vessel. It was found that the concentration of \({\rm{N}}{{\rm{O}}_2}\) increases by \(2.0 \times {10^{ – 2}}\,{\rm{mol}}\,{{\rm{L}}^{ – 1}}\) in five seconds. Calculate (i) the rate of reaction (ii) the rate of change of concentration of \({{\rm{N}}_2}{{\rm{O}}_5}.\)
Ans: (i) Rate of reaction\( = \frac{1}{4}\frac{{{\rm{d}}\left[ {{\rm{N}}{{\rm{O}}_2}} \right]}}{{{\rm{dt}}}}\)
Rate of reaction\( = \frac{1}{4} \times \frac{{2.0 \times {{10}^{ – 2}}\,{\rm{mol}}\,{{\rm{L}}^{ – 1}}}}{{5\,{\rm{s}}}}\)
Rate of reaction\( = \frac{1}{4} \times 4 \times {10^{ – 3}}\,{\rm{mol}}\,{{\rm{L}}^{ – 1}}{{\rm{S}}^{ – 1}}\)
Rate of reaction\( = {10^{ – 3}}\,{\rm{mol}}\,{{\rm{L}}^{ – 1}}{{\rm{S}}^{ – 1}}\)
(ii) Rate of change of conc. of \({{\rm{N}}_2}{{\rm{O}}_5} = – \frac{{{\rm{d}}\left[ {{{\rm{N}}_2}{{\rm{O}}_5}} \right]}}{{{\rm{dt}}}} = – \frac{1}{2} \times {\rm{Rate}}\,{\rm{of}}\,{\rm{formation}}\,{\rm{of}}\,{\rm{N}}{{\rm{O}}_2}\)
Rate of change of conc. of \({{\rm{N}}_2}{{\rm{O}}_5} = – \frac{1}{2} \times 4 \times {10^{ – 3}}\,{\rm{mol}}\,{{\rm{L}}^{ – 1}}{{\rm{S}}^{ – 1}}\)
Rate of change of conc. of \({{\rm{N}}_2}{{\rm{O}}_5} = – 2 \times {10^{ – 3}}\,{\rm{mol}}\,{{\rm{L}}^{ – 1}}{{\rm{S}}^{ – 1}}\)

Summary

In this article, you have been inspired with information on the rate of reaction, its meaning, units, calculation, factors affecting it, etc. This will become a base for all further chemical kinetics studies in detail.

FAQs

Q. 1. How do you calculate the rate of a chemical reaction?
Ans: The rate of a chemical reaction is calculated in terms of a decrease in the concentration of any of the reactants per unit time or an increase in the concentration of any of the products per unit time.
\({\rm{Rate}}\,{\rm{of}}\,{\rm{reaction}} = \frac{{{\rm{Decrease}}\,{\rm{in}}\,{\rm{the}}\,{\rm{concentration}}\,{\rm{of}}\,{\rm{a}}\,{\rm{reactant}}\,{\rm{R}}}}{{{\rm{Time}}\,{\rm{taken}}\,{\rm{for}}\,{\rm{the}}\,{\rm{change}}}} = – \frac{{\Delta \left[ {\rm{R}} \right]}}{{\Delta {\rm{t}}}}\)
\({\rm{Rate}}\,{\rm{of}}\,{\rm{reaction}} = \frac{{{\rm{Increase}}\,{\rm{in}}\,{\rm{the}}\,{\rm{concentration}}\,{\rm{of}}\,{\rm{a}}\,{\rm{product}}\,{\rm{P}}}}{{{\rm{Time}}\,{\rm{taken}}\,{\rm{for}}\,{\rm{the}}\,{\rm{change}}}} = + \frac{{\Delta \left[ {\rm{P}} \right]}}{{\Delta {\rm{t}}}}\)

Q.2. Which will increase the rate of a chemical reaction?
Ans: The rate of a chemical reaction increases with an increase in temperature, concentration, the surface area of the reactant.

Q.3. What is the rate of reaction in science?
Ans: The rate of a chemical reaction means the speed with which the reactants change into products. The rate of reaction is the change in the concentration of any one of the reactants or products per unit time.

Q.4. Why is the rate of a chemical reaction important?
Ans: The rate of the chemical reaction is important to determine the speed of the reaction and to alter the reaction by changing temperature, concentration, etc., to obtain the product at a suitable rate.

Q.5. What are five factors that affect the rate of a chemical reaction?
Ans: The five factors that affect the rate of a chemical reaction are the nature of the reactant, the concentration of the reactants, temperature, presence of a catalyst, and surface area of the reactant. 

Q.6. What determines the rate of reaction?
Ans: The nature of reactant, concentration and surface area of the reactants, temperature, presence of catalyst determines the rate of reaction.

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