Balancing Chemical Equations: Methods, Steps, Examples

What are reactants?

• Reactants are substances or compounds that undergo a chemical change in a chemical reaction.
• Reactants are present on the left side of the arrow, indicating the progression of a chemical reaction.
• The number of reactants in a chemical equation might differ in different reactions. In some reactions, a single reactant can give rise to one or more products whereas, in others, two or more reactants might be present.
• Depending on the chemical reaction, the same compound or substance can act as either reactant or product.
• Some reactants are highly reactive and can undergo chemical change without any catalyst, whereas others might require catalysts and specific reaction conditions.

What are products?

• Products are substances or compounds that are formed from reactants after the chemical reaction.
• Products are written on the right side of the arrow, indicating the progression of the chemical reactions from reactants to products.
• Like reactants, the number of products formed from the same reactants might differ in different reactions on the basis of the presence of catalysts and reaction conditions.
• In reversible reactions, the products can act as reactants when the chemical reaction is reversed.
• The number and concentration of products formed depend on the reactivity of the reactant compounds.

What are Coefficients?

• Coefficient or stoichiometric coefficient is the total number of molecules of a chemical substance that takes part in a chemical reaction.
• Stoichiometric coefficients are assigned to different chemical species in order to balance the total number of atoms of reactants and products.
• These coefficients provide a ration between the number of reactant species and products in a chemical reaction.
• Stoichiometric coefficients are also important in determining the total number of atoms of an element involved in the chemical reaction. 
• The value of the stoichiometric coefficient in different molecules involved in the reaction might change in order to balance the equation.  

What are Subscripts?

• Subscripts are values that indicate the number of atoms of elements present in the molecules of reactants and products.
• A subscript reflects the contribution of elements in different molecules and is present below the elemental abbreviations. Subscripts are written under the type line and are typically smaller in size.
• While balancing a chemical equation, the value of subscripts remains unchanged, but the total number of atoms in the molecule has to be obtained by multiplying the value of subscript with the stoichiometric coefficient of the particular molecule.

What is the law of conservation of mass?

• The law of conservation of mass states that in a chemical reaction, the reactants react with one another to give the products, but the total mass of the reactants before the chemical change is equal to the total mass of the products after the chemical change.
• In other words, the law of conservation of mass indicates that the total mass of chemical species during a chemical reaction remains conserved.
• The law of conservation of mass is equivalent to the law of conservation of energy. It determines the mathematical relationship between the mass of the reactants and the mass of the products.
• The law was put forward by the French chemist Lavoisier in 1774 after the understanding that mass can neither be created nor be destroyed.
• The law is in accordance with Dalton’s atomic theory which states that atoms can neither be created nor be destroyed and rearrangement of atoms takes place during the reaction. As a result, the total mass of the chemical species in a reaction remains conserved.

Methods of Balancing a Chemical Equation

A balanced chemical equation is essential to obtain meaningful information about the chemical change occurring in the reaction. There are two different methods of balancing a chemical equation.

A. Hit and trial method

The hit and trial method is a simple method with no specified rules or guidelines. But the following steps can be performed while balancing a chemical equation with the hit and trial method;

1. All elementary gases are written in atomic forms while the rest of the chemical species are written in their molecular form.
2. The total number of atoms of each element on reactants and products is compared.
3. The compound with the largest number of atoms is selected, and balancing is begun with individual atoms.
4. If the above method fails, the molecule with the smallest number of atoms is selected and balanced.
5. While balancing the stoichiometric coefficient should be multiplied with the subscript to determine the actual number of atoms in the molecule.
6. The previous step is repeated until the number of different atoms in the reactants and products is equal.
7. Elementary gases are balanced at the end.

Example of balancing a chemical equation by hit and trial method

Mg₃N₂ + H₂O         →            Mg(OH)₂ + NH₃

i. To balance the Mg atoms, Mg(OH)₂ is multiplied by 3.

Mg₃N₂ + H₂O         →           3Mg(OH)₂ + NH₃

ii. To balance the N atom, NH₃ is multiplied by 2.

Mg₃N₂ + H₂O         →          3Mg(OH)₂ + 2NH₃

iii. To balance the H and O atoms, H₂O is multiplied by 6.

Mg₃N₂ + 6H₂O          →        3Mg(OH)₂ + 2NH₃

B. Algebraic Method

The algebraic method involves the assignment of algebraic variables as stoichiometric coefficients to each of the chemical species involved in the reaction. The algebraic variables are solved to obtain the values of each of the stoichiometric coefficients. The following are the steps of balancing a chemical equation by the algebraic method;

1. The unbalanced chemical equation is written in the form of molecular formulas of the chemical species involved.
2. Algebraic variables are assigned to each of the species as the stoichiometric coefficient in the unbalanced equation.
3. Now, a set of equations are prepared in order to obtain the value of each of the algebraic variables.
4.  These equations can have multiple solutions, and the minimum values of the variables are to be selected.
5. The values of all the algebraic variables are substituted into the chemical equation to obtain the balanced chemical equation.

Example of balancing chemical equation by the algebraic method

C₆H₁₂O₆ + O₂          →          CO₂ + H₂O

i. Algebraic variables are added as the stoichiometric coefficient to each of the chemical species in the chemical equation.

aC₆H₁₂O₆ + bO₂           →          cCO₂ + dH₂O

ii. Different equations are generated for all the variables based on the chemical reaction.

Equation for ‘a’

• In the reactant, ‘a’ molecules of C₆H₁₂O₆ contain 6a carbon atoms and in the product, ‘c’ molecules of CO₂ contain ‘c’ carbon atoms; 6a=c.

Equation for ‘b’

• In the reactant, ‘a’ molecules of C₆H₁₂O₆ contains 12a hydrogen atoms, whereas in the product, ‘d’ H₂O molecules contain ‘2d’ hydrogen atoms; 12a = 2d.

iii. The overall equation for the algebraic variables is then obtained by analyzing different equations.

6a + 2b = 2c + d

iv. Since the minimal values of the variables are to be calculated, one of the variables is assigned a value.

If a=1, 

c= 2a = 6

d= 6a= 6

The value of ‘b’ can be obtained by substituting the values of a, c and d in the equation;

6×1 + 2b = 2×6 + 6

2b= 12; b=6.

v. The values of the variables are substituted in the chemical equation to obtain the balanced chemical equation.

C₆H₁₂O₆ + 6O₂          →          6CO₂ + 6H₂O

References and Sources

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