Balancing Chemical Equation Formula

A Balancing Chemical Equation is a concise representation of the components of a chemical reaction, symbolically shown with the reactants on the left and the products on the right. On an everyday basis, we can observe various chemical reactions taking place. These involve rearranging matter to create something new or different. Balancing such equations necessitates adding stoichiometric coefficients to both reactants and products to obey the law of constant proportions and the law of conservation of mass – i.e. so that equal numbers of atoms for every element appear on both sides of the equation. Two main methods are used for this purpose: traditional balancing equations and algebraic balancing.

Follow these four simple steps to balance a chemical equation:

• Write the imbalanced equation to show the reactants and products.
• Calculate the number of atoms of each element on each side of the reaction arrow.
• Multiply coefficients (the numbers in front of the formulas) to make the number of atoms of each element the same.
• Last to balance are the hydrogen and oxygen atoms.
• You should indicate the state of matter of the reactants and products in your work.

Chemical Equation

Chemical equations represent chemical reactions by denoting their respective chemical formulas as reactants and products.

In chemistry, 2H2 + O2→ 2H2O represents the reaction between hydrogen and oxygen to produce water.

Chemical equations have reactant and product sides. The reactant side is to the left of the arrow symbol, and the product side is to the right.

Also Check – Value of Gas Constant

Stoichiometric Coefficient

Stoichiometric coefficients describe how many molecules of a chemical species participate in a reaction.

• A ratio is provided between the reacting species and their products.
• In the reaction described by the CH4 + 2O2 → CO2 + 2H2O reaction, the stoichiometric coefficient of O2 and H2O  is 2. At the same time, that of CH4 and CO2 is 1.
• A balanced chemical equation has the number of atoms of an element in a species equal to the product of the stoichiometric coefficient and the number of atoms in one molecule.
• The reacting species ‘2O2‘ has four oxygen atoms in total.
• The stoichiometric coefficients are assigned in a manner that balances the total number of atoms of an element on both sides of the reaction.

Also Check – Lead (II) Chloride Formula

The Traditional Balancing Chemical Equation

This method is illustrated using the combustion reaction between propane and oxygen. To balance chemical equations, the first step is to obtain the complete unbalanced equation.

Step – 1 

• Chemical formulae of the reactants and products (if not already provided) must be used to obtain the unbalanced equation.
• As propane burns with oxygen (O2), it produces carbon dioxide (CO2) and water (H2O).
• An unbalanced chemical equation can be written as C3H8 + O2 → CO2+ H2O

Step 2

In this example, the number of atoms on each side of the reaction can be tabulated as follows.

Step 3

• Stoichiometric coefficients are now added to molecules containing an element with a different number of atoms on the reactant and product sides.
• There must be a balance between the number of atoms on each side of the coefficient.
• The stoichiometric coefficients are usually assigned to hydrogen and oxygen atoms last.
• The number of atoms must now be updated on the reactant and product sides.
• To calculate the number of atoms in a species, multiply the stoichiometric coefficient by the total number of atoms in 1 molecule of that species.
• When the coefficient 3 is assigned to CO2, the total number of oxygen atoms in CO2 becomes 6. In this example, the coefficient is first assigned to carbon.

Step 4 

The chemical equation is transformed by repeating Step 3 until all the atoms of the reacting elements are equal on both sides. In this example, hydrogen is balanced next.

After the hydrogen atoms have been balanced, the next element is oxygen. The product side contains 10 oxygen atoms, implying that the reactant side must also contain 10. The O2 molecule contains two oxygen atoms. As a result, the stoichiometric coefficient for the O2 molecule is 5. The updated chemical equation can be found below.

Step 5 

The total number of atoms of each element on the reactant and product sides are compared again when all the elements have been balanced. 

When there are no inequalities in the chemical equation, it is said to be balanced. As a result, every element in this example has an equal number of atoms in the reactant and product sides. Therefore, the chemical equation that balances is C3H8 + 5O2 → 3CO2 + 4H2O.

Also Check – Iron (III) Hydroxide Formula

The Algebraic Balancing Method

Using this method, each species in an unbalanced chemical equation receives a stoichiometric coefficient determined by algebraic variables. These variables are used in mathematical equations and solved to obtain each stoichiometric coefficient’s values. An example of how this method works is the reaction between glucose and oxygen that produces carbon dioxide and water.

Step 1

• The chemical formulas of the reactants and products must be written down to obtain the unbalanced chemical equation.
• The reactants in this example are glucose (C6H12O6) and oxygen (O2), and the products are carbon dioxide (CO2) and water (H2O).
• Unbalanced chemical equation: C6H12O6 + O2 → CO2 + H2O

Step 2 

In the unbalanced chemical equation, algebraic variables are assigned to each species (as stoichiometric coefficients).

The formula for water is A6C12O6 + bO2 → cCO2 + dH2O

To balance each element in the reaction, a set of equations must be formulated (between the reactant and product sides). The following equations can be used as an example.

The equation for Carbon

• ‘A’ molecules of C6H12O6 contain ‘6a’ carbon atoms on the reactant side.
• ‘C’ molecules of CO2 contain ‘c’ carbon atoms on the product side.
• C6H12O6 and CO2 are the only species containing carbon in this equation.

Therefore, carbon can be expressed as 6a = c.

The equation for Hydrogen

• C6H12O6 and H2 are the species containing hydrogen in this equation,
• C6H12O6 molecules contain 12a hydrogen atoms, whereas H2O molecules contain 2d hydrogen atoms.
• As a result, 12a = 2d becomes the equation for hydrogen.
• By dividing both sides by 2, the equation becomes: 6a = d

The equation for Oxygen

There is oxygen in every species in this chemical equation. Therefore, the equation for oxygen can be derived from the following relationships:

‘A’ are six oxygen atoms in a molecule of C6H12O6.

‘B’ molecules of O2 contain a total of ‘2b’ oxygen atoms.

‘C’ molecules of CO2 contain ‘2c’ oxygen atoms.

‘d’ molecules of H2O contain ‘d’ oxygen atoms.

As a result, oxygen’s equation is: 6a + 2b = 2c+ d

Step 3

The equations for each element are listed together to form a system of equations. In this example, the system of equations is as follows:

6a = c (for carbon); 6a = d (for hydrogen); 6a + 2b = 2c + d (for oxygen)

This system of equations can have multiple solutions, but the solution with minimal values of the variables is required. Obtaining this solution requires assigning a value to one of the coefficients. The system of equations is transformed as follows by assuming that a = 1.

a = 1

c = 6a = 6*1 = 6

d = 6a = 6

Substituting the values of a,c, and d in the equation 6a + 2b = 2c + d, the value of ‘b’ can be obtained as follows:

6*1 + 2b = 2*6 + 6

2b = 12; b = 6

It is important to note that these equations must be solved in a manner that makes each variable a positive integer. To obtain fractional values, multiply each variable by the lowest common denominator of all the variables. The variables contain stoichiometric coefficients, which are positive integers, so this is necessary.

Step 4

After obtaining the smallest value of each variable, their values can be substituted into the chemical equation obtained in step 2.

In other words, aC6H12O6 + bO2 → cCO2 + dH2O C6H12O6 + 6O2 → 6CO2 + 6H2O

While algebraic methods are considered to be more efficient, they can yield fractional values for the stoichiometric coefficients, which must then be converted to integers.