Question

Balance the following equation stepwise:
${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{7}}}_{\left( {\text{l}} \right)}{\text{ + }}{{\text{H}}_{\text{2}}}{{\text{O}}_{\left( {\text{l}} \right)}} \to {{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}_{\left( {\text{l}} \right)}$

Answer 1

Hint:. Balancing equations is done by adding stoichiometric coefficients such that the total number of atoms of the products is the same as that of reactants. To balance any unbalanced chemical equation one has to check the number of atoms of all species on the reactant side as well as product side.

Complete step by step answer:
Step 1) Firstly identify and note down all the elements in the above given equation.
The given reaction is ${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{7}}}_{\left( {\text{l}} \right)}{\text{ + }}{{\text{H}}_{\text{2}}}{{\text{O}}_{\left( {\text{l}} \right)}} \to {{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}_{\left( {\text{l}} \right)}$. The elements in the reaction are Sulphur, hydrogen, oxygen.

Step 2) Now count the number of atoms of all these elements on the left hand side from the values in the subscript of the respective elements.
So on the left side i.e. reactant side there are 2 sulphur atoms, 8 oxygen atoms, 4 hydrogen atoms in total.

Step 3) Count the number of atoms of each element on the right hand side from the values on the subscript of the respective elements.
So the number of atoms on the product side is 1 sulphur atom, 4 oxygen atoms and 2 hydrogen atoms.

Step 4) Identify the difference, balance the equation and finally check the total number of elements to be the same on both sides.

The table provided below shows all the above discussed details.

ELEMENT	ATOMS ON LHS	ATOMS ON RHS
Sulphur	2	1
Hydrogen	4	2
Oxygen	8	4

From the above information atoms of all the elements are lacking by the multiple of 2. So upon multiplying the product side with 2, the balanced equation would be as given below. ${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{7}}}_{\left( {\text{l}} \right)}{\text{ + }}{{\text{H}}_{\text{2}}}{{\text{O}}_{\left( {\text{l}} \right)}} \to 2{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}_{\left( {\text{l}} \right)}$ .

Note: After listing down the numbers of atoms of all the elements identify the difference and add the atoms of respective elements on the side they are lacking. This could be done by multiplying the number the element lacks with the total compound which adds to the stoichiometric coefficient of the compound.