Question

Balance the equation $$\begin{gathered} {\mathrm{KMnO}}_4\left(\mathrm{s}\right)+\mathrm{HCl}\left(\mathrm{g}\right)\to \mathrm{KCl}\left(\mathrm{s}\right)+{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Answer 1

The reaction can be solved in two steps:

1. Complete the reaction by writing the products.
2. Balance the equation.

1. Complete the reaction by writing the products:

$$\begin{gathered} {\mathrm{KMnO}}_4\left(\mathrm{s}\right)+\mathrm{HCl}\left(\mathrm{g}\right)\to \mathrm{KCl}\left(\mathrm{s}\right)+{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

2. Balancing of the reaction by hit and trial method:

A balanced equation is a chemical reaction equation in which the overall charge and the number of atoms for each element in the reaction are the same for both the reactants and the products.

To balance the chemical equation, begin by multiplying the element or compound which has less number of atoms with a number that would make the number equal on both sides.

$$\begin{gathered} {\mathrm{KMnO}}_4\left(\mathrm{s}\right)+\mathrm{HCl}\left(\mathrm{g}\right)\to \mathrm{KCl}\left(\mathrm{s}\right)+{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Types of atoms	Number of atoms on reactant side	Number of atoms on product side
Potassium	1	1
Hydrogen	1	2
Oxygen	4	1
Manganese	1	1
Chloride	1	5

Balance the equation by multiplying water with 4 on product side as the number of oxygen atoms are less on product side.

$$\begin{gathered} {\mathrm{KMnO}}_4\left(\mathrm{s}\right)+\mathrm{HCl}\left(\mathrm{g}\right)\to \mathrm{KCl}\left(\mathrm{s}\right)+{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Types of atoms	Number of atoms on reactant side	Number of atoms on product side
Potassium	1	1
Hydrogen	1	8
Oxygen	4	4
Manganese	1	1
Chloride	1	5

As the number of atoms are still unequal on both side, multiplying hydrochloric acid with 8.

$$\begin{gathered} {\mathrm{KMnO}}_4\left(\mathrm{s}\right)+8\mathrm{HCl}\left(\mathrm{g}\right)\to \mathrm{KCl}\left(\mathrm{s}\right)+{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Types of atoms	Number of atoms on reactant side	Number of atoms on product side
Potassium	1	1
Hydrogen	8	8
Oxygen	4	4
Manganese	1	1
Chloride	8	5

As the number of atoms are still unequal on both side, multiplying potassium chloride, manganese chloride and chloride with 2.

$$\begin{gathered} {\mathrm{KMnO}}_4\left(\mathrm{s}\right)+8\mathrm{HCl}\left(\mathrm{g}\right)\to 2\mathrm{KCl}\left(\mathrm{s}\right)+2{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+2{\mathrm{Cl}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Types of atoms	Number of atoms on reactant side	Number of atoms on product side
Potassium	1	2
Hydrogen	8	8
Oxygen	4	4
Manganese	1	2
Chloride	8	10

As the number of atoms are still unequal on both side, multiplying chloride with potassium permanganate with 2.

$$\begin{gathered} 2{\mathrm{KMnO}}_4\left(\mathrm{s}\right)+8\mathrm{HCl}\left(\mathrm{g}\right)\to 2\mathrm{KCl}\left(\mathrm{s}\right)+2{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+2{\mathrm{Cl}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Types of atoms	Number of atoms on reactant side	Number of atoms on product side
Potassium	2	2
Hydrogen	8	8
Oxygen	8	4
Manganese	2	2
Chloride	8	10

Number of atoms of each element is stil not equal on both sides. Multiply water with 8 on product side.

$$\begin{gathered} 2{\mathrm{KMnO}}_4\left(\mathrm{s}\right)+8\mathrm{HCl}\left(\mathrm{g}\right)\to 2\mathrm{KCl}\left(\mathrm{s}\right)+2{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+2{\mathrm{Cl}}_2\left(\mathrm{g}\right)+8{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Types of atoms	Number of atoms on reactant side	Number of atoms on product side
Potassium	2	2
Hydrogen	8	16
Oxygen	8	8
Manganese	2	2
Chloride	8	10

To balance the above equation, multiply hydrochloric acid with 16 and chloride with 5

$$\begin{gathered} 2{\mathrm{KMnO}}_4\left(\mathrm{s}\right)+16\mathrm{HCl}\left(\mathrm{g}\right)\to 2\mathrm{KCl}\left(\mathrm{s}\right)+2{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+5{\mathrm{Cl}}_2\left(\mathrm{g}\right)+8{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$

Types of atoms	Number of atoms on reactant side	Number of atoms on product side
Potassium	2	2
Hydrogen	16	16
Oxygen	8	8
Manganese	2	2
Chloride	16	16

As the number of all the atoms is equal on both sides, the chemical equation is now balanced.

So, the overall complete and balanced chemical equation is

$$\begin{gathered} 2{\mathrm{KMnO}}_4\left(\mathrm{s}\right)+16\mathrm{HCl}\left(\mathrm{g}\right)\to 2\mathrm{KCl}\left(\mathrm{s}\right)+2{\mathrm{MnCl}}_2\left(\mathrm{s}\right)+5{\mathrm{Cl}}_2\left(\mathrm{g}\right)+8{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right) \\ (\mathrm{potassium}(\mathrm{hydrochloride}(\mathrm{potassium}(\mathrm{manganese}\left(\mathrm{chloride}\right)\left(\mathrm{water}\right) \\ \mathrm{per}\mathrm{mangante})\mathrm{acid})\mathrm{chloride})\mathrm{II}\mathrm{chloride}) \end{gathered}$$