Balance the equation: ${\mathrm{Na}}_2{\mathrm{CO}}_3+\mathrm{HCl}\to \mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

Step 1: Given equation

${\mathrm{Na}}_2{\mathrm{CO}}_3+\mathrm{HCl}\to \mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

Step 2: Method used for balancing the equation

Using the traditional method of balancing chemical equations. According to the method:

• First, compare the total number of atoms of each element on the reactant side and the product side.
• Add stoichiometric coefficients to molecules containing an element that has a different number of atoms on the reactant side and the product side.
• The coefficient must balance the number of atoms on each side.
• Usually, the stoichiometric coefficients for hydrogen and oxygen atoms are assigned last.
• The number of atoms of an element in one species must be obtained by multiplying the stoichiometric coefficient by the total number of atoms of that element present in 1 molecule of the species.
• Repeat this process till the number of all the atoms of the reacting elements are equal on both the reactant and product sides.

Step 3: Balancing the given equation

The given equation is: ${\mathrm{Na}}_2{\mathrm{CO}}_3+\mathrm{HCl}\to \mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

Equation: ${\mathrm{Na}}_2{\mathrm{CO}}_3+\mathrm{HCl}\to \mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$
Reactant Side	Product Side
2 Sodium atoms	1 Sodium atom
1 Carbon atom	1 Carbon atom
3 Oxygen atoms	3 Oxygen atoms
1 Hydrogen atom	2 Hydrogen atoms
1 Chlorine atom	1 Chlorine atom

First, the sodium atoms are balanced. After balancing the equation becomes: ${\mathrm{Na}}_2{\mathrm{CO}}_3+\mathrm{HCl}\to 2\mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

The carbon atoms and oxygen atoms are already balanced.

Finally, the hydrogen atoms are balanced. After balancing the equation becomes: ${\mathrm{Na}}_2{\mathrm{CO}}_3+2\mathrm{HCl}\to 2\mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

The updated equation is: ${\mathrm{Na}}_2{\mathrm{CO}}_3+2\mathrm{HCl}\to 2\mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

Equation: ${\mathrm{Na}}_2{\mathrm{CO}}_3+2\mathrm{HCl}\to 2\mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$
Reactant Side	Product Side
2 Sodium atoms	2 Sodium atoms
1 Carbon atom	1 Carbon atom
3 Oxygen atoms	3 Oxygen atoms
2 Hydrogen atoms	2 Hydrogen atoms
2 Chlorine atoms	2 Chlorine atoms

Since the number of all the atoms of the reacting elements are equal on both the reactant and product sides are equal, the equation is balanced.

Hence the balanced equation is: ${\mathrm{Na}}_2{\mathrm{CO}}_3+2\mathrm{HCl}\to 2\mathrm{NaCl}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$.