To balance the equation, coefficients are used to ensure that the number of atoms of each element is equal on both sides of the equation. The balanced equation for the reaction between NH4Cl and Na2CO3 is:

NH4Cl (aq) + Na2CO3 (aq) → NH3 (g) + CO2 (g) + H2O (l) + NaCl (aq)

Step 1: Start by balancing the ammonium (NH4) ions. There is one NH4+ ion on the left side and one NH3 molecule on the right side. To balance this, we can put a coefficient of 2 in front of NH3:

NH4Cl (aq) + Na2CO3 (aq) → 2NH3 (g) + CO2 (g) + H2O (l) + NaCl (aq)

Step 2: Now, we need to balance the sodium (Na) atoms. There are two Na atoms on the left side and one NaCl molecule on the right side. To balance this, we can put a coefficient of 2 in front of NaCl:

NH4Cl (aq) + Na2CO3 (aq) → 2NH3 (g) + CO2 (g) + H2O (l) + 2NaCl (aq)

Step 3: Moving on to balancing the carbonate (CO3) ions. There is one CO32- ion on the left side and one CO2 molecule on the right side. This is already balanced.

Step 4: Lastly, we need to make sure the chlorine (Cl) atoms are balanced. There is one Cl- ion on the left side and two NaCl molecules on the right side. To balance this, we can put a coefficient of 2 in front of NH4Cl:

2NH4Cl (aq) + Na2CO3 (aq) → 2NH3 (g) + CO2 (g) + H2O (l) + 2NaCl (aq)