To balance the given chemical equation:
[tex]\[ \text{BaCl}_2(aq) + \text{Na}_2\text{CO}_3(aq) \rightarrow \text{BaCO}_3(s) + \text{NaCl}(aq) \][/tex]
we proceed with the following steps:
1. Write down the number of atoms of each element on both sides of the equation:
- Reactants:
[tex]\[ \text{BaCl}_2(aq) + \text{Na}_2\text{CO}_3(aq) \][/tex]
- Barium (Ba): 1
- Chlorine (Cl): 2
- Sodium (Na): 2
- Carbon (C): 1
- Oxygen (O): 3
- Products:
[tex]\[ \text{BaCO}_3(s) + \text{NaCl}(aq) \][/tex]
- Barium (Ba): 1
- Chlorine (Cl): 1
- Sodium (Na): 1
- Carbon (C): 1
- Oxygen (O): 3
2. Compare the number of atoms of each element on both sides of the equation to identify the imbalance:
- Barium (Ba): 1 (Reactants) vs. 1 (Products) → Balanced
- Chlorine (Cl): 2 (Reactants) vs. 1 (Products) → Not balanced
- Sodium (Na): 2 (Reactants) vs. 1 (Products) → Not balanced
- Carbon (C): 1 (Reactants) vs. 1 (Products) → Balanced
- Oxygen (O): 3 (Reactants) vs. 3 (Products) → Balanced
3. Balance the elements that are not balanced by adjusting the coefficients:
Since there are 2 Cl atoms and 2 Na atoms on the reactants side and only 1 of each on the products side, we can balance the equation by placing the coefficient 2 in front of NaCl on the products side:
[tex]\[ \text{BaCl}_2(aq) + \text{Na}_2\text{CO}_3(aq) \rightarrow \text{BaCO}_3(s) + 2 \text{NaCl}(aq) \][/tex]
4. Verify the balance:
- Reactants:
[tex]\[ \text{BaCl}_2(aq) + \text{Na}_2\text{CO}_3(aq) \][/tex]
- Barium (Ba): 1
- Chlorine (Cl): 2
- Sodium (Na): 2
- Carbon (C): 1
- Oxygen (O): 3
- Products:
[tex]\[ \text{BaCO}_3(s) + 2 \text{NaCl}(aq) \][/tex]
- Barium (Ba): 1
- Chlorine (Cl): 2
- Sodium (Na): 2
- Carbon (C): 1
- Oxygen (O): 3
Now, all elements are balanced on both sides of the equation.
Therefore, the coefficient that should be placed in front of [tex]\(\text{NaCl}\)[/tex] to balance the equation is:
[tex]\[ \boxed{2} \][/tex]
