To balance the chemical equation for the reaction between calcium acetate and sodium carbonate, follow these steps:
1. Write the unbalanced equation:
[tex]\[
\text{Ca(C}_2\text{H}_3\text{O}_2)_2 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 + \text{NaC}_2\text{H}_3\text{O}_2
\][/tex]
2. List the atoms for each element in the reactants and products:
- Calcium (Ca): 1 on the reactant side, 1 on the product side
- Carbon (C): 3 on the reactant side (2 from acetate, 1 from carbonate), 3 on the product side (1 from carbonate, 2 from acetate)
- Oxygen (O): 6 on the reactant side, 6 on the product side
- Hydrogen (H): 6 on the reactant side, 6 on the product side
- Sodium (Na): 2 on the reactant side, 1 on the product side
3. Adjust coefficients to balance the number of atoms for each element:
Start with the solid calcium carbonate, CaCO3, and multiply sodium acetate by 2 to balance sodium atoms.
[tex]\[
\text{Ca(C}_2\text{H}_3\text{O}_2)_2 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 + 2\text{NaC}_2\text{H}_3\text{O}_2
\][/tex]
4. Verify the atom balance:
- Calcium (Ca): 1 on both sides
- Carbon (C): 4 on both sides (2 from acetate, 1 from carbonate on the reactant side; 1 from carbonate, 3 from acetate on the product side)
- Oxygen (O): 7 on both sides (4 from acetate, 3 from carbonate)
- Hydrogen (H): 6 on both sides (6 from acetate both reactant and product sides)
- Sodium (Na): 2 on both sides
Thus, the balanced equation is:
[tex]\[
1 \text{ Ca(C}_2\text{H}_3\text{O}_2)_2 + 1 \text{ Na}_2\text{CO}_3 \rightarrow 1 \text{ CaCO}_3 + 2 \text{ NaC}_2\text{H}_3\text{O}_2
\][/tex]
When expressed with the coefficients in the respective blanks:
- Coefficient for [tex]\(\text{Ca(C}_2\text{H}_3\text{O}_2)_2\)[/tex] = 1
- Coefficient for [tex]\(\text{Na}_2\text{CO}_3\)[/tex] = 1
- Coefficient for [tex]\(\text{CaCO}_3\)[/tex] = 1
- Coefficient for [tex]\(\text{NaC}_2\text{H}_3\text{O}_2\)[/tex] = 2
So, the balanced equation can be written as:
[tex]\[
\boxed{1} \, \text{Ca(C}_2\text{H}_3\text{O}_2)_2 + \boxed{1} \, \text{Na}_2\text{CO}_3 \rightarrow \boxed{1} \, \text{CaCO}_3 + \boxed{2} \, \text{NaC}_2\text{H}_3\text{O}_2
\][/tex]
