To balance the chemical reaction [tex]\( \text{CaCl}_2 + \text{H}_2\text{CO}_3 \rightarrow \text{CaCO}_3 + \text{HCl} \)[/tex], we need to ensure that the number of each type of atom on the reactant side is equal to the number on the product side. Let's go through it step by step:
1. Write down the number of each type of atom in the reactants and products:
Reactants:
- [tex]\( \text{CaCl}_2 \)[/tex]:
- [tex]\( 1 \text{ Ca} \)[/tex]
- [tex]\( 2 \text{ Cl} \)[/tex]
- [tex]\( \text{H}_2\text{CO}_3 \)[/tex]:
- [tex]\( 2 \text{ H} \)[/tex]
- [tex]\( 1 \text{ C} \)[/tex]
- [tex]\( 3 \text{ O} \)[/tex]
Products:
- [tex]\( \text{CaCO}_3 \)[/tex]:
- [tex]\( 1 \text{ Ca} \)[/tex]
- [tex]\( 1 \text{ C} \)[/tex]
- [tex]\( 3 \text{ O} \)[/tex]
- [tex]\( \text{HCl} \)[/tex]:
- [tex]\( 1 \text{ H} \)[/tex]
- [tex]\( 1 \text{ Cl} \)[/tex]
2. Compare the number of atoms of each element on both sides:
- Calcium ([tex]\( \text{Ca} \)[/tex]): [tex]\( 1 \)[/tex] on both sides
- Carbon ([tex]\( \text{C} \)[/tex]): [tex]\( 1 \)[/tex] on both sides
- Oxygen ([tex]\( \text{O} \)[/tex]): [tex]\( 3 \)[/tex] on both sides
- Hydrogen ([tex]\( \text{H} \)[/tex]): [tex]\( 2 \)[/tex] on the reactant side and [tex]\( 1 \)[/tex] on the product side
- Chlorine ([tex]\( \text{Cl} \)[/tex]): [tex]\( 2 \)[/tex] on the reactant side and [tex]\( 1 \)[/tex] on the product side
3. Balance chlorine ([tex]\( \text{Cl} \)[/tex]) by placing a coefficient of 2 before [tex]\( \text{HCl} \)[/tex]:
- Adjusted reaction: [tex]\( \text{CaCl}_2 + \text{H}_2\text{CO}_3 \rightarrow \text{CaCO}_3 + 2 \text{HCl} \)[/tex]
- Now, the chlorine atoms are balanced: 2 [tex]\( \text{Cl} \)[/tex] on both sides.
4. Check the numbers of other atoms after the adjustment:
- Calcium ([tex]\( \text{Ca} \)[/tex]): [tex]\( 1 \)[/tex] on both sides
- Carbon ([tex]\( \text{C} \)[/tex]): [tex]\( 1 \)[/tex] on both sides
- Oxygen ([tex]\( \text{O} \)[/tex]): [tex]\( 3 \)[/tex] on both sides
- Hydrogen ([tex]\( \text{H} \)[/tex]): [tex]\( 2 \)[/tex] on both sides (now with 2 [tex]\( \text{HCl} \)[/tex], we have [tex]\( 2 \times 1 = 2 \text{ H} \)[/tex])
Thus, the reaction is balanced with the coefficient of 2 for [tex]\( \text{HCl} \)[/tex]. The balanced chemical equation is:
[tex]\[ \text{CaCl}_2 + \text{H}_2\text{CO}_3 \rightarrow \text{CaCO}_3 + 2 \text{HCl} \][/tex]
Therefore, the correct answer is:
A. [tex]\( 2 \text{HCl} \)[/tex]
