To balance the chemical equation \( \text{HCl} + \text{CaCO}_3 \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \), we need to ensure that we have the same number of each type of atom on both sides of the equation.
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Identify the compounds and their constituent atoms:
- Reactants: HCl and CaCO₃
- Products: CaCl₂, H₂O, and CO₂
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List out the elements involved:
- H (Hydrogen)
- Cl (Chlorine)
- Ca (Calcium)
- C (Carbon)
- O (Oxygen)
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Set up the initial counts of each element:
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Reactants:
- 1 H from HCl
- 1 Cl from HCl
- 1 Ca from CaCO₃
- 1 C from CaCO₃
- 3 O from CaCO₃
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Products:
- 2 Cl from CaCl₂
- 1 Ca from CaCl₂
- 1 C from CO₂
- 2 O from H₂O and CO₂ (1 from H₂O and 2 from CO₂)
- 2 H from H₂O
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Now we begin balancing:
- The Cl atoms are unbalanced (1 on reactant side and 2 on product side).
- To balance Cl, place a coefficient of 2 in front of HCl: \[ 2 \text{HCl} + \text{CaCO}_3 \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \]
New counts:
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Reactants:
- H: 2
- Cl: 2
- Ca: 1
- C: 1
- O: 3
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Products:
- Ca: 1
- Cl: 2
- C: 1
- O: 3 (2 in CO₂ + 1 in H₂O)
- H: 2
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The equation is now balanced: \[ \text{Final balanced equation: } 2 \text{HCl} + \text{CaCO}_3 \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \]
Thus, the coefficients are:
- 2 for HCl
- 1 for CaCO₃
- 1 for CaCl₂
- 1 for H₂O
- 1 for CO₂
Therefore, the balanced equation is: \[ \boxed{2 \text{HCl} + 1 \text{CaCO}_3 \rightarrow 1 \text{CaCl}_2 + 1 \text{H}_2\text{O} + 1 \text{CO}_2} \]