To determine which of the given reactions is balanced, we need to check whether the number of each type of atom is the same on both the reactant and product sides.
The reactions presented are:
A. [tex]\( CaCl_2 + H_2CO_3 \rightarrow 2 CaCO_3 + HCl \)[/tex]
B. [tex]\( 2 CaCl_2 + H_2CO_3 \rightarrow CaCO_3 + HCl \)[/tex]
C. [tex]\( CaCl_2 + H_2CO_3 \rightarrow CaCO_3 + 2 HCl \)[/tex]
D. [tex]\( CaCl_2 + 2 H_2CO_3 \rightarrow CaCO_3 + HCl \)[/tex]
Let's balance each reaction step by step:
Reaction A:
[tex]\[ CaCl_2 + H_2CO_3 \rightarrow 2 CaCO_3 + HCl \][/tex]
- Left side (reactants):
- Ca: 1
- Cl: 2
- H: 2
- C: 1
- O: 3
- Right side (products):
- Ca: 2 (from [tex]\(2 CaCO_3\)[/tex])
- Cl: 1 (from [tex]\(HCl\)[/tex])
- H: 1 (from [tex]\(HCl\)[/tex])
- C: 2 (from [tex]\(2 CaCO_3\)[/tex])
- O: 6 (from [tex]\(2 CaCO_3\)[/tex])
This reaction is not balanced.
Reaction B:
[tex]\[ 2 CaCl_2 + H_2CO_3 \rightarrow CaCO_3 + HCl \][/tex]
- Left side (reactants):
- Ca: 2 (from [tex]\(2 CaCl_2\)[/tex])
- Cl: 4 (from [tex]\(2 CaCl_2\)[/tex])
- H: 2 (from [tex]\(H_2CO_3\)[/tex])
- C: 1 (from [tex]\(H_2CO_3\)[/tex])
- O: 3 (from [tex]\(H_2CO_3\)[/tex])
- Right side (products):
- Ca: 1 (from [tex]\(CaCO_3\)[/tex])
- Cl: 1 (from [tex]\(HCl\)[/tex])
- H: 1 (from [tex]\(HCl\)[/tex])
- C: 1 (from [tex]\(CaCO_3\)[/tex])
- O: 3 (from [tex]\(CaCO_3\)[/tex])
This reaction is not balanced.
Reaction C:
[tex]\[ CaCl_2 + H_2CO_3 \rightarrow CaCO_3 + 2 HCl \][/tex]
- Left side (reactants):
- Ca: 1 (from [tex]\(CaCl_2\)[/tex])
- Cl: 2 (from [tex]\(CaCl_2\)[/tex])
- H: 2 (from [tex]\(H_2CO_3\)[/tex])
- C: 1 (from [tex]\(H_2CO_3\)[/tex])
- O: 3 (from [tex]\(H_2CO_3\)[/tex])
- Right side (products):
- Ca: 1 (from [tex]\(CaCO_3\)[/tex])
- Cl: 2 (from [tex]\(2 HCl\)[/tex])
- H: 2 (from [tex]\(2 HCl\)[/tex])
- C: 1 (from [tex]\(CaCO_3\)[/tex])
- O: 3 (from [tex]\(CaCO_3\)[/tex])
This reaction is balanced.
Reaction D:
[tex]\[ CaCl_2 + 2 H_2CO_3 \rightarrow CaCO_3 + HCl \][/tex]
- Left side (reactants):
- Ca: 1 (from [tex]\(CaCl_2\)[/tex])
- Cl: 2 (from [tex]\(CaCl_2\)[/tex])
- H: 4 (from [tex]\(2 H_2CO_3\)[/tex])
- C: 2 (from [tex]\(2 H_2CO_3\)[/tex])
- O: 6 (from [tex]\(2 H_2CO_3\)[/tex])
- Right side (products):
- Ca: 1 (from [tex]\(CaCO_3\)[/tex])
- Cl: 1 (from [tex]\(HCl\)[/tex])
- H: 1 (from [tex]\(HCl\)[/tex])
- C: 1 (from [tex]\(CaCO_3\)[/tex])
- O: 3 (from [tex]\(CaCO_3\)[/tex])
This reaction is not balanced.
After checking all the reactions, we can conclude that reaction C is the balanced one. Therefore, the correct answer is:
C. [tex]\( CaCl_2 + H_2CO_3 \rightarrow CaCO_3 + 2 HCl \)[/tex]
