1. $$ -\mathrm{MnO}_{2}+\ldots \mathrm{HCl} \rightarrow-\mathrm{MnCl}_{2}+\ldots \mathrm{H}_{2} \mathrm{O}+\ldots \mathrm{Cl}_{2} $$

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Certainly! Let's balance the chemical equation you've provided:

**Unbalanced Equation:**
$$ \mathrm{MnO}_2 + \mathrm{HCl} \rightarrow \mathrm{MnCl}_2 + \mathrm{H}_2\mathrm{O} + \mathrm{Cl}_2 $$

**Step-by-Step Balancing:**

1. **Identify the Oxidation States:**
   - **Manganese (Mn):** In $$\mathrm{MnO}_2$$, Mn has an oxidation state of +4. In $$\mathrm{MnCl}_2$$, it’s +2.
   - **Chlorine (Cl):** In $$\mathrm{HCl}$$, Cl is -1. In $$\mathrm{Cl}_2$$, it’s 0.

2. **Write the Half-Reactions:**
   - **Reduction (Mn reduction):**
     $$ \mathrm{MnO}_2 + 4\mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{Mn}^{2+} + 2\mathrm{H}_2\mathrm{O} $$
   - **Oxidation (Cl oxidation):**
     $$ 2\mathrm{Cl}^- \rightarrow \mathrm{Cl}_2 + 2\mathrm{e}^- $$

3. **Combine the Half-Reactions:**
   $$ \mathrm{MnO}_2 + 4\mathrm{H}^+ + 2\mathrm{Cl}^- \rightarrow \mathrm{Mn}^{2+} + 2\mathrm{H}_2\mathrm{O} + \mathrm{Cl}_2 $$

4. **Incorporate HCl as the Source of H$$^+$$ and Cl$$^-$$:**
   Since each $$\mathrm{HCl}$$ provides one $$\mathrm{H}^+$$ and one $$\mathrm{Cl}^-$$, multiply HCl by 4 to balance the $$\mathrm{H}^+$$ and $$\mathrm{Cl}^-$$ ions:

$$ \mathrm{MnO}_2 + 4\mathrm{HCl} \rightarrow \mathrm{MnCl}_2 + 2\mathrm{H}_2\mathrm{O} + \mathrm{Cl}_2 $$

**Balanced Equation:**
$$ \boxed{\mathrm{MnO}_2 +\,4\,\mathrm{HCl}\ \rightarrow\ \mathrm{MnCl}_2 +\,2\,\mathrm{H}_2\mathrm{O} +\,\mathrm{Cl}_2} $$

**Verification:**

- **Manganese (Mn):** 1 atom on both sides.
- **Oxygen (O):** 2 atoms on both sides.
- **Hydrogen (H):** 4 atoms on both sides.
- **Chlorine (Cl):** 4 atoms on both sides.

All elements are balanced, and the charge is balanced as well.
The balanced chemical equation is: $$ \mathrm{MnO}_2 + 4\,\mathrm{HCl} \rightarrow \mathrm{MnCl}_2 + 2\,\mathrm{H}_2\mathrm{O} + \mathrm{Cl}_2 $$

1. \( -\mathrm{MnO}_{2}+\ldots \mathrm{HCl} \rightarrow-\mathrm{MnCl}_{2}+\ldots \mathrm{H}_{2} \mathrm{O}+\ldots \mathrm{Cl}_{2} \)

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