What is the correct representation of reaction occurring when HCl is heated with `MnO_(2)` ?

Options

A. `MnO_(4)^(-)+5Cl^(-)+8H^(+)rarr Mn^(2+)+5Cl^(-)+5H_(2)O`
B. `MnO_(2)+2Cl^(-)+4H^(+)rarr Mn^(2+)+Cl_(2)+2H_(2)O`
C. `2MnO_(2)+4Cl^(-)+8H^(+)rarr 2 Mn^(2+)+2Cl_(2)+4H_(2)O`
D. `MnO_(2)+4HCl rarr MnCl_(4)+Cl_(2)+H_(2)O`

Explanation

To determine the correct representation of the reaction occurring when HCl is heated with MnO2, we can follow these steps:

### Step 1: Identify Reactants
The reactants in this reaction are manganese dioxide (MnO2) and hydrochloric acid (HCl).

### Step 2: Write the Unbalanced Reaction
The initial unbalanced equation can be written as:
\[ \text{MnO}_2 + \text{HCl} \rightarrow \text{MnCl}_2 + \text{Cl}_2 + \text{H}_2\text{O} \]

### Step 3: Determine Oxidation States
- In MnO2, manganese (Mn) has an oxidation state of +4 (since each oxygen is -2, and there are two oxygens).
- In HCl, chlorine (Cl) has an oxidation state of -1.
- In MnCl2, manganese has an oxidation state of +2 (to balance with two -1 charges from chlorine).
- In Cl2, chlorine has an oxidation state of 0 (as it is in its elemental form).

### Step 4: Identify Oxidation and Reduction
- Chlorine is oxidized from -1 in HCl to 0 in Cl2, indicating a loss of electrons.
- Manganese is reduced from +4 in MnO2 to +2 in MnCl2, indicating a gain of electrons.

### Step 5: Balance the Reaction
1. **Balance Chlorine**: Since there are 4 chlorine atoms in the products (2 from MnCl2 and 2 from Cl2), we need 4 HCl on the reactant side:
\[ \text{MnO}_2 + 4\text{HCl} \rightarrow \text{MnCl}_2 + \text{Cl}_2 + \text{H}_2\text{O} \]

2. **Balance Hydrogen and Oxygen**:
- We have 4 H from 4 HCl, which will produce 2 H2O (2 H from each H2O gives 4 H total).
- The oxygen is balanced as we have 2 O from MnO2 and 2 O from 2 H2O.

The balanced equation is:
\[ \text{MnO}_2 + 4\text{HCl} \rightarrow \text{MnCl}_2 + \text{Cl}_2 + 2\text{H}_2\text{O} \]

### Step 6: Write the Ionic Equation
In ionic form, the reaction can be represented as:
\[ \text{MnO}_2 + 4\text{H}^+ + 4\text{Cl}^- \rightarrow \text{Mn}^{2+} + \text{Cl}_2 + 2\text{H}_2\text{O} \]

### Step 7: Simplify the Ionic Equation
By canceling out the spectator ions, we can simplify to:
\[ \text{MnO}_2 + 4\text{H}^+ + 4\text{Cl}^- \rightarrow \text{Mn}^{2+} + \text{Cl}_2 + 2\text{H}_2\text{O} \]

### Conclusion
The final balanced reaction when HCl is heated with MnO2 is:
\[ \text{MnO}_2 + 4\text{HCl} \rightarrow \text{MnCl}_2 + \text{Cl}_2 + 2\text{H}_2\text{O} \]