Among the following statement choose the true or false statements(s).
`K_(2)Cr_(2)O_(7)`on heating with charcoal gives mettalic potassium and `Cr_(2)O_(3)`
on heating in current of `H_(2)` the crystalline `KMnO_(4)` is converted into `KOH` and `Mn_(3)O_(4)`
Hydrated ferric chloride on treatment with `2-2`-dimethoxypropane gives anhydrous ferric chloride.

Explanation

To determine the truthfulness of the three statements provided, we will analyze each statement by writing down the corresponding chemical reactions and evaluating the products formed.

### Step 1: Analyze the first statement
**Statement:** `K2Cr2O7` on heating with charcoal gives metallic potassium and `Cr2O3`.

**Reaction:**
When potassium dichromate (`K2Cr2O7`) is heated with charcoal (carbon), the reaction can be represented as follows:

\[ K_2Cr_2O_7 + 3C \rightarrow 2K_2CO_3 + Cr_2O_3 + 3CO_2 \]

**Analysis:**
- The products formed are potassium carbonate (`K2CO3`), chromium(III) oxide (`Cr2O3`), and carbon dioxide (`CO2`).
- The statement claims that metallic potassium is produced, but the reaction shows that potassium carbonate is formed instead.

**Conclusion:** The first statement is **False**.

### Step 2: Analyze the second statement
**Statement:** On heating in a current of `H2`, the crystalline `KMnO4` is converted into `KOH` and `Mn3O4`.

**Reaction:**
When potassium permanganate (`KMnO4`) is heated in the presence of hydrogen (`H2`), the reaction can be represented as:

\[ 2KMnO_4 + 5H_2 \rightarrow 2KOH + 2MnO + 2H_2O \]

**Analysis:**
- The products formed are potassium hydroxide (`KOH`), manganese(II) oxide (`MnO`), and water (`H2O`).
- The statement claims that manganese(IV) oxide (`Mn3O4`) is produced, but the reaction shows that manganese(II) oxide is formed instead.

**Conclusion:** The second statement is **False**.

### Step 3: Analyze the third statement
**Statement:** Hydrated ferric chloride on treatment with `2,2-dimethoxypropane` gives anhydrous ferric chloride.

**Reaction:**
When hydrated ferric chloride (`FeCl3·6H2O`) reacts with `2,2-dimethoxypropane`, the reaction can be represented as:

\[ FeCl_3·6H_2O + 2,2-dimethoxypropane \rightarrow FeCl_3 + 2CH_3OH + CH_3COOH \]

**Analysis:**
- The products formed are anhydrous ferric chloride (`FeCl3`), methanol (`CH3OH`), and acetic acid (`CH3COOH`).
- The statement correctly indicates that anhydrous ferric chloride is produced.

**Conclusion:** The third statement is **True**.

### Final Summary of Statements:
1. **First Statement:** False
2. **Second Statement:** False
3. **Third Statement:** True

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