`2MnO_(4)^(-) + 5H_(2)O_(2) + 6H^(+) rarr 2Z + 5O_(2) + 8H_(2)O` Identify Z in the above reaction.

Options

A. `Mn^(2+)`
B. `Mn^(4+)`
C. `Mn`
D. `MnO_(2)`

Explanation

To identify Z in the reaction \( 2MnO_4^{-} + 5H_2O_2 + 6H^{+} \rightarrow 2Z + 5O_2 + 8H_2O \), we can follow these steps:

### Step 1: Determine the oxidation state of manganese in \( MnO_4^{-} \)
Manganese in \( MnO_4^{-} \) has an oxidation state of +7. This is calculated as follows:
- The oxidation state of oxygen is -2.
- In \( MnO_4^{-} \), there are 4 oxygen atoms contributing a total of -8.
- Let the oxidation state of manganese be \( x \). Therefore, the equation is:
\[ x + 4(-2) = -1 \implies x - 8 = -1 \implies x = +7 \]

**Hint:** Remember that the sum of oxidation states in a compound must equal the overall charge of the compound.

### Step 2: Identify the reduction process
Since \( MnO_4^{-} \) is being reduced, we need to determine what it is reduced to. The oxidation state of manganese will decrease from +7 to a lower oxidation state.

**Hint:** Reduction involves a decrease in oxidation state, so look for a manganese species with a lower oxidation state.

### Step 3: Analyze the products
The products of the reaction include \( 2Z \), \( 5O_2 \), and \( 8H_2O \). We need to find out what \( Z \) is. The key is to balance the charges and the atoms.

### Step 4: Balance the reaction
1. **Count the oxygen atoms:**
- Left side: \( 2 \times 4 \) (from \( MnO_4^{-} \)) + \( 5 \times 2 \) (from \( H_2O_2 \)) = 8 + 10 = 18 oxygen atoms.
- Right side: \( 5 \times 2 \) (from \( O_2 \)) + \( 8 \) (from \( H_2O \)) = 10 + 8 = 18 oxygen atoms.
- Oxygen is balanced.

2. **Count the charges:**
- Left side: \( 2 \times (-1) + 6 \) (from \( H^{+} \)) = -2 + 6 = +4.
- Right side: The charge from \( 2Z \) must equal +4.

### Step 5: Determine the charge of Z
To balance the charge, we need \( 2Z \) to have a total charge of +4. Therefore, the charge of \( Z \) must be +2:
\[ 2Z = +4 \implies Z = +2 \]

### Step 6: Identify Z
The species that has a +2 oxidation state for manganese is \( MnO_2^{+} \) (manganese in +2 oxidation state).

Thus, \( Z \) is \( MnO_2^{+} \).

### Final Answer
**Z = \( MnO_2^{+} \)**

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