Which atom in the following reactions undergoes a change of oxidation state of -5 ?

Options

A. `MnO_(4)^(-)toMn^(2+)`
B. `Cr_(2)O_(7)^(2-)to2Cr^(3+)`
C. `MnO_(4)^(-)toMnO_(2)`
D. `CrO_(4)^(2-)toCr^(3+)`

Answer

To determine which atom undergoes a change of oxidation state of -5 in the given reactions, we will analyze each reaction step by step.

### Step 1: Analyze the first reaction (MnO4⁻)
1. **Identify the oxidation state of manganese (Mn) in MnO4⁻.**
- Let the oxidation state of Mn be \( x \).
- The oxidation state of oxygen is -2, and there are 4 oxygen atoms: \( 4 \times (-2) = -8 \).
- The total charge on the ion is -1.
- Therefore, we set up the equation:
\[ x + (-8) = -1 \]
- Solving for \( x \):
\[ x - 8 = -1 \implies x = +7 \]

2. **Determine the change in oxidation state.**
- In the reaction, MnO4⁻ is reduced to Mn²⁺.
- The oxidation state of Mn in Mn²⁺ is +2.
- The change in oxidation state is:
\[ +7 \text{ (initial)} \to +2 \text{ (final)} \implies \text{Change} = +7 - (+2) = +5 \]

### Step 2: Analyze the second reaction (Cr2O7²⁻ to Cr³⁺)
1. **Identify the oxidation state of chromium (Cr) in Cr2O7²⁻.**
- Let the oxidation state of Cr be \( x \).
- There are 2 Cr atoms and 7 oxygen atoms: \( 7 \times (-2) = -14 \).
- The total charge on the ion is -2.
- Therefore, we set up the equation:
\[ 2x + (-14) = -2 \]
- Solving for \( x \):
\[ 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]

2. **Determine the change in oxidation state.**
- In the reaction, Cr2O7²⁻ is reduced to Cr³⁺.
- The oxidation state of Cr in Cr³⁺ is +3.
- The change in oxidation state for 2 Cr atoms is:
\[ 2 \times (+6 \text{ (initial)} \to +3 \text{ (final)}) \implies \text{Change for each Cr} = +6 - (+3) = +3 \]
- Total change for 2 Cr atoms = \( 2 \times 3 = 6 \).

### Step 3: Analyze the third reaction (MnO4⁻ to MnO2)
1. **Identify the oxidation state of Mn in MnO2.**
- The oxidation state of oxygen is -2, and there are 2 oxygen atoms: \( 2 \times (-2) = -4 \).
- Therefore, we set up the equation for MnO2:
\[ x + (-4) = 0 \]
- Solving for \( x \):
\[ x = +4 \]

2. **Determine the change in oxidation state.**
- The change in oxidation state from MnO4⁻ to MnO2 is:
\[ +7 \text{ (initial)} \to +4 \text{ (final)} \implies \text{Change} = +7 - (+4) = +3 \]

### Step 4: Analyze the fourth reaction (CrO4²⁻ to Cr³⁺)
1. **Identify the oxidation state of Cr in CrO4²⁻.**
- Let the oxidation state of Cr be \( x \).
- There are 4 oxygen atoms: \( 4 \times (-2) = -8 \).
- Therefore, we set up the equation:
\[ x + (-8) = -2 \]
- Solving for \( x \):
\[ x - 8 = -2 \implies x = +6 \]

2. **Determine the change in oxidation state.**
- The change in oxidation state from CrO4²⁻ to Cr³⁺ is:
\[ +6 \text{ (initial)} \to +3 \text{ (final)} \implies \text{Change} = +6 - (+3) = +3 \]

### Conclusion
After analyzing all reactions, the only reaction that shows a change of oxidation state of -5 is the first reaction (MnO4⁻ to Mn²⁺), where manganese goes from +7 to +2, resulting in a change of +5.

### Final Answer
The atom that undergoes a change of oxidation state of -5 is manganese (Mn) in the reaction MnO4⁻ to Mn²⁺.