In which one of the following changes there are transfer of five electrons?

Options

A. `MnO_(4)^(-) to Mn^(2+)`
B. `CrO_(4)^(2-) to Cr^(3+)`
C. `MnO_(4)^(-) to MnO_(2)`
D. `Cr_(2)O_(7)^(2-) to 2Cr^(3+)`

Answer

To determine which of the given changes involves the transfer of five electrons, we will analyze each option by calculating the oxidation states of the metal ions involved in the reactions.

### Step-by-Step Solution:

1. **Option 1: MnO4⁻ to Mn²⁺**
- Calculate the oxidation state of Mn in MnO4⁻:
- Let the oxidation state of Mn be \( x \).
- The equation is:
\[ x + 4(-2) = -1 \]
\[ x - 8 = -1 \implies x = +7 \]
- The oxidation state of Mn changes from +7 to +2:
- Change in oxidation state = \( +7 - (+2) = 5 \)
- Therefore, this change involves the transfer of **5 electrons**.

2. **Option 2: CrO4²⁻ to Cr³⁺**
- Calculate the oxidation state of Cr in CrO4²⁻:
- Let the oxidation state of Cr be \( x \).
- The equation is:
\[ x + 4(-2) = -2 \]
\[ x - 8 = -2 \implies x = +6 \]
- The oxidation state of Cr changes from +6 to +3:
- Change in oxidation state = \( +6 - (+3) = 3 \)
- Therefore, this change involves the transfer of **3 electrons**.

3. **Option 3: MnO4⁻ to MnO2**
- We already calculated the oxidation state of Mn in MnO4⁻ as +7.
- Now calculate the oxidation state of Mn in MnO2:
- Let the oxidation state of Mn be \( x \).
- The equation is:
\[ x + 2(-2) = 0 \]
\[ x - 4 = 0 \implies x = +4 \]
- The oxidation state of Mn changes from +7 to +4:
- Change in oxidation state = \( +7 - (+4) = 3 \)
- Therefore, this change involves the transfer of **3 electrons**.

4. **Option 4: Cr2O7²⁻ to 2Cr³⁺**
- Calculate the oxidation state of Cr in Cr2O7²⁻:
- Let the oxidation state of Cr be \( x \).
- The equation is:
\[ 2x + 7(-2) = -2 \]
\[ 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]
- The oxidation state of Cr changes from +6 to +3:
- Change in oxidation state = \( +6 - (+3) = 3 \)
- Therefore, this change involves the transfer of **3 electrons**.

### Conclusion:
After analyzing all the options, we find that only the first option, **MnO4⁻ to Mn²⁺**, involves the transfer of **5 electrons**.

### Final Answer:
The correct option is **MnO4⁻ changes to Mn²⁺**.

---