How many coulombs of electricity are required for the reduction of 1 mole of `MnO_(4) ^(-)` to `Mn^(2+)`?

Options

A. 96500 C
B. `9.65 xx l0^(6)` C
C. `4.83 xx10^(5)` C
D. `1.93 xx 10^(5)` C

Answer

To determine how many coulombs of electricity are required for the reduction of 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \), we can follow these steps:

### Step 1: Determine the oxidation states
First, we need to find the oxidation states of manganese in both \( \text{MnO}_4^{-} \) and \( \text{Mn}^{2+} \).

- In \( \text{MnO}_4^{-} \):
- Let the oxidation state of Mn be \( x \).
- The oxidation state of oxygen is -2, and there are 4 oxygen atoms.
- The overall charge of the ion is -1.

Thus, the equation is:
\[ x + 4(-2) = -1 \implies x - 8 = -1 \implies x = +7 \]

- In \( \text{Mn}^{2+} \):
- The oxidation state of Mn is +2.

### Step 2: Calculate the change in oxidation state
Now, we can calculate the change in oxidation state:
\[ \text{Change in oxidation state} = +7 - (+2) = +5 \]
This indicates that manganese is reduced by gaining 5 electrons.

### Step 3: Relate moles of electrons to Faraday's constant
Since 1 mole of \( \text{MnO}_4^{-} \) requires 5 moles of electrons for reduction, we can relate this to Faraday's constant. Faraday's constant (\( F \)) is approximately \( 96500 \, \text{C/mol} \).

### Step 4: Calculate total charge in coulombs
To find the total charge (in coulombs) required for the reduction of 1 mole of \( \text{MnO}_4^{-} \):
\[ \text{Total charge} = \text{moles of electrons} \times F = 5 \, \text{mol} \times 96500 \, \text{C/mol} \]
Calculating this gives:
\[ \text{Total charge} = 5 \times 96500 = 482500 \, \text{C} \]

### Step 5: Express the answer in scientific notation
We can express \( 482500 \, \text{C} \) in scientific notation:
\[ 482500 \, \text{C} = 4.825 \times 10^5 \, \text{C} \]

### Final Answer
Thus, the total amount of electricity required for the reduction of 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \) is:
\[ \boxed{4.83 \times 10^5 \, \text{C}} \]