Find the charge in coulombs required to convert 0.2 mole `VO_(3)^(2-)` into `VO_(4)^(3-)`

Options

A. `1.93 xx 10^(4)`
B. `9.65 xx 10^(4)`
C. `1.93 xx 10^(5)`
D. `9.65 xx 10^(5)`

Explanation

To find the charge in coulombs required to convert 0.2 moles of \( VO_3^{2-} \) into \( VO_4^{3-} \), we can follow these steps:

### Step 1: Identify the oxidation states
In the conversion from \( VO_3^{2-} \) to \( VO_4^{3-} \), we need to determine the change in the oxidation state of vanadium (V).

- In \( VO_3^{2-} \), vanadium is in the +4 oxidation state.
- In \( VO_4^{3-} \), vanadium is in the +5 oxidation state.

### Step 2: Determine the number of electrons transferred
The change in oxidation state from +4 to +5 indicates that one electron is lost during the conversion. Therefore, the number of electrons exchanged (n) is 1.

### Step 3: Use Faraday's law of electrolysis
According to Faraday's law, the charge (Q) required can be calculated using the formula:
\[ Q = n \times F \times m \]
Where:
- \( Q \) is the total charge in coulombs,
- \( n \) is the number of moles of electrons transferred,
- \( F \) is Faraday's constant (approximately \( 96500 \, C/mol \)),
- \( m \) is the number of moles of the substance.

### Step 4: Calculate the total charge
Given that we have 0.2 moles of \( VO_3^{2-} \) and that 1 electron is transferred per mole of \( VO_3^{2-} \) to convert it to \( VO_4^{3-} \):

\[ Q = n \times F \times \text{moles of } VO_3^{2-} \]
\[ Q = 1 \times 96500 \, C/mol \times 0.2 \, mol \]
\[ Q = 19300 \, C \]

### Final Answer
The charge required to convert 0.2 moles of \( VO_3^{2-} \) into \( VO_4^{3-} \) is **19300 coulombs**.

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