How many faradays are required to reduce one mole of `Cr_(2)O_(7)^(-2)to Cr^(+3)` ?

Options

A. 3
B. 6
C. 12
D. 9

Answer

To determine how many Faradays are required to reduce one mole of \( \text{Cr}_2\text{O}_7^{2-} \) to \( \text{Cr}^{3+} \), we can follow these steps:

### Step 1: Determine the oxidation state of chromium in \( \text{Cr}_2\text{O}_7^{2-} \)
Let the oxidation state of chromium be \( x \). The equation for the overall charge can be set up as follows:

\[ 2x + 7(-2) = -2 \]

This simplifies to:

\[ 2x - 14 = -2 \]

Solving for \( x \):

\[ 2x = 12 \implies x = 6 \]

### Step 2: Calculate the change in oxidation state
In \( \text{Cr}_2\text{O}_7^{2-} \), the oxidation state of chromium is +6. In \( \text{Cr}^{3+} \), the oxidation state is +3. Therefore, the change in oxidation state for one chromium atom is:

\[ 6 - 3 = 3 \]

Since there are 2 chromium atoms in \( \text{Cr}_2\text{O}_7^{2-} \), the total change in oxidation state for both chromium atoms is:

\[ 3 \times 2 = 6 \]

### Step 3: Relate the change in oxidation state to moles of electrons
The change in oxidation state corresponds to the number of moles of electrons required for the reduction. Thus, to reduce \( \text{Cr}_2\text{O}_7^{2-} \) to \( \text{Cr}^{3+} \), we need 6 moles of electrons.

### Step 4: Calculate the number of Faradays required
Since 1 mole of electrons corresponds to 1 Faraday, the total number of Faradays required is equal to the number of moles of electrons:

\[ \text{Faradays required} = 6 \text{ moles of electrons} = 6 \text{ Faradays} \]

### Final Answer
Therefore, the number of Faradays required to reduce one mole of \( \text{Cr}_2\text{O}_7^{2-} \) to \( \text{Cr}^{3+} \) is **6 Faradays**.

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