What is the number of electrons transferred in an equation if the Nernst equation is `E(cell) = E°(cell) – 9.83 × 10^(-3) × log_10 `(Anode / Cathode)?

Options

A. 2
B. 4
C. 6
D. 1

Answer

To determine the number of electrons transferred in the given Nernst equation, we can follow these steps:

### Step 1: Write down the given Nernst equation
The provided Nernst equation is:
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - 9.83 \times 10^{-3} \log_{10} \left(\frac{\text{Anode}}{\text{Cathode}}\right) \]

### Step 2: Recall the standard form of the Nernst equation
The standard form of the Nernst equation is:
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.059}{n} \log_{10} \left(\frac{\text{Anode}}{\text{Cathode}}\right) \]
where \( n \) is the number of electrons transferred.

### Step 3: Compare the two equations
From the two equations, we can compare the coefficients of the logarithmic term:
\[ -9.83 \times 10^{-3} = -\frac{0.059}{n} \]

### Step 4: Rearrange the equation to solve for \( n \)
Rearranging the equation gives:
\[ 9.83 \times 10^{-3} = \frac{0.059}{n} \]
Multiplying both sides by \( n \) gives:
\[ 9.83 \times 10^{-3} n = 0.059 \]

### Step 5: Solve for \( n \)
Now, divide both sides by \( 9.83 \times 10^{-3} \):
\[ n = \frac{0.059}{9.83 \times 10^{-3}} \]

### Step 6: Calculate the value of \( n \)
Calculating this gives:
\[ n = \frac{0.059}{0.00983} \approx 6 \]

### Conclusion
Thus, the number of electrons transferred in the equation is:
\[ n = 6 \]

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