Calculate the emf of the following cell:
`Cu(s)|Cu^(2+) (aq)||Ag^(+) (aq)| Ag(s)`
Given that, `E_(Cu^(2+)//Cu)^(@)=0.34 V, E_(Ag//Ag^(+))^(@)=-0.80 V`

Options

A. 0.046 V
B. 0.46 V
C. 0.57 V
D. `-0.46 V`

Answer

To calculate the EMF (Electromotive Force) of the given electrochemical cell, we will follow these steps:

### Step 1: Identify the half-reactions
The cell notation is given as:
`Cu(s)|Cu^(2+) (aq)||Ag^(+) (aq)|Ag(s)`

From this notation:
- The left side (anode) involves the oxidation of copper:
\[ \text{Cu(s)} \rightarrow \text{Cu}^{2+}(aq) + 2e^- \]
- The right side (cathode) involves the reduction of silver:
\[ \text{Ag}^+(aq) + e^- \rightarrow \text{Ag(s)} \]

### Step 2: Write the standard reduction potentials
We are given the standard reduction potentials:
- For copper: \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} = 0.34 \, \text{V} \)
- For silver: \( E^\circ_{\text{Ag}/\text{Ag}^+} = -0.80 \, \text{V} \)

### Step 3: Determine the standard electrode potentials
Since the copper is oxidized at the anode, we will use the reduction potential for copper in the opposite direction (as oxidation):
- Oxidation potential for copper: \( E^\circ_{\text{Cu}/\text{Cu}^{2+}} = -0.34 \, \text{V} \)

The reduction potential for silver remains the same:
- Reduction potential for silver: \( E^\circ_{\text{Ag}/\text{Ag}^+} = -0.80 \, \text{V} \)

### Step 4: Calculate the EMF of the cell
The EMF of the cell can be calculated using the formula:
\[ \text{EMF} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \]
Substituting the values:
\[ \text{EMF} = E^\circ_{\text{Ag}/\text{Ag}^+} - E^\circ_{\text{Cu}/\text{Cu}^{2+}} \]
\[ \text{EMF} = (-0.80 \, \text{V}) - (-0.34 \, \text{V}) \]
\[ \text{EMF} = -0.80 \, \text{V} + 0.34 \, \text{V} \]
\[ \text{EMF} = -0.46 \, \text{V} \]

### Step 5: Finalize the answer
Since the EMF is typically expressed as a positive value, we take the absolute value:
\[ \text{EMF} = 0.46 \, \text{V} \]

Thus, the EMF of the cell is **0.46 V**.