Consider an electrochemical cell in which the following reaction occurs and predict which changes will decrease the cell voltage :
`Fe^(2+)(aq)+Ag^(+)(aq)toAg(s)+Fe^(3+)(aq)`
(I) Decrease the Ag+
(II)Increase in Fe3+
(III)Increase the amount of Ag
(a) I
(b) II and III
(c) II
(d) I and II

Options

A. I
B. II and III
C. II
D. I and II

Answer

To solve the problem, we need to analyze the given electrochemical reaction and how changes in concentrations affect the cell voltage (E_cell). The reaction is:

\[ \text{Fe}^{2+}(aq) + \text{Ag}^{+}(aq) \rightarrow \text{Ag}(s) + \text{Fe}^{3+}(aq) \]

### Step 1: Identify the half-reactions
The half-reactions for this electrochemical process can be identified as follows:
- Oxidation: \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^{-} \)
- Reduction: \( \text{Ag}^{+} + e^{-} \rightarrow \text{Ag}(s) \)

### Step 2: Understand the Nernst equation
The Nernst equation is given by:

\[ E_{cell} = E^{\circ}_{cell} - \frac{0.0591}{n} \log \left( \frac{[\text{Fe}^{3+}]}{[\text{Ag}^{+}][\text{Fe}^{2+}]} \right) \]

Where:
- \( E^{\circ}_{cell} \) is the standard cell potential (constant for a given reaction).
- \( n \) is the number of moles of electrons transferred (which is 1 in this case).

### Step 3: Analyze the effects of changes in concentration
1. **Decrease in \([\text{Ag}^{+}]\)**:
- If \([\text{Ag}^{+}]\) decreases, the denominator of the log expression decreases, which increases the value of the log term. Hence, \( E_{cell} \) decreases.

2. **Increase in \([\text{Fe}^{3+}]\)**:
- If \([\text{Fe}^{3+}]\) increases, the numerator of the log expression increases, which also increases the value of the log term. Hence, \( E_{cell} \) decreases.

3. **Increase in the amount of Ag**:
- Since Ag is a solid, its concentration does not affect the cell voltage. Therefore, increasing the amount of Ag will not change \( E_{cell} \).

### Step 4: Conclusion
From the analysis:
- Changes that decrease the cell voltage are:
- Decrease in \([\text{Ag}^{+}]\) (I)
- Increase in \([\text{Fe}^{3+}]\) (II)
- Increasing the amount of Ag (III) does not affect the cell voltage.

Thus, the correct answer is **(d) I and II**.