For the reaction,
`Fe^(+2) (aq) + Ag^(+) (aq) rarr Ag(s) + Fe^(+3) (aq)`
Predict which change will decrease the cell voltage?

Options

A. Increase the amount of Ag
B. Decrease the concentration of `Ag^(+)`
C. Increase the concentration of `Fe^(+3)`
D. Both (2) & (3)

Answer

To determine which change will decrease the cell voltage for the given electrochemical reaction:

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

**Step 1: Understand the Reaction**
- In this reaction, Fe²⁺ is oxidized to Fe³⁺, and Ag⁺ is reduced to Ag(s).
- Oxidation involves the loss of electrons, while reduction involves the gain of electrons.

**Step 2: Use the Nernst Equation**
- The Nernst equation is given by:
\[ E_{cell} = E^0_{cell} - \frac{2.303RT}{nF} \log \left( \frac{[\text{Products}]}{[\text{Reactants}]} \right) \]
- Here, \( E^0_{cell} \) is the standard cell potential, R is the universal gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant.

**Step 3: Identify the Concentrations in the Nernst Equation**
- For this reaction, the products are Ag(s) and Fe³⁺, and the reactants are Fe²⁺ and Ag⁺.
- The concentration terms in the Nernst equation will be:
\[ E_{cell} = E^0_{cell} - \frac{2.303RT}{nF} \log \left( \frac{[\text{Fe}^{3+}]}{[\text{Fe}^{2+}][\text{Ag}^{+}]} \right) \]

**Step 4: Analyze Changes to Concentrations**
- Increasing the concentration of Fe³⁺ (product) will increase the value in the numerator, which will make the logarithm more positive, thereby decreasing \( E_{cell} \).
- Decreasing the concentration of Ag⁺ (reactant) will decrease the value in the denominator, which will also make the logarithm more positive, thus decreasing \( E_{cell} \).

**Step 5: Determine Which Changes Decrease Cell Voltage**
- From the analysis:
- Increasing the concentration of Fe³⁺ decreases cell voltage.
- Decreasing the concentration of Ag⁺ also decreases cell voltage.
- Therefore, both these changes will lead to a decrease in cell voltage.

**Conclusion:**
The changes that will decrease the cell voltage are:
1. Increasing the concentration of Fe³⁺.
2. Decreasing the concentration of Ag⁺.

**Final Answer:**
Both increasing Fe³⁺ and decreasing Ag⁺ will decrease the cell voltage. Thus, the correct option is D (both 2nd and 3rd statements).

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