`Zn(s)+Cl_(2)(1atm)toZn^(2+)+2Cl^(-)`. `E_(cell)^(o)` of the cell is 2.12 V. To increase E

Options

A. `[Zn^(2+)]` should be increased
B. `[Zn^(2+)]` should be decreased
C. `[Cl^(-)]` should be decreased
D. `P_(Cl_(2))` should be decreased

Explanation

To solve the problem of how to increase the standard cell potential \( E^\circ_{cell} \) for the reaction:

\[ \text{Zn(s)} + \text{Cl}_2(g) \rightarrow \text{Zn}^{2+} + 2\text{Cl}^- \]

with a given \( E^\circ_{cell} \) of 2.12 V, we can follow these steps:

### Step 1: Understand the Nernst Equation
The Nernst equation relates the standard cell potential to the concentrations of the reactants and products:

\[ E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q \]

where:
- \( E_{cell} \) is the cell potential under non-standard conditions.
- \( E^\circ_{cell} \) is the standard cell potential (2.12 V in this case).
- \( R \) is the universal gas constant (8.314 J/(mol·K)).
- \( T \) is the temperature in Kelvin.
- \( n \) is the number of moles of electrons transferred in the reaction.
- \( F \) is Faraday's constant (96485 C/mol).
- \( Q \) is the reaction quotient.

### Step 2: Determine the Reaction Quotient \( Q \)
For the given reaction, the reaction quotient \( Q \) is defined as:

\[ Q = \frac{[\text{Zn}^{2+}]}{P_{\text{Cl}_2}} \]

where:
- \([\text{Zn}^{2+}]\) is the concentration of zinc ions.
- \(P_{\text{Cl}_2}\) is the partial pressure of chlorine gas.

### Step 3: Analyze How to Increase \( E_{cell} \)
To increase \( E_{cell} \), we need to decrease the value of \( Q \). This can be achieved by:

1. **Increasing the concentration of the reactants** (in this case, decreasing \([\text{Zn}^{2+}]\)).
2. **Decreasing the concentration of the products** (in this case, decreasing \(P_{\text{Cl}_2}\)).

### Step 4: Conclusion
To increase \( E_{cell} \), we can:
- **Decrease the concentration of \(\text{Zn}^{2+}\)**.
- **Decrease the partial pressure of \(\text{Cl}_2\)**.

Thus, the most effective way to increase \( E_{cell} \) is to **decrease the concentration of \(\text{Zn}^{2+}\)** or **decrease the partial pressure of \(\text{Cl}_2\)**.