For the cell `Ti|Ti^(+) (0.001 M)|Cu^(2+)(0.1 M)|Cu. E_("cell")" at "256^@` is 0.83 V which can be increased

Options

A. by increasing `[Cu^(2+)]`
B. by increasing `[Ti^(+)]`
C. by decreasing `[Cu^(2+)]`
D. by decreasing `[Ti^(+)]`

Answer

To solve the problem of how to increase the cell potential (E_cell) for the given electrochemical cell, we can follow these steps:

### Step 1: Write the Cell Reaction
The electrochemical cell consists of titanium (Ti) and copper (Cu). The half-reactions are:
- At the anode (oxidation):
\[ \text{Ti} \rightarrow \text{Ti}^{2+} + 2e^- \]
- At the cathode (reduction):
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]

The overall cell reaction can be written as:
\[ 2 \text{Ti} + \text{Cu}^{2+} \rightarrow 2 \text{Ti}^{2+} + \text{Cu} \]

### Step 2: Write the Nernst Equation
The Nernst equation relates the cell potential (E_cell) to the standard cell potential (E°_cell) and the concentrations of the reactants and products:
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( n \) is the number of moles of electrons transferred,
- \( F \) is Faraday's constant,
- \( Q \) is the reaction quotient.

For our reaction, \( Q \) can be expressed as:
\[ Q = \frac{[\text{Ti}^{2+}]^2}{[\text{Cu}^{2+}]} \]

### Step 3: Analyze the Effect of Concentration Changes
To increase \( E_{\text{cell}} \), we need to manipulate the concentrations of the ions involved in the reaction:
- If we **decrease the concentration of \(\text{Ti}^{2+}\)**, the value of \( Q \) will decrease, leading to an increase in \( E_{\text{cell}} \).
- If we **increase the concentration of \(\text{Cu}^{2+}\)**, the value of \( Q \) will also decrease, leading to an increase in \( E_{\text{cell}} \).

### Step 4: Conclusion
From the analysis, we can conclude that:
- Decreasing the concentration of \(\text{Ti}^{2+}\) will increase \( E_{\text{cell}} \).
- Increasing the concentration of \(\text{Cu}^{2+}\) will also increase \( E_{\text{cell}} \).

Thus, the conditions that will increase \( E_{\text{cell}} \) are:
1. Decreasing the concentration of \(\text{Ti}^{2+}\).
2. Increasing the concentration of \(\text{Cu}^{2+}\).

### Final Answer
To increase \( E_{\text{cell}} \), you can:
1. Decrease the concentration of \(\text{Ti}^{2+}\).
2. Increase the concentration of \(\text{Cu}^{2+}\).

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