The potential of the Daniell cell,
`Zn|(ZnSO_4),((1M))||(CuSO_4),((1M))|Cu` was reported by Buckbee, Surdzial, and Metz at `E^@ = 1 . 1028 - 0. 41 xx 10^(-3) T + 0. 72 xx 10^(-5) T^2` where T is the Celsius temperature. Calculate `Delta S^@` for the cell reaction at `235^@ C`,.

Options

A. `-45.32 EU`
B. `-34.52 EU`
C. `-25.43 EU`
D. `-54.23 EU`

Explanation

To calculate the standard entropy change (ΔS°) for the Daniell cell reaction at 25°C (298 K), we will follow these steps:

### Step 1: Understand the Reaction
The Daniell cell reaction can be represented as:
\[ \text{Zn}^{2+} + \text{Cu} \rightarrow \text{Zn} + \text{Cu}^{2+} \]
In this reaction, zinc is oxidized and copper is reduced.

### Step 2: Identify the Number of Electrons Transferred (n)
From the balanced equation, we see that 2 electrons are transferred in the reaction:
\[ n = 2 \]

### Step 3: Write the Expression for ΔS°
The relationship between the change in standard entropy (ΔS°) and the change in standard cell potential (E°) with respect to temperature (T) is given by:
\[ \Delta S° = -nF \frac{dE°}{dT} \]
where:
- \( F \) is Faraday's constant (approximately 96500 C/mol).

### Step 4: Differentiate E° with Respect to Temperature
The given expression for the standard cell potential E° is:
\[ E° = 1.1028 - 0.41 \times 10^{-3} T + 0.72 \times 10^{-5} T^2 \]
To find \( \frac{dE°}{dT} \), we differentiate E° with respect to T:
\[ \frac{dE°}{dT} = -0.41 \times 10^{-3} + 2 \times 0.72 \times 10^{-5} T \]

### Step 5: Substitute T = 298 K into the Derivative
Now, substituting \( T = 298 \) K into the derivative:
\[ \frac{dE°}{dT} = -0.41 \times 10^{-3} + 2 \times 0.72 \times 10^{-5} \times 298 \]
Calculating this gives:
\[ \frac{dE°}{dT} = -0.41 \times 10^{-3} + 0.00042816 \approx -0.641 \times 10^{-3} \]

### Step 6: Calculate ΔS°
Now we can substitute \( n \), \( F \), and \( \frac{dE°}{dT} \) into the ΔS° expression:
\[ \Delta S° = -nF \frac{dE°}{dT} = -2 \times 96500 \times (-0.641 \times 10^{-3}) \]
Calculating this gives:
\[ \Delta S° = 2 \times 96500 \times 0.641 \times 10^{-3} \approx 54.233 \text{ EU} \]

### Step 7: Final Answer
Thus, the standard entropy change for the cell reaction at 25°C is:
\[ \Delta S° \approx -54.23 \text{ EU} \]