The standard potential of the cell formed by combining the `Cl_(2)//Cl^(-)(aq)` half - cell with the standard hydrogen electrode is `+1.36V and ((delE^(@))/(delT))_(P)=-1.2xx10^(-3)VK^(-1)`. What is the value of `DeltaS_("reaction")^(@)` for reaction
`H_(2(g))+Cl_(2(g))rarr2H_((aq))^(+)+2Cl_((aq))^(-)`

Options

A. `-1xx10^(2)JK^(-1)`
B. `2.3xx10^(2)JK^(-1)`
C. `-2.3xx10^(2)JK^(-1)`
D. `1JK^(-1)`

Answer

To find the value of ΔS° for the reaction \( H_2(g) + Cl_2(g) \rightarrow 2H^+(aq) + 2Cl^-(aq) \), we can use the relationship between the standard cell potential, temperature coefficient, and the change in entropy. Here are the steps to solve the problem:

### Step 1: Identify the given data
- Standard cell potential, \( E° = +1.36 \, V \)
- Temperature coefficient, \( \left( \frac{\Delta E°}{\Delta T} \right)_{P} = -1.2 \times 10^{-3} \, V/K \)
- The reaction: \( H_2(g) + Cl_2(g) \rightarrow 2H^+(aq) + 2Cl^-(aq) \)

### Step 2: Determine the number of electrons transferred (n)
In the given reaction:
- \( H_2 \) is oxidized to \( 2H^+ \), releasing 2 electrons.
- \( Cl_2 \) is reduced to \( 2Cl^- \), consuming 2 electrons.

Thus, the total number of electrons transferred, \( n = 2 \).

### Step 3: Use the formula to calculate ΔS°
The relationship between the change in entropy (ΔS°), Faraday's constant (F), the number of electrons (n), and the temperature coefficient of the cell potential is given by:
\[ \Delta S° = -nF \left( \frac{\Delta E°}{\Delta T} \right)_{P} \]
Where:
- \( F \) (Faraday's constant) = \( 96500 \, C/mol \)

### Step 4: Substitute the values into the formula
Substituting the known values into the equation:
\[ \Delta S° = -2 \times 96500 \, C/mol \times (-1.2 \times 10^{-3} \, V/K) \]

### Step 5: Calculate ΔS°
Now, calculating the value:
\[ \Delta S° = 2 \times 96500 \times 1.2 \times 10^{-3} \]
\[ \Delta S° = 2 \times 96500 \times 0.0012 \]
\[ \Delta S° = 2 \times 115.8 \, J/K \]
\[ \Delta S° = 231.6 \, J/K \]

### Final Result
Thus, the value of \( \Delta S° \) for the reaction is:
\[ \Delta S° \approx 232 \, J/K \]