For `Pt(H_(2))|H_(2)O` , reduction potential at `298 K` and `1 atm` is `:`

Options

A. `-0.23V`
B. `-0.41V`
C. `0.41V`
D. `0.00V`

Explanation

To find the reduction potential for the half-cell reaction `Pt(H₂)|H₂O` at 298 K and 1 atm, we can follow these steps:

### Step 1: Write the oxidation half-reaction
The oxidation reaction for hydrogen can be written as:
\[ \text{H}_2 \rightarrow 2\text{H}^+ + 2e^- \]

### Step 2: Determine the reaction quotient (Q)
For this reaction, the reaction quotient \( Q \) is given by the concentration of the products raised to the power of their coefficients divided by the concentration of the reactants raised to the power of their coefficients. In this case:
\[ Q = \frac{[\text{H}^+]^2}{P_{\text{H}_2}} \]
Given that the concentration of \( \text{H}^+ \) in pure water is \( 10^{-7} \, \text{M} \) and the pressure of \( \text{H}_2 \) is 1 atm, we can calculate \( Q \):
\[ Q = \frac{(10^{-7})^2}{1} = 10^{-14} \]

### Step 3: Use the Nernst equation
The Nernst equation is given by:
\[ E = E^0 - \frac{0.0591}{n} \log Q \]
Where:
- \( E^0 \) is the standard reduction potential (0 V for the hydrogen electrode).
- \( n \) is the number of moles of electrons transferred (2 for this reaction).

Substituting the values into the equation:
\[ E = 0 - \frac{0.0591}{2} \log(10^{-14}) \]

### Step 4: Calculate the logarithm
The logarithm of \( 10^{-14} \) is:
\[ \log(10^{-14}) = -14 \]

### Step 5: Substitute the logarithm value into the Nernst equation
Now substituting back:
\[ E = -\frac{0.0591}{2} \times (-14) \]
\[ E = \frac{0.0591 \times 14}{2} \]

### Step 6: Perform the calculation
Calculating the above expression:
\[ E = \frac{0.8264}{2} = 0.4132 \, \text{V} \]

### Step 7: Change the sign for reduction potential
Since we are looking for the reduction potential, we take the negative of the calculated value:
\[ E_{\text{reduction}} = -0.4132 \, \text{V} \]

### Final Answer
The reduction potential at 298 K and 1 atm for the half-cell `Pt(H₂)|H₂O` is approximately:
\[ \text{E} = -0.4132 \, \text{V} \]