`Pt |{:((H_(2))),(1atm):}:| pH = 2:|:|:pH =3 |:{:((H_(2))Pt),(1atm):}:|`. The cell reaction for the given cell is:-

Options

A. spontaneous
B. non-spontaneous
C. equilibrium
D. none is correct

Explanation

To determine the cell reaction for the given electrochemical cell, we will follow these steps:

### Step 1: Identify the Components of the Cell
The cell representation is given as:
\[ \text{Pt} | \text{H}_2 (1 \text{ atm}) | \text{pH} = 2 || \text{pH} = 3 | \text{H}_2 \text{Pt} (1 \text{ atm}) \]

This indicates that we have two half-cells:
- The left half-cell has hydrogen gas at 1 atm and a pH of 2.
- The right half-cell has hydrogen gas at 1 atm and a pH of 3.

### Step 2: Determine the pH Values
- For the left half-cell, pH = 2.
- For the right half-cell, pH = 3.

### Step 3: Use the Nernst Equation
The Nernst equation relates the cell potential (E_cell) to the pH values:
\[ E_{\text{cell}} = 0.059 \times (pH_1 - pH_2) \]

Where:
- \( pH_1 \) is the pH of the left half-cell (2).
- \( pH_2 \) is the pH of the right half-cell (3).

### Step 4: Substitute the pH Values into the Equation
Substituting the values into the equation:
\[ E_{\text{cell}} = 0.059 \times (2 - 3) \]
\[ E_{\text{cell}} = 0.059 \times (-1) \]
\[ E_{\text{cell}} = -0.059 \, \text{V} \]

### Step 5: Analyze the Result
The calculated cell potential \( E_{\text{cell}} \) is negative:
- A negative \( E_{\text{cell}} \) indicates that the cell reaction is non-spontaneous.

### Conclusion
The cell reaction for the given electrochemical cell is non-spontaneous.

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