Which one of the following could not be liberated from a suitable electrolyte by the passage of `0.25` faraday of electricity through that electrolyte

Options

A. `0.25` mole of Ag
B. 16gm of Cu
C. 2gm of `O_(2)` (g)
D. `2.8` ltrs of `H_(2)` at STP

Explanation

To solve the problem of which substance cannot be liberated from a suitable electrolyte by the passage of 0.25 Faraday of electricity, we need to calculate the equivalents of each substance provided in the options and determine how much Faraday of electricity is required for each.

### Step-by-Step Solution:

1. **Understanding Faraday's Law of Electrolysis**:
- One equivalent of any substance requires one Faraday of electricity to be liberated.

2. **Calculate the equivalents for each substance**:
- **Silver (Ag)**:
- Given: 0.25 moles of Ag
- n-factor for Ag (Ag⁺ + e⁻ → Ag) = 1
- Equivalents = moles × n-factor = 0.25 × 1 = **0.25 equivalents**
- Faraday required = 0.25 equivalents → **0.25 Faraday**.

- **Copper (Cu)**:
- Given: 16 grams of Cu
- Molar mass of Cu = 63.5 g/mol
- n-factor for Cu (Cu²⁺ + 2e⁻ → Cu) = 2
- Equivalents = mass / (molar mass × n-factor) = 16 / (63.5 / 2) = 16 / 31.75 = **0.504 equivalents**.
- Faraday required = 0.504 equivalents → **0.504 Faraday**.

- **Oxygen (O₂)**:
- Given: 2 grams of O₂
- Molar mass of O₂ = 32 g/mol
- n-factor for O₂ (O₂ + 4e⁻ → 2O²⁻) = 4
- Equivalents = mass / (molar mass × n-factor) = 2 / (32 / 4) = 2 / 8 = **0.25 equivalents**.
- Faraday required = 0.25 equivalents → **0.25 Faraday**.

- **Hydrogen (H₂)**:
- Given: 2.8 liters of H₂ at STP
- Volume = 2.8 L
- Molar volume at STP = 22.4 L/mol
- Moles of H₂ = volume / molar volume = 2.8 / 22.4 = **0.125 moles**.
- n-factor for H₂ (2H⁺ + 2e⁻ → H₂) = 2
- Equivalents = moles × n-factor = 0.125 × 2 = **0.25 equivalents**.
- Faraday required = 0.25 equivalents → **0.25 Faraday**.

3. **Determine which substance cannot be liberated**:
- From the calculations:
- Silver (Ag) requires 0.25 Faraday.
- Oxygen (O₂) requires 0.25 Faraday.
- Hydrogen (H₂) requires 0.25 Faraday.
- Copper (Cu) requires **0.504 Faraday**.

- Since copper requires more than 0.25 Faraday, it cannot be liberated by the passage of 0.25 Faraday of electricity.

### Final Answer:
**Copper (Cu)** cannot be liberated from a suitable electrolyte by the passage of 0.25 Faraday of electricity.