Question

When 1 g hydrogen (ECE = \(1.044 \times 10^{-8} \, \text{kg C}^{-1}\)) forms water, 34 kcal heat is liberated. The minimum voltage required to decompose water is :

• A. 0.75 V
• B. 3 V
• C. 1.5 V
• D. 4.5 V

Hint:

Use \(E = VQ\) and electrochemical equivalent relation to connect energy and charge.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The electrical energy supplied (\( V \cdot q \)) must be equal to or greater than the energy required for the chemical decomposition (heat of formation).
: Key Formula or Approach:
1. Energy in Joules \( E = 34 \text{ kcal} \times 10^3 \times 4.2 \text{ J} \).
2. Charge \( q = \frac{\text{mass}}{ECE} \).
3. \( V = E/q \).
Step 2: Detailed Explanation:
- Mass of hydrogen \( m = 1 \text{ g} = 10^{-3} \text{ kg} \).
- Charge required to liberate 1 g H:
\[ q = \frac{10^{-3} \text{ kg}}{1.044 \times 10^{-8} \text{ kg/C}} \approx 0.958 \times 10^5 \text{ C} \]
- Energy liberated/required:
\[ E = 34 \times 10^3 \times 4.2 = 142.8 \times 10^3 \text{ J} \]
- Minimum voltage:
\[ V = \frac{E}{q} = \frac{142.8 \times 10^3}{0.958 \times 10^5} \approx 1.49 \text{ V} \approx 1.5 \text{ V} \]
Step 3: Final Answer:
The minimum voltage is 1.5 V.