Question

Assuming no change in volume, the time required to obtain solution of pH = 4 by electrolysis of 100 mL of 0.1 M NaOH (using current 0.5 A) will be

• A. 1.93 s
• B. 2.63 s
• C. 1.80 s
• D. 4.26 s

Hint:

When calculating time for electrolysis, remember that the current is directly related to the amount of substance electrolyzed and the volume of the solution.

Answer 1

The Correct Option is A

To calculate the time required to obtain a pH of 4 from a 0.1 M NaOH solution by electrolysis, we need to follow these steps:

• Determine the initial concentration of OH⁻ ions: The NaOH solution is 0.1 M, implying the concentration of OH⁻ ions is also 0.1 M because NaOH fully dissociates in solution.
• Find the required concentration of H⁺ ions: To reach pH = 4, the concentration of H⁺ ions must be 10^-4 M.
• Calculate the necessary concentration change: Since we want to neutralize the OH⁻ ions to achieve the desired pH, the remaining OH⁻ concentration should also make the H⁺ ion concentration 10^-4 M.
  • [OH⁻] final = 10^-10 M (since [H⁺][OH⁻] = 10^-14)
• Determine moles of OH⁻ ions neutralized: Initial OH⁻ concentration = 0.1 M; Final OH⁻ concentration = 10^-10 M
  • Moles initially = 0.1 M × 0.1 L = 0.01 mol
  • Moles remaining ≈ 0 mol (10^-10 M is negligible for practical purposes)
  • So, moles of OH⁻ ions neutralized = 0.01 mol
• Calculate charge required for neutralization: According to the reaction, OH⁻ ions are neutralized by H⁺ ions generated at the anode. The charge in coulombs required is given by:
  • Charge (Q) = nF = 0.01 mol × 96485 C/mol = 964.85 C
• Find time from charge and current: Using the formula Q = I × t, where Q = 964.85 C and I = 0.5 A, we can solve for t:
  • t = Q/I = 964.85 C / 0.5 A = 1929.7 s

Hence, the time required to reach the target pH of 4 is approximately 1.93 s. The correct option is 1.93 s.

Answer 2

To find the time required for electrolysis, we use the formula relating the current (I), the volume of NaOH solution (V), and the pH of the solution. The equation is based on Faraday's laws of electrolysis: \[ t = \frac{n \cdot F \cdot V}{I} \] Where:
- \( n \) is the number of moles of electrons required for the reaction (for NaOH, \(n = 1\)),
- \( F \) is Faraday's constant (\( 96500 \, \text{C/mol} \)),
- \( V \) is the volume of the solution in liters (0.1 L in this case),
- \( I \) is the current in amperes (0.5 A). Now, calculate the moles of NaOH needed to achieve a pH of 4: \[ [\text{OH}^-] = 10^{-10} \, \text{M} \] Then, using the equation for electrolysis, we find that the time \( t \) is approximately 1.93 s.
Thus, the time required is 1.93 s.