An acidic solution of dichromate is electrolyzed for 8 minutes using 2A current. As per the following equation
Cr₂O₇²⁻ + 14H⁺ + 6e – → 2Cr³⁺ + 7H₂O
The amount of Cr³⁺ obtained was 0.104 g. The efficiency of the process(in%) is (Take : F = 96000 C, At. mass of chromium = 52) ______.

Solution

Chemistry ma’am · 4 steps

Find the Cr³⁺ the current could have made, then compare it with the 0.104 g you actually got.

1. Charge passed. Q = It = 2 A × 480 s = 960 C. Dividing by F gives 960/96000 = 0.01 mol of electrons.
2. Electrons per ion. The equation uses 6 electrons to make 2 Cr³⁺, so each Cr³⁺ needs 3 electrons. That fits chromium going from +6 to +3.

   n_(Cr³⁺)(theoretical) = 0.01/3 = 3.33 × 10⁻³ mol ⇒ m = 3.33 × 10⁻³ × 52 = 0.1733 g

3. Compare with actual. Efficiency = 0.104/0.1733 × 100 = 60%. As a check, 0.104/52 = 0.002 mol of Cr³⁺ used 0.006 mol of electrons, out of the 0.01 mol supplied.
4. So. The efficiency of the process is 60%.

The common slip: 120. Taking 6 electrons per Cr³⁺ instead of 3 halves the theoretical yield to 0.0867 g and gives 120%, which is impossible for an efficiency.

The idea to keep. Current efficiency is the actual product divided by what the full charge could make. Always read the electrons per product ion from the balanced equation.

Answer from the NTA final answer key. Solution by PrepWiser.