Question

In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to $ \text{Cr}^{3+} $. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of $ \text{Cr}^{3+} $ is ____. {Use: 1 Faraday $ = 96500 \, \text{C mol}^{-1} $

Hint:

For electrochemical calculations, always relate the number of moles of electrons to moles of substance using Faraday's law: \( Q = nF \), and then apply \( Q = it \) to find the current.

Answer 1

Correct Answer: 100

Step 1: Write the balanced half-reaction
The reduction of dichromate ions in acidic medium is given by: \[ {Cr_2O_7^{2-} + 14H^+ + 6e^- -> 2Cr^{3+} + 7H2O} \] From the equation, 6 moles of electrons reduce 2 moles of \( {Cr^{3+}} \). So, to produce 1 mole of \( {Cr^{3+}} \), only 3 moles of electrons are needed.
Step 2: Use Faraday's laws of electrolysis 
Total charge \( Q = n \times F = 3 \times 96500 = 289500 \, \text{C} \)
Step 3: Use relation \( Q = i \times t \) 
Time \( t = 48.25 \, \text{minutes} = 48.25 \times 60 = 2895 \, \text{seconds} \)
So, \[ i = \frac{Q}{t} = \frac{3 \times 96500}{48.25 \times 60} = \frac{289500}{2895} = \boxed{100 \, \text{A}} \]