Final answer:
To calculate the average current in an electrolytic cell, determine the change in hydroxide ion concentration from the pH change, calculate the total charge transferred using Faraday's constant, and divide by the total elapsed time.
Step-by-step explanation:
The question is asking to calculate the average current that flowed through an electrolytic cell given a change in hydroxide ion concentration, the volume of the solution, and the total elapsed time of the electrolysis.
First, we calculate the moles of hydroxide ions (OH-) produced using the pH change. The pH scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration. The relationship between pH and hydroxide ion concentration is given by the equation:
\( pOH = 14 - pH \)
\( [OH^-] = 10^{-pOH} \)
To find the change in concentration of OH-, we calculate for both initial and final pH values:
\( pOH_{initial} = 14 - 4.63 = 9.37 \)
\( pOH_{final} = 14 - 11.87 = 2.13 \)
\( [OH^-]_{initial} = 10^{-9.37} \)
\( [OH^-]_{final} = 10^{-2.13} \)
We then find the difference in moles of OH- in the 50.0 mL solution:
\( \Delta[OH^-] = [OH^-]_{final} - [OH^-]_{initial} \)
\( \Delta moles_{OH^-} = \Delta[OH^-] \times Volume \)
\( Volume = 50.0 mL = 0.050 L \)
The total charge (in coulombs) associated with the production of OH- can be found using Faraday's laws of electrolysis, which state that one mole of electrons corresponds to the Faraday constant (F = 96485 C/mol).
\( Charge = n \times F \)
where n is the moles of electrons, which equals the moles of OH- in the case of water electrolysis (since each OH- ion is produced by the acceptance of one electron).
Finally, the average current, I, is given by:
\( I = \frac{Charge}{Time} \)
Time is the total elapsed time in seconds (23 minutes and 47 seconds).
The electrolysis problem combines stoichiometry and electric current calculations to determine the required answer.