How long in minutes must a cell run to produce 14.25g of Na(l) in molten NaCl(l) elecrolytic cell that is operating at 14.0 A?
To determine the time required, we need to use Faraday's laws of electrolysis, which state that the amount of substance produced or consumed in an electrochemical reaction is directly proportional to the charge passed through the cell.
Since we are given the current, we can use the equation:
Q = I * t
where Q is the charge in Coulombs (C), I is the current in Amperes (A), and t is the time in seconds (s).
We need to find the charge required to produce 14.25g of Na. First, we need to convert the grams of Na to moles:
molar mass of Na = 22.99 g/mol
moles of Na = 14.25 g / 22.99 g/mol = 0.620 mol
Next, we can calculate the charge using Faraday's constant:
1 mol of electrons = 1 Faraday
1 Faraday = 96485 C
charge (Q) = moles of electrons * Faraday's constant
Q = 0.620 mol * 96485 C/mol = 59697 C
Now, we can rearrange the equation Q = I * t to solve for time (t):
t = Q / I
t = 59697 C / 14.0 A = 4264 seconds
Finally, we can convert seconds to minutes:
4264 seconds = 4264 seconds * (1 minute / 60 seconds) = 71.07 minutes
Therefore, the cell must run for approximately 71.07 minutes to produce 14.25g of Na.