The time required to produce 10.0g of chromium metal from a 0.10mol/L solution of chromium (3) nitrate in an electrolytic cell is dependent on
several factors including the current applied, the size of the electrodes, and the efficiency of the electrolytic cell.
The amount of chromium metal produced in an electrolytic cell is directly related to the amount of charge passed through the cell. According to Faraday’s laws of electrolysis, one mole of electrons (e-) is required to produce one mole of chromium metal.
To calculate the time required to produce 10.0g of chromium metal, we need to determine the number of moles of chromium metal and then the amount of charge needed to produce that amount.
First, we convert the mass of chromium metal to moles using the molar mass of chromium (Cr), which is 52.00 g/mol:
10.0 g Cr × (1 mol Cr / 52.00 g Cr) = 0.192 mol Cr
Since one mole of chromium metal requires one mole of electrons (e-), the amount of charge needed can be calculated using Faraday's constant (F), which is 96,485 C/mol:
Charge (C) = 0.192 mol Cr × 96,485 C/mol = 18,565 C
Once the amount of charge needed is known, we can determine the time required to pass that amount of charge through the cell using the current (I) and the equation Q = I × t, where Q is the charge in coulombs and t is the time in seconds. Rearranging the equation gives us t = Q / I.
The current depends on the size of the electrodes and the efficiency of the electrolytic cell. A higher current will result in a faster rate of production, while a lower current will require a longer time.
Therefore, the specific time required to produce 10.0g of chromium metal from a 0.10mol/L solution of chromium (3) nitrate in an electrolytic cell cannot be determined without more information about the current and the efficiency of the cell.