A total charge of 96.5 kC is passed through an electrolytic cell. What mass of copper will be produced from a copper(II) chloride solution?
Answer in units of g
To calculate the mass of copper produced from a copper(II) chloride solution, we need to use the Faraday's law of electrolysis. According to this law, the amount of substance produced at an electrode is directly proportional to the total charge passed through the cell.
The formula to calculate the mass of a substance produced can be given by:
Mass = (Total charge passed * molar mass) / (Faraday's constant * charge on the ion)
First, we need to determine the relevant information for the calculation.
The molar mass of copper (Cu) is 63.5 g/mol.
The charge on copper (Cu²⁺) ion is +2.
Faraday's constant (F) is 96,485 C/mol.
Next, we substitute the values into the formula to calculate the mass of copper produced:
Mass = (96.5 kC * 63.5 g/mol) / (96,485 C/mol * 2)
Simplifying this equation, we get:
Mass = (96,500 C * 63.5 g) / (96,485 C * 2)
Mass = 6,124,750 g / 192,970 C
Mass ≈ 31.76 g
Therefore, approximately 31.76 grams of copper will be produced from the copper(II) chloride solution.
To determine the mass of copper produced, we need to calculate the number of moles of copper and then convert it to grams using the molar mass of copper.
To find the number of moles of copper, we can use Faraday's law of electrolysis, which states that the amount of substance produced during electrolysis is directly proportional to the charge passed through the cell.
The formula for Faraday's law is:
moles of substance = (charge passed / Faraday's constant) * (1 / n)
Where:
- charge passed is given as 96.5 kC (kC = kilocoulombs)
- Faraday's constant is 96,485 C/mol
- n is the number of electrons involved in the reaction, which is determined by the balanced equation for the reaction.
In this case, we're electrolyzing copper(II) chloride (CuCl2) solution. The balanced half-reaction for the reduction of copper(II) ions (Cu^2+) to copper (Cu) during electrolysis is:
Cu^2+ + 2e^- → Cu
Here, we can see that 2 electrons are involved in the reduction of each Cu^2+ ion.
Now, substituting the values into the equation:
moles of copper = (96.5 kC / 96,485 C/mol) * (1 / 2)
Simplifying the equation:
moles of copper = 0.000501 mol
To find the mass of copper, we need to multiply the number of moles by the molar mass of copper. The molar mass of copper is approximately 63.55 g/mol.
Mass of copper = moles of copper * molar mass of copper
Mass of copper = 0.000501 mol * 63.55 g/mol
Mass of copper ≈ 0.0318 g
Therefore, the mass of copper produced from the copper(II) chloride solution is approximately 0.0318 grams.