If 4.00 g of metal is plated in the voltaic cell (which contains Ag and Ni with the total potential of 2.98 V) , how much metal is plated in the electrolytic cell (contains Ag and Zn with the total of 1.98 V)?
To determine how much metal is plated in the electrolytic cell, we can use Faraday's laws of electrolysis.
Faraday's first law states:
"The mass of any element deposited during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte."
Mathematically, this can be expressed as:
m = (Q * M) / (n * F)
where:
m = mass of the metal plated
Q = quantity of electricity passed through the electrolyte (in Coulombs)
M = molar mass of the metal
n = number of moles of electrons transferred
F = Faraday's constant (96485 C/mol)
Faraday's second law states:
"The mass of different elements deposited during electrolysis is directly proportional to their molar masses and the quantity of electricity passed through the electrolyte."
For the voltaic cell, we are given the total potential of 2.98 V. Since the potential difference is related to the quantity of electricity (Q) passed through the cell, we can use this to calculate the value of Q for the voltaic cell.
For the electrolytic cell, we are given the total potential of 1.98 V. Again, we can use this potential difference to find the quantity of electricity (Q) passed through the cell.
Since we are comparing the amount of metal plated in the voltaic and electrolytic cells, we assume that the same quantity of electricity passes through both cells.
Now, let's calculate the quantity of electricity (Q) passed through the voltaic cell:
E = Q * V
Q = E / V
Q = 4.00 g * (1 mol / M) * (96485 C / 1 mol) / 2.98 V
Q = (4.00 g / M) * 32505 C / V
where E is the energy (in Joules) produced by the voltaic cell. The molar mass of the plated metal (M) is unknown at this point.
Using the same logic, we can calculate the quantity of electricity (Q) passed through the electrolytic cell:
Q = (m / M) * 32505 C / 1.98 V
Now, we can set the two equations for Q equal to each other:
(4.00 g / M) * 32505 C / V = (m / M) * 32505 C / 1.98 V
Simplifying, we can cancel out C, V, and the constant factor (32505):
4.00 / V = m / (1.98 M)
Now, we can rearrange the equation to solve for m:
m = (4.00 / V) * (1.98 M)
Substituting the given values for V (1.98 V) and M (molar mass of the metal in the electrolytic cell), we can calculate the mass of the metal plated in the electrolytic cell (m).