If 3.25x10-3 kg of gold is deposited onto the negative electrode of an electrolytic cell in a period of 2.78 hours, what is the current through this cell in amperes? Assume that the gold ions carry one elementary unit of charge
To find the current through the cell, you can use the formula:
Current (I) = Charge (Q) / Time (t)
To find the charge deposited on the electrode, you can use the formula:
Charge (Q) = Mass (m) * charge per unit mass (z)
The given mass is 3.25x10^-3 kg, and we are assuming that the gold ions carry one elementary unit of charge. Therefore, the charge per unit mass (z) is 1.
Let's calculate the charge first:
Q = m * z
Q = (3.25x10^-3 kg) * 1
Q = 3.25x10^-3 C
Now, we can calculate the current:
I = Q / t
I = (3.25x10^-3 C) / (2.78 hours)
To convert hours to seconds, we multiply by 3600:
I = (3.25x10^-3 C) / (2.78 hours * 3600 s/hour)
I = (3.25x10^-3 C) / (10008 s)
I ≈ 3.25x10^-7 A
Therefore, the current through the cell is approximately 3.25x10^-7 Amperes.
To determine the current through the electrolytic cell, we can use Faraday's law of electrolysis. According to this law, the amount of substance deposited at an electrode is directly proportional to the electric charge passed through the cell.
Faraday's law can be written as:
m = (Q * M) / (n * F)
Where:
m is the mass of the substance deposited (in kilograms)
Q is the electric charge passed through the cell (in coulombs)
M is the molar mass of the substance (in kilograms per mole)
n is the number of moles of substance
F is the Faraday constant (approximately 96485 C/mol)
In this case, we need to find the electric charge passed through the cell, given the mass of gold deposited and assuming gold ions carry one elementary unit of charge.
Step 1: Convert the mass of gold deposited to moles.
To do this, we divide the mass of gold by its molar mass.
molar mass of gold (Au) = 197 g/mol
mass of gold deposited = 3.25 x 10^(-3) kg = 3.25 g
moles of gold = (mass of gold deposited) / (molar mass of gold)
Step 2: Calculate the electric charge passed through the cell.
Since each gold ion carries one elementary unit of charge, the number of moles of gold is equal to the number of elementary charges (Q).
Q = moles of gold
Step 3: Convert the electric charge from elementary charges to coulombs.
To do this, we multiply the elementary charges by the charge of one electron (1.602 x 10^(-19) C) to get the charge in coulombs.
charge in coulombs (Q) = (moles of gold) * (Avogadro's number) * (elementary charge)
Step 4: Convert the time period to seconds.
The time given is in hours. We know that 1 hour is equal to 3600 seconds.
time in seconds = 2.78 hours * 3600 seconds/hour
Step 5: Calculate the current through the cell.
Current (I) is defined as the electric charge (Q) passing through the cell divided by the time (t) taken.
Current (I) = charge (Q) / time (t)
Substitute the calculated values into the equation to find the current in amperes.
Please let me know if you need any further assistance in calculating the current through the cell.