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, we can use Faraday's law of electrolysis, which states that the amount of substance deposited or liberated at an electrode is directly proportional to the quantity of electricity passed through the cell.
First, we need to calculate the amount of charge (in coulombs) required to deposit the given mass of gold. To do this, we'll use the formula:
Q = n * F
Where:
Q = charge (in coulombs)
n = number of moles of gold
F = Faraday's constant (approximately 96,485 C/mol)
To find the number of moles (n) of gold, we can use the formula:
n = mass / molar mass
The molar mass of gold (Au) is 197 g/mol, so we need to convert the given mass of gold into grams:
Mass of gold = 3.25 x 10^(-3) kg = 3.25 x 10^(-3) * 1000 g = 3.25 g
Now we can calculate the number of moles (n):
n = 3.25 g / 197 g/mol = 0.0165 mol
Now let's calculate the charge (Q):
Q = 0.0165 mol * 96,485 C/mol = 1.591 C
Finally, we can calculate the current (I) using the formula:
I = Q / t
Where:
I = current (in amperes)
Q = charge (in coulombs)
t = time (in seconds)
The given time is 2.78 hours, so we need to convert it into seconds:
Time = 2.78 hours * 60 minutes/hour * 60 seconds/minute = 10,008 seconds
Now we can calculate the current (I):
I = 1.591 C / 10,008 s = 0.000159 A
Therefore, the current through the cell is approximately 0.000159 amperes or 0.159 milliamperes.
To find the current through the electrolytic cell, we can use Faraday's Law of Electrolysis, which states that the mass of the substance deposited during electrolysis is directly proportional to the electric charge passed through the cell. The equation can be written as:
m = (Q × M) / (n × F)
Where:
m = mass of the substance deposited (kg)
Q = electric charge passed through the cell (Coulombs)
M = molar mass of the substance (kg/mol)
n = number of electrons transferred in the reaction
F = Faraday's constant (96485 C/mol)
In this case, we are given:
m = 3.25 × 10^(-3) kg (mass of gold deposited)
M = molar mass of gold = 197.0 g/mol = 0.197 kg/mol (rounded to three decimal places)
n = 1 (one elementary unit of charge for gold ions)
F = Faraday's constant = 96485 C/mol
We need to find Q, the electric charge passed through the cell.
Rearranging the equation, we have:
Q = (m × n × F) / M
Substituting the known values into the equation, we get:
Q = (3.25 × 10^(-3) kg) × (1) × (96485 C/mol) / (0.197 kg/mol)
Simplifying the equation, we find:
Q = 16,556.345 C
The electric charge passed through the cell is approximately 16,556.345 Coulombs.
Now, we can find the current (I) using the equation:
I = Q / t
where:
I = current (Amperes)
t = time (hours)
We are given:
t = 2.78 hours
Substituting the values, we get:
I = 16,556.345 C / 2.78 hours
Since 1 hour is equal to 3600 seconds, we convert the time to seconds:
t = 2.78 hours × (3600 seconds/hour) = 10008 seconds
Now, we can calculate the current (I):
I = 16,556.345 C / 10008 seconds
Calculating this expression, we find:
I ≈ 1.654 A
Therefore, the current through the electrolytic cell is approximately 1.654 Amperes.