Chromium metal can be plated onto an object from an acidic solution of dichromate ions. What average current is required to plate 17.8 g of chromium metal in a time of 2.20 h?
amperes x seconds = coulombs.
96,485 coulombs will deposit 1 equivalent weight of Cr.
Equivalent weight Cr = atomic mass/change in number of electrons in the half reaction.
To find the average current required to plate 17.8 g of chromium metal in a time of 2.20 hours, we can use Faraday's law of electrolysis and the molar mass of chromium.
The key equation is:
Q = n * F
Where:
- Q is the total electric charge (measured in coulombs)
- n is the number of moles of metal being plated
- F is the Faraday constant, which is the charge of one mole of electrons (1 F = 96,485 C/mol)
To find the number of moles (n) of chromium being plated, we can use the molar mass of chromium (Cr), which is approximately 52 g/mol.
n = mass / molar mass
n = 17.8 g / 52 g/mol
n ≈ 0.342 moles
Next, we need to find the total charge (Q) required to plate this amount of chromium. We can use the equation:
Q = n * F
Q = 0.342 moles * 96,485 C/mol
Q ≈ 33,023 C
Now, we can find the average current (I) required using the equation:
I = Q / t
Where:
- I is the average current (in amperes)
- Q is the total charge (in coulombs)
- t is the time taken (in seconds)
First, we need to convert the time from hours to seconds:
t = 2.20 hours * 3600 seconds/hour
t = 7,920 seconds
Now, we can calculate the average current:
I = 33,023 C / 7920 s
I ≈ 4.17 A
Therefore, the average current required to plate 17.8 g of chromium metal in a time of 2.20 hours is approximately 4.17 Amperes.
To determine the average current required to plate a certain amount of chromium metal in a given time, we can use Faraday's law of electrolysis. The formula is as follows:
Mass of substance (g) = (Current (A) x Time (s) x Atomic mass (g/mol)) / (Faraday's constant (C/mol))
First, we need to calculate the moles of chromium (Cr) using its atomic mass. The atomic mass of chromium is approximately 52 g/mol.
Moles of Cr = Mass of Cr / Atomic mass of Cr
Moles of Cr = 17.8 g / 52 g/mol
Next, we need to convert the given time into seconds. Since the given time is in hours, we multiply it by 60 (minutes) and again by 60 (seconds).
Time (s) = 2.20 h x 60 min/h x 60 s/min
Now we can calculate the average current by rearranging the formula and solving for it.
Current (A) = (Mass of Cr x Faraday's constant) / (Time (s) x Atomic mass of Cr)
The Faraday's constant is approximately 96485 C/mol.
Now let's substitute the values in the formula:
Current (A) = (17.8 g x 96485 C/mol) / (2.20 h x 60 min/h x 60 s/min x 52 g/mol)
Evaluating this expression will give us the average current required to plate 17.8 g of chromium metal in a time of 2.20 hours.