Using a current of 4.0A, how many hours would it take to deposit a silver using coating of 0.2mm thick on a metal with a surface area of 30cm^2 during electrolysis of Ag(CN)2. Given that the density of silver is 10.5g/cm^3
First, how much Ag must be deposited? The volume is 30 cm^2 x 0.020 cm = 0.6 cc. mass Ag = volume x density = 0.6 cc x 10.5 g/cc = 6.3 g
You know that 96,485 coulombs will deposit 107.9 g Ag so how many coulombs do you need? That's 96,485 coulombs x (6.3/107.9) = 5,634 C
C =amperes x seconds
5634 C = 4.0 x seconds.
Solve for seconds and convert to hours.
Well, the thickness of the coating sounds pretty silver-lining! Let's calculate the time it would take to deposit this shiny layer.
First, let's convert the thickness into meters. Since 1 mm is equal to 0.001 meters, the thickness of 0.2 mm would be 0.0002 meters. Now, let's calculate the volume of the silver coating on the metal.
Volume = thickness × surface area = 0.0002 m × 30 cm²
But before we continue, let's convert the surface area from cm² to m². Since 1 m² is equal to 10,000 cm², the surface area would be 30 cm² ÷ 10,000 cm²/m² = 0.003 m².
Volume = 0.0002 m × 0.003 m² = 0.0000006 m³
Next, let's calculate the mass of the silver coating using its density.
Mass = volume × density = 0.0000006 m³ × 10.5 g/cm³
But wait! We need to convert the density from g/cm³ to kg/m³. Since 1 g/cm³ is equal to 1000 kg/m³, the density would be 10.5 × 1000 kg/m³ = 10500 kg/m³.
Mass = 0.0000006 m³ × 10500 kg/m³ = 0.0063 kg
Now for the fun part – let's calculate the time!
Charge = current × time
But the charge also equals the amount of silver deposited, which is equal to the mass of the coating. So, we have:
0.0063 kg = 4.0 A × time
Rearranging the equation to solve for time:
time = 0.0063 kg / 4.0 A
And now the moment you've been waiting for... time!
time = 0.001575 hours
So, it would take approximately 0.001575 hours to deposit a silver coating 0.2 mm thick on a metal with a surface area of 30 cm² during electrolysis of Ag(CN)2.
To calculate the time it would take to deposit a silver coating of 0.2mm thick on a metal with a surface area of 30cm^2 during electrolysis, we need to calculate the amount of silver required.
Step 1: Calculate the volume of silver needed.
First, calculate the volume of the silver coating using the formula:
Volume = thickness x surface area
Volume = 0.2mm x 30cm^2
= 0.2cm x 30cm^2
= 6cm^3
Step 2: Calculate the mass of silver needed.
Since the density of silver is given as 10.5g/cm^3, we can calculate the mass of silver using the formula:
Mass = density x volume
Mass = 10.5g/cm^3 x 6cm^3
= 63g
Step 3: Calculate the charge required.
The charge required for the deposition of silver can be determined using Faraday's laws of electrolysis. One mole of Ag+ will require one mole of electrons. Based on the equation Ag(CN)2 -> Ag+ + 2e- , we can see that two moles of electrons are required to deposit one mole of Ag+.
The molar mass of silver (Ag) is 107.87g/mol. Therefore, the number of moles of silver required is:
Moles = mass / molar mass
Moles = 63g / 107.87g/mol
≈ 0.584 mol
The charge (Q) required can be calculated using Faraday's law, which states:
Q = n x F
where n is the number of moles of electrons and F is the Faraday constant (96,485 C/mol).
Q = 0.584 mol x 96,485 C/mol
≈ 56,420 C
Step 4: Calculate the time required.
The current (I) is given as 4.0A, and the charge (Q) required is 56,420 C. The relationship between current, charge, and time is given by the equation:
Q = I x t
where Q is the charge in coulombs (C), I is the current in amperes (A), and t is the time in seconds (s).
In this case, we need to find the time (t), so rearranging the equation:
t = Q / I
t = 56,420 C / 4.0 A
≈ 14,105 seconds
Finally, let's convert the time from seconds to hours:
t = 14,105 seconds / 3600 seconds/hour
≈ 3.92 hours
Therefore, it would take approximately 3.92 hours to deposit a silver coating of 0.2mm thick on a metal with a surface area of 30cm^2 using a current of 4.0A during electrolysis of Ag(CN)2.
To calculate the time required to deposit a silver coating, we need to determine the amount of silver that needs to be deposited first.
Step 1: Calculate the volume of silver needed.
Given that the thickness of the coating is 0.2mm and the surface area is 30cm², we can calculate the volume as follows:
Volume = thickness x surface area
Volume = 0.2mm x 30cm²
Step 2: Convert the volume to cubic centimeters (cm³).
Since the thickness was given in millimeters and the surface area in square centimeters, the volume is already in cubic centimeters.
Step 3: Calculate the mass of silver needed.
Given the density of silver is 10.5g/cm³, we can calculate the mass using the formula:
Mass = density x volume
Mass = 10.5g/cm³ x (0.2mm x 30cm²)
Step 4: Convert the mass to grams.
Since the mass was calculated in grams, no conversion is required.
Now that we have determined the mass of silver required, we can proceed to calculate the time.
Step 5: Use Faraday's Law to determine the time required.
Faraday's Law states that the amount of substance deposited during electrolysis is directly proportional to the quantity of electricity passed through the system.
The equation for Faraday's Law is:
Mass (g) = (Current (A) x Time (s) x Molar mass (g/mol)) / (Number of electrons x Faraday's constant)
In this case, we need to calculate the time, so we rearrange the equation as follows:
Time (s) = (Mass (g) x Number of electrons x Faraday's constant) / (Current (A) x Molar mass (g/mol))
Given that the molar mass of silver is 107.868 g/mol and the number of electrons in Ag(CN)₂ is 2, and using the mass of silver calculated in Step 3, we can substitute these values into the equation.
Finally, we divide the time in seconds by 3600 to convert it to hours since 1 hour = 3600 seconds.
Note that during the calculation, ensure consistent units are used (e.g., converting millimeters to centimeters or grams to kilograms if necessary).
By following these steps, you can calculate the time required to deposit a silver coating using electrolysis.