Using a current of 4.0A, how many hours would it take to deposit a silver 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/cm3
Oh, so you're looking to get all scientific on me, huh? Alright, hold on tight because I'm about to electrify you with some electrifying humor!
If you want to deposit a silver coating, well, I hope you have strong currents running through you to keep up with all the electricity puns flowing your way. Now, let's calculate how long it would take to deposit that silver coating.
First, we need to convert the thickness to meters because we're all about using the metric system. So, 0.2mm becomes 0.002m.
Next, let's calculate the volume by multiplying the thickness (0.002m) by the surface area (30cm^2). But hey, since we're all about using consistent units, let's convert the surface area to square meters because that's what the cool kids do. So, 30cm^2 becomes 0.003m^2.
Now, let's multiply the volume (0.002m * 0.003m^2) with the density of silver (10.5g/cm^3). But oh no, we need to convert the volume to cubic meters since that's what density wants. So, 0.002m * 0.003m^2 becomes 0.000018m^3.
Finally, divide the volume (0.000018m^3) by the current (4.0A) to determine the time it would take. And voila! You'd get the time in seconds.
But hey, since you asked for hours, we'll divide the time in seconds by 3600 (because there's 3600 seconds in an hour) to give you the final answer in terms of hours.
And there you have it! The time it would take to deposit that silver coating using electrolysis of Ag(CN)2 using a current of 4.0A on a metal with a surface area of 30cm^2.
But hey, instead of giving you the boring answer, how about this: it would take "long enough for you to sit back and watch a full season of your favorite TV show... twice!" Now that's electrifyingly entertaining, isn't it? Keep shining bright!
To determine the time required for depositing a silver coating, we need to calculate the amount of silver that needs to be deposited and then use Faraday's law of electrolysis to relate this amount to the current and time.
Step 1: Calculate the volume of silver to be deposited:
The volume (V) of silver needed can be calculated using the formula:
V = A × d × t
where A is the surface area, d is the thickness, and t is the volume.
Given:
Surface area (A) = 30 cm^2
Thickness (d) = 0.2 mm = 0.02 cm
V = 30 cm^2 × 0.02 cm
V = 0.6 cm^3
Step 2: Calculate the mass of silver to be deposited:
The mass (m) of silver needed can be calculated using the formula:
m = V × density
where V is the volume and density is the density of silver.
Given:
Density of silver = 10.5 g/cm^3
m = 0.6 cm^3 × 10.5 g/cm^3
m = 6.3 g
Step 3: Use Faraday's law to calculate the time required:
Faraday's law states that the mass of a substance produced or consumed during electrolysis is directly proportional to the electric charge (Q) passed through the electrolyte.
The formula for Faraday's law is:
m = Q × M / (z × F)
where m is the mass, Q is the charge, M is the molar mass, z is the number of electrons involved in the reaction, and F is Faraday's constant.
Given:
Current (I) = 4.0 A
Molar mass of Ag(CN)2 = 133.9 g/mol (Ag: 107.9 g/mol, C: 12.0 g/mol, N: 14.0 g/mol)
Number of electrons involved (z) = 2 (from the formula Ag(CN)2)
First, we need to calculate the moles (n) of silver using the mass formula:
n = m / M
n = 6.3 g / 133.9 g/mol
n = 0.0471 mol
Next, we can calculate the charge using Faraday's law:
Q = n × z × F
Q = 0.0471 mol × 2 × 96,485 C/mol
Q = 9,101 C
Now, we can find the time (t) required using the formula for charge and current:
Q = I × t
t = Q / I
t = 9,101 C / 4.0 A
t = 2,275.25 s
To convert the time to hours, divide the above result by 3600 (60 seconds × 60 minutes):
t = 2,275.25 s / 3600
t = 0.6318 hours (rounded to 4 decimal places)
Therefore, it would take approximately 0.632 hours to deposit a silver coating of 0.2 mm thick on a metal with a surface area of 30 cm^2 during electrolysis of Ag(CN)2 using a current of 4.0 A.
To determine the time it would take to deposit a silver coating of 0.2mm thickness on a metal during electrolysis, we need to use Faraday's laws of electrolysis. Faraday's laws state that the amount of a substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.
First, let's calculate the volume of the silver coating:
Volume = surface area x thickness
Volume = 30 cm^2 x 0.2 mm
However, since the density of silver is given in g/cm^3, we need to convert the volume into cubic centimeters.
Volume = 30 cm^2 x 0.2 mm x 0.1 cm/mm
Next, we can determine the mass of the silver coating using the volume and the density of silver:
Mass = Volume x Density
Mass = 30 cm^2 x 0.2 mm x 0.1 cm/mm x 10.5 g/cm^3
Now, to find the quantity of electricity passed through the electrolyte, we can use the formula:
Quantity of electricity (Coulombs) = Current (Amperes) x Time (seconds)
Since we want to find the time, we can rearrange the formula:
Time (seconds) = Quantity of electricity (Coulombs) / Current (Amperes)
Now we need to determine the quantity of electricity required to deposit the calculated mass of silver. For this, we can use the equation:
Quantity of electricity (Coulombs) = (Mass in grams) / (Molar mass of silver) x (Faraday's constant)
The molar mass of silver (Ag) is 107.87 g/mol, and Faraday's constant is approximately 96,500 C/mol. Substituting the values:
Quantity of electricity (Coulombs) = (Mass in grams) / 107.87 g/mol x 96,500 C/mol
Lastly, we can substitute this quantity of electricity into the earlier formula to find the time:
Time (seconds) = [(Mass in grams) / 107.87 g/mol x 96,500 C/mol] / Current (Amperes)
Since the current is given as 4.0 Amperes, we can now calculate the time:
Time (seconds) = [(Mass in grams) / 107.87 g/mol x 96,500 C/mol] / 4.0 Amperes
This calculation will give us the time required in seconds. If you wish to convert it to hours, you can divide the result by 3600 (since there are 3600 seconds in an hour).