A baby's spoon with an area of 6.25 cm^2 is plated with silver from AgNO3 using a current of 2.00 A for two hours and 25 minutes.
a) If the current efficiency is 82.0%, how many grams of silver are plated?
b) What is the thickness of the silver plate formed (d= 10.5 g/cm^3)?
I think the efficiency part is tripping me up; I can't even think of how to start the problem. I'm guessing the efficiency has something to do with the amount done over the amount of time taken? But still; I don't know how I can relate the area of the spoon to grams of silver. Any help is appreciated.
Just calculate the current OR coulombs and multiply by 0.82 and proceed. That 82% simply means that 100 A appears to be only 82 A or 500 coulombs (just a made up number) appears to be only 0.82*500).
0.246 is the answer
i mean 0.243
To solve this problem, let's break it down step-by-step:
a) Calculating grams of silver plated:
1. We know that the current efficiency is 82.0%. This means that only 82% of the total available current is actually utilized for plating the silver.
2. To find the actual current used for plating, we need to multiply the given current by the efficiency. In this case, we have a current of 2.00 A, so the actual current used for plating is 2.00 A * 0.82 = 1.64 A.
3. We need to convert the time of plating from hours and minutes to hours. Given that plating occurred for 2 hours and 25 minutes, we have: 2 hours + 25 minutes / 60 = 2 hours + 0.42 hours = 2.42 hours.
4. Next, we calculate the total charge passed through the circuit during plating using the formula Q = I * t, where Q is the charge in Coulombs, I is the current in Amperes, and t is the time in hours.
Q = 1.64 A * 2.42 hours = 3.97 Coulombs.
5. Now we will use Faraday's law of electrolysis to calculate the grams of silver plated. The law states that 1 Faraday of charge (F) deposits 1 mol of silver.
1 Faraday of charge = 1 F = 96,485 Coulombs.
So, the number of moles of silver plated can be calculated as:
Moles of silver = Q / 96,485 = 3.97 Coulombs / 96,485 Coulombs/mol = 0.0000411 mol.
6. Finally, we can calculate the grams of silver plated by multiplying the moles of silver by the molar mass of silver (Ag), which is 107.87 g/mol.
Grams of silver = 0.0000411 mol * 107.87 g/mol = 0.00443 g (rounded to 4 significant figures).
Therefore, the mass of silver plated on the baby's spoon is approximately 0.0044 g.
b) Calculating the thickness of the silver plate formed:
1. We can use the formula for density (ρ) to find the volume (V) of the silver plated. Density is given as 10.5 g/cm^3.
Density = Mass / Volume
Rearranging the formula to solve for volume:
Volume = Mass / Density = 0.0044 g / 10.5 g/cm^3 = 0.000419 cm^3.
2. The volume of the silver plated will be equal to the volume of the silver plate formed on the spoon.
The volume of a rectangular prism (V) is calculated by multiplying the area of the base (A) by the height (h).
V = A * h
Since the spoon is assumed to be a rectangular prism, and we are given the area of the spoon as 6.25 cm^2, we can rearrange the formula to solve for height:
h = V / A = 0.000419 cm^3 / 6.25 cm^2 = 0.000067 cm (rounded to 3 significant figures).
Therefore, the thickness of the silver plate formed on the baby's spoon is approximately 0.000067 cm (rounded to 3 significant figures).
To solve this problem, we'll start by calculating the amount of silver that is plated onto the spoon, taking into account the current efficiency.
a) The current efficiency is given as 82.0%. This means that only 82% of the current is used to plate the silver onto the spoon. In other words, if we had a total current of 2.00 A, the effective current used for plating would be 0.82*2.00 A = 1.64 A.
To find the total charge (coulombs) passed during the plating process, we need to convert the time from hours and minutes to hours. In this case, the time is given as two hours and 25 minutes. We can convert the minutes to hours by dividing 25 minutes by 60 minutes/hour, which gives us 0.42 hours.
The total time for plating in hours is then 2.00 hours + 0.42 hours = 2.42 hours.
Now, we can calculate the total charge passed by multiplying the effective current by the time:
Total charge = effective current * time
Total charge = 1.64 A * 2.42 hours
Next, we need to convert the total charge to coulombs. Since 1 Ampere (A) is equal to 1 Coulomb/second (C/s), and our time is in hours, we need to convert from hours to seconds. There are 3600 seconds in one hour. Therefore, we have:
Total charge in Coulombs = 1.64 A * 2.42 hours * 3600 s/hour
Now we can proceed to calculate the grams of silver plated using Faraday's Law of Electrolysis. Faraday's Law states that the mass of a substance deposited or liberated during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte and inversely proportional to the molar mass of the substance.
The equation for Faraday's Law is:
Amount of substance (in moles) = (Charge in Coulombs) / (Faraday's constant, 1 mol/e)
In this case, the substance is silver (Ag) and its molar mass is 107.87 g/mol. So, we have:
Amount of silver (in moles) = (Total charge in Coulombs) / (1 mol/e)
Next, we can calculate the mass of silver plated by multiplying the amount in moles by the molar mass of silver:
Mass of silver (in grams) = (Amount of silver in moles) * (Molar mass of silver)
b) To find the thickness of the silver plate formed, we need to calculate the volume of silver plated and then divide it by the area of the spoon.
The volume of silver plated can be found using the density of silver (d = 10.5 g/cm^3):
Volume of silver (in cm^3) = Mass of silver (in grams) / Density of silver
Finally, we can calculate the thickness of the silver plate by dividing the volume by the area of the spoon:
Thickness of silver plate (in cm) = Volume of silver (in cm^3) / Area of spoon (in cm^2)
By following these steps, you should be able to find the answers to both parts of the problem.