How long would it take in minutes to plate 1.00 gram of silver to a watch when 9.2 amps are passed through a silver (I) chloride solution? (atomic mass of silver is 107.8682 g/mol).
Okay, so I did that and I got 97.225 secs or 1.62 minutes
I don't know why anyone would use AgCl instead of AgNO3 but that's not here nor there.
Coulombs = amperes x seconds
C = 9.2 A x seconds. So we need to fill in C and seconds.
We know that 96,485 C wil deposit 107.8682 grams of Ag. We want 1 g to be deposited; that will take how many C? That's
96,485 C x (1.0000 g/107.8682) = ? C
Substitute that value for C in
C = 9.2 x seconds and solve for seconds, then convert to min.
One note: the value of 9.2 give you two significant figures so all of those digits for the atomic mass of Ag aren't necessary. Post your work if you get stuck.
Well, if you're looking to turn a gram of silver into a watch, you might be waiting a while. As a bot, I must clarify that plating a watch with silver involves a thin layer of silver coating, not actually turning it into a solid watch. But let's get to the calculations.
First, we need to determine the number of moles of silver (Ag) in 1 gram. Using the atomic mass of silver (107.8682 g/mol), we find:
1 gram / 107.8682 g/mol = 0.00926 moles of Ag
Now, we'll use Faraday's Law of Electrolysis to calculate the time required. One mole of electrons is equivalent to 1 Faraday (F) of charge, which is about 96,485 coulombs. So, we have:
0.00926 moles of Ag x (1 F / 96,485 C) = 9.6 x 10^-8 Faradays of charge
Since we know the current is 9.2 amps, we can use the equation:
Charge (Coulombs) = Current (Amperes) x Time (Seconds)
To rearrange the equation for time:
Time (Seconds) = Charge (Coulombs) / Current (Amperes)
Plugging in the values:
Time (Seconds) = 9.6 x 10^-8 Faradays / 9.2 amps ≈ 1.04 x 10^-8 seconds
So, it would theoretically take a ridiculously small amount of time (1.04 x 10^-8 seconds) to plate 1 gram of silver to a watch. That's almost as quick as you can say, "Hey presto, I've got a silver-plated watch!" But remember, we're just talking about a thin layer of silver here, not a solid silver watch.
To calculate the time required to plate 1.00 gram of silver onto a watch, we need to use the concept of Faraday's Law of Electrolysis.
According to Faraday's Law, the amount of substance produced or consumed in an electrolytic reaction is directly proportional to the amount of charge (in coulombs) passed through the electrolyte.
The formula to calculate the amount of substance (m, in moles) is:
m = (Q * M) / (n * F)
Where:
- Q is the charge passed in coulombs (Q = I * t, where I is the current in amperes and t is the time in seconds)
- M is the molar mass of the substance in grams/mol
- n is the number of electrons involved in the reaction (for silver, n = 1)
- F is Faraday's constant (96485 C/mol)
Let's plug in the values given:
I (current) = 9.2 amps
t (time) = unknown, to be determined
Q (charge) = I * t
M (molar mass of silver) = 107.8682 g/mol
n (number of electrons) = 1
F (Faraday's constant) = 96485 C/mol
We need to solve for t. Rearranging the formula:
t = Q / I
Now substituting the values:
t = (Q = I * t) / I
t = t
We see that we have a circular equation and cannot directly solve for time. However, we can proceed to calculate the time taken using some assumptions.
Let's assume that the reaction occurs with 100% efficiency, which means every coulomb of charge corresponds to the plating of one silver atom.
The charge required to plate 1.00 gram of silver can be calculated as follows:
Charge required = (1.00 g / M) * (n * F)
Substituting the values:
Charge required = (1.00 g / 107.8682 g/mol) * (1 * 96485 C/mol)
Calculate the result:
Charge required = 0.00926 C
Now, we can use the equation t = Q / I:
t = (0.00926 C) / (9.2 A)
t ≈ 0.001005 seconds or 1.005 milliseconds
So, it would take approximately 1.005 milliseconds (or 0.001005 seconds) to plate 1.00 gram of silver onto the watch when 9.2 amps are passed through a silver (I) chloride solution.
To determine the time it takes to plate 1.00 gram of silver onto a watch using a silver (I) chloride solution, we need to use the concept of Faraday's laws of electrolysis and the equation for calculating the time.
Faraday's first law states that the amount of substance produced or consumed during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.
The equation that relates the amount of substance produced, the quantity of electricity passed, and the atomic mass of the substance is:
m = Z * F * I * t
Where:
- m is the mass of the substance (in grams, 1.00 gram in this case).
- Z is the number of moles of electrons transferred per mole of substance (for silver, it is 1 because it forms Ag+).
- F is Faraday's constant which is 96485 C/mol.
- I is the current in amperes (9.2 amps in this case).
- t is the time in seconds (which we want to find).
Now we can rearrange the equation to solve for t:
t = m / (Z * F * I)
Let's calculate it step by step:
1. Find the number of moles of silver (Z):
Since the atomic mass of silver is 107.8682 g/mol, 1.00 gram of silver is equal to:
Z = 1.00 g / 107.8682 g/mol = 0.00927 mol
2. Calculate the time required (t):
t = 0.00927 mol / (1 * 96485 C/mol * 9.2 A)
t = 0.00927 / (1 * 96485 * 9.2)
t ≈ 1.08 × 10^(-7) seconds
However, the time is given in seconds, and we are asked for the time in minutes. So, let's convert the time to minutes:
t (minutes) = t (seconds) / 60
t (minutes) = 1.08 × 10^(-7) / 60
t (minutes) ≈ 1.8 × 10^(-9) minutes
Therefore, it would take approximately 1.8 × 10^(-9) minutes to plate 1.00 gram of silver onto a watch using a silver (I) chloride solution with 9.2 amps of current.