If a current of 1.5 A is passed for 4.00 hours through a molten tin salt and 13.3g of tin is deposited, what is the oxidation state of the metal in the salt?
(Sn = 118.7, F = 96500 C mol-1)
A. 1
B. 2
C. 3
D. 4
To find the oxidation state of the metal in the salt, we can use Faraday's law of electrolysis.
The amount of substance deposited at an electrode during electrolysis is directly proportional to the charge passed through the electrolyte.
The formula to calculate the amount of substance deposited is:
Amount of substance = (Charge passed / Faraday constant) * Molar mass
Charge passed = Current * Time
The given current is 1.5 A, and the given time is 4.00 hours. We need to convert the time to seconds to match the unit of the Faraday constant, which is coulombs per mole.
4.00 hours = 4.00 * 60 * 60 seconds = 14,400 seconds
Charge passed = 1.5 A * 14,400 seconds = 21,600 C
Now, we can calculate the amount of substance deposited:
Amount of substance = (21,600 C / 96500 C mol-1) * 118.7 g mol-1
Amount of substance = 26.6 g
The amount of tin deposited is given as 13.3 g. This indicates that the oxidation state of tin in the salt is 2.
Therefore, the answer is B. 2.
To find the oxidation state of the metal in the salt, we can use Faraday's laws of electrolysis.
Step 1: Calculate the amount of charge passed through the molten tin salt.
Q = I * t
where
Q = amount of charge in Coulombs (C)
I = current in Amperes (A)
t = time in seconds (s)
First, convert the time from hours to seconds:
4 hours * 60 minutes/hour * 60 seconds/minute = 14,400 seconds
Substitute the values into the equation:
Q = 1.5 A * 14,400 s = 21,600 C
Step 2: Calculate the number of moles of tin deposited.
Use Faraday's first law of electrolysis, which states that the amount of substance deposited or liberated at an electrode is directly proportional to the quantity of electricity passed through the cell.
mol = Q / (n * F)
where
mol = number of moles of tin
Q = amount of charge in Coulombs (C)
n = number of electrons transferred (charges balanced in the balanced chemical equation)
F = Faraday's constant (96500 C mol^-1)
The balanced chemical equation for the deposition of tin is:
Sn^4+ + 4e^- → Sn
From the equation, we can see that 4 moles of electrons are required per mole of tin (Sn).
Substitute the values into the equation:
mol = 21,600 C / (4 * 96500 C mol^-1) = 0.056 mol
Step 3: Calculate the mass of tin deposited.
Use the molar mass of tin to convert moles to grams.
Molar mass of Sn = 118.7 g/mol
mass = mol * molar mass
mass = 0.056 mol * 118.7 g/mol ≈ 6.65 g
Step 4: Calculate the oxidation state of tin.
From the balanced chemical equation for the deposition of tin, we can determine the oxidation state of tin.
Sn^4+ + 4e^- → Sn
The oxidation state of Sn is +4.
Therefore, the correct answer is:
D. 4