When a solution of a certain gadolinium salt is electrolyzed with a current of 1.0 A for 2.0 h, 0.025 mol of Gd metal forms. Calculate the charge on the gadolinium ion in the salt.
coulomhs = A x seconds = about 7,200.
96,485 coulombs will plate out, in grams, atomic mass Gd/#e = 157.25 g/#e.
grams Gd plated = 0.025 x 157.25 = about 3.93 grams.
atomic mass Gd/#e x 7,200/96,485 = 3.93
Solve for #e and I would round to the nearest whole number. My guess, for Gd, is for that to be +3 since Gd is a lanthanide element.
To calculate the charge on the gadolinium ion in the salt, we can use Faraday's Law of Electrolysis.
Faraday's Law states that the amount of substance formed in an electrolysis process is directly proportional to the quantity of electricity passed through the electrolyte.
The equation relating the quantity of electricity (Q), current (I), time (t), and Faraday's constant (F) is:
Q = I * t
The charge on one mole of electrons is known as the Faraday constant and is approximately equal to 96,485 C/mol.
First, let's calculate the quantity of electricity (Q) that passed through the electrolyte:
Q = I * t = 1.0 A * 2.0 h = 2.0 C
Now, let's calculate the number of moles of electrons (n) that were involved in the electrolysis process. Since 1 mole of electrons carries a charge of 1 Faraday (F):
n = Q / F = 2.0 C / 96,485 C/mol = 0.0000207 mol
Since 0.025 mol of Gd metal formed, and for every mole of Gd metal, the same number of oxygen ions were reduced, we can conclude that the gadolinium ion (Gd3+) has a charge of 3+.
Therefore, the charge on the gadolinium ion in the salt is +3.
To calculate the charge on the gadolinium ion in the salt, we need to use Faraday's laws of electrolysis.
1. Start by finding the number of electrons involved in the reduction of Gd3+ to Gd metal.
Since 0.025 mol of Gd metal is formed, this means that 0.025 mol of Gd3+ ions are reduced.
The balanced equation for the reduction of Gd3+ is: Gd3+ + 3e- → Gd
Therefore, the number of electrons involved is 3 times the number of moles of Gd3+ ions reduced:
Number of electrons = 3 * 0.025 mol = 0.075 mol e-
2. Use Faraday's constant (F), which represents the charge per mole of electrons, to calculate the total charge.
Faraday's constant (F) = 96,485 C/mol (charge/mole of electrons)
Total charge = Number of electrons * Faraday's constant = 0.075 mol e- * 96,485 C/mol = 7,236.375 C
3. Finally, calculate the charge on the gadolinium ion.
The charge on the gadolinium ion is equal to the total charge divided by the number of moles of gadolinium ions:
Charge on gadolinium ion = Total charge / Number of moles of gadolinium ions
= 7,236.375 C / 0.025 mol (from the question)
= 289,455 C/mol
Therefore, the charge on the gadolinium ion in the salt is 289,455 C/mol.