Question

An aqueous solution of an unknown salt of ruthenium is electrolyzed by a current of 2.50 A passing for 50.0 min. If 2.618 g Ru is produced at the cathode, what is the charge on the ruthenium ions in solution?

Short answer

The charge on the unknown salt of ruthenium ions in solution is approximately +3.

Step-by-step solution

Calculate the charge passed during electrolysis

First, let's calculate the charge passed during electrolysis using the formula Q = I * t. I = 2.50 A t = 50.0 min * (60 s/min) = 3000 s Now, plug the values into the formula. Q = I * t Q = 2.50 A * 3000 s Q = 7500 C So, the charge passed during the electrolysis process is 7500 C.

Calculate moles of electrons involved in the electrolysis process

Now, we will use the charge passed during the electrolysis and Faraday's constant to find the moles of electrons involved in the electrolysis process using the formula Q = n * F. F = 96,485 C/mol Rearrange the formula to solve for n n = Q / F Now, plug in the values. n = 7500 C / 96,485 C/mol n = 0.0777 mol So, about 0.0777 moles of electrons were involved in the electrolysis process.

Calculate the moles of ruthenium produced

Given that Ru has a molar mass of 101.07 g/mol, we can calculate the moles of ruthenium produced at the cathode using the mass of Ru. moles of Ru = mass of Ru / molar mass of Ru moles of Ru = 2.618 g Ru / 101.07 g/mol Ru moles of Ru = 0.0259 mol

Determine the charge on the ruthenium ions

Since the electrolysis process involves the exchange of electrons between cathode and ruthenium ions, the moles of electrons should be equal to the product of moles of Ru and the charge on the Ru ions. Let's denote the charge on the ruthenium ions as x. moles of electrons = moles of Ru * x Now, plug in the values and solve for x. 0.0777 mol = 0.0259 mol * x x = 0.0777 mol / 0.0259 mol x ≈ 3 Hence, the charge on the unknown salt of ruthenium ions in solution is approximately +3.