Final answer:
To find the molarity of the unknown Cu(II) solution, calculate the change in mass of the cathode, which corresponds to the mass of copper deposited during electrolysis. The molarity of the unknown Cu(II) solution is 0.342 M (to three decimal places).
Step-by-step explanation:
In this question, a 50.0 ml aliquot of unknown Cu(II) solution was electrolyzed to deposit all the copper on the cathode. The mass of the cathode was 15.327 g before electrolysis and 16.414 g after electrolysis. To find the molarity of the unknown Cu(II) solution, we can calculate the change in mass of the cathode, which corresponds to the mass of copper deposited during electrolysis.
The change in mass of the cathode is 16.414 g - 15.327 g = 1.087 g (to three decimal places). Since two electrons are required to reduce a single Cu(II) ion, the moles of Cu deposited can be calculated. The molar mass of Cu is 63.5 g/mol.
The moles of Cu deposited = 1.087 g / 63.5 g/mol = 0.0171 mol (to four significant figures).
Finally, using the volume of the aliquot (50.0 mL) and the moles of Cu deposited, we can calculate the molarity of the unknown Cu(II) solution.
Molarity = moles of Cu / volume of solution = 0.0171 mol / 0.0500 L = 0.342 M (to three decimal places).