Electrolysis of a metal nitrate solution M(NO3)2(aq) for 325 min with a constant current of 20.0 A gives 111 g of the metal. Identify the metal ion M2+.

Verified step by step guidance

1. Identify the relevant electrochemical equation for the reduction of the metal ion: \( \text{M}^{2+} + 2e^- \rightarrow \text{M} \).
2. Calculate the total charge (in coulombs) passed through the solution using the formula: \( Q = I \times t \), where \( I \) is the current in amperes and \( t \) is the time in seconds.
3. Use Faraday's laws of electrolysis to relate the charge to the amount of substance deposited. The number of moles of electrons is given by \( n = \frac{Q}{F} \), where \( F \) is Faraday's constant (approximately 96485 C/mol).
4. Determine the moles of metal deposited using the stoichiometry of the reduction reaction. Since 2 moles of electrons reduce 1 mole of \( \text{M}^{2+} \), divide the moles of electrons by 2 to find the moles of metal.
5. Calculate the molar mass of the metal by dividing the mass of the metal deposited (111 g) by the moles of metal calculated in the previous step. Compare this molar mass to known values to identify the metal.

Key Concepts

Electrolysis

Electrolysis is a chemical process that uses electrical energy to drive a non-spontaneous reaction. In this process, an electric current is passed through an electrolyte solution, causing the ions to migrate towards the electrodes, where they undergo reduction or oxidation. The amount of substance produced at the electrodes can be calculated using Faraday's laws of electrolysis.

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis quantify the relationship between the amount of substance transformed at an electrode and the electric charge passed through the electrolyte. The first law states that the mass of a substance deposited or dissolved at an electrode is directly proportional to the quantity of electricity that passes through the electrolyte. The second law states that the mass of different substances deposited by the same quantity of electricity is proportional to their equivalent weights.

Molar Mass and Stoichiometry

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. In electrolysis, stoichiometry is used to relate the amount of metal produced to the charge passed through the solution. By knowing the mass of the metal obtained and the current used, one can calculate the molar mass of the metal ion, which helps identify the metal ion M2+ in the reaction.