Question

A solution containing a metal ion \(\left(\mathrm{M}^{2+}(a q)\right)\) is electrolyzed by a current of 5.00 A. After 15.3 minutes, \(2.83 \mathrm{~g}\) of the metal plated out. (a) How many coulombs are supplied by the battery? (b) What is the metal? (Assume \(100 \%\) efficiency.)

Short answer

Answer: The metal involved in the electrolysis process is Tin (Sn).

Step-by-step solution

Calculate the total charge supplied by the battery

The formula for calculating the charge in an electrochemical cell is: Charge (Coulombs) = Current (Amperes) × Time (seconds) We are given the current (5.00 A) and the time in minutes (15.3 minutes), which we need to convert to seconds: 15.3 minutes × 60 seconds/minute = 918 seconds Now we can calculate the total charge supplied by the battery: Charge = 5.00 A × 918 s = 4590 Coulombs

Determine the number of moles of electrons supplied

Using Faraday's law of electrolysis, we can determine the number of moles of electrons involved in the process: 1 Faraday = 96485 Coulombs/mol of electrons So, the number of moles of electrons supplied by the battery is: Moles of electrons = Charge (Coulombs) / 1 Faraday (Coulombs/mol of electrons) Moles of electrons = 4590 Coulombs / 96485 Coulombs/mol = 0.04755 mol

Calculate the number of moles of the metal ion

Since the metal ion has a charge of 2+ (M²⁺), it will require 2 moles of electrons to reduce 1 mole of the metal ion to its neutral state (M). The stoichiometric ratio between the metal ion and the electrons will be 1:2. Therefore, the number of moles of the metal ion will be: Moles of metal ion = Moles of electrons / 2 Moles of metal ion = 0.04755 mol / 2 = 0.02377 mol

Determine the Molar mass of the metal

We are given the mass of the metal that has been plated out (2.83 g) and have calculated the number of moles of the metal ion (0.02377 mol). Now we can find the Molar mass of the metal: Molar mass (g/mol) = Mass (g) / Moles (mol) Molar mass = 2.83 g / 0.02377 mol = 119 g/mol

Identify the metal

Now we match the calculated Molar mass to the Molar mass of a known metal. The metal with a Molar mass closest to 119 g/mol is Tin (Sn) with a Molar mass of 118.71 g/mol. Therefore, the metal in the solution is Tin (Sn).