Question

Electrolysis of an alkaline earth metal chloride using a current of 5.00 A for 748 s deposits 0.471 g of metal at the cathode. What is the identity of the alkaline earth metal chloride?

Short answer

The identity of the alkaline earth metal chloride is Calcium chloride (CaCl2), as the calculated molar mass of the metal (40.08 g/mol) is closest to the molar mass of Calcium (40.078 g/mol).

Step-by-step solution

Calculate moles of electrons transferred

Faraday's law relates the charge, the moles of electrons transferred, and the current: Charge \(= n * e * Current * time\) We can rearrange this to solve for moles of electrons transferred (n): \(n = \dfrac{Charge}{e * Current * time}\) where e is the elementary charge, 1.602 x 10^-19 C. First, we will calculate the total charge passed: Charge \(= Current * time\) \(= 5.00A * 748s\) \(= 3740C\) Now, we will find the moles of electrons (n): \(n = \dfrac{3740C}{(1.602 * 10^{-19}C) * 5.00A * 748s}\) \(n = 3.119 * 10^{-2} \thinspace mol\)

Calculate moles of metal deposited and molar mass

The stoichiometry between the alkaline earth metal (M) and its chloride (MCl2) is 1:1. Therefore, the moles of metal deposited are equal to the moles of electrons transferred. Moles of metal deposited \(= 3.119 * 10^{-2} \thinspace mol\) Next, we will determine the molar mass of the alkaline earth metal. The molar mass of the metal (MM) can be found using the following formula: MM \(= \dfrac{Weight of metal deposited}{Moles of metal deposited}\) \(MM = \dfrac{0.471g}{3.119 * 10^{-2} \thinspace mol}\) \(MM \approx 40.08 \thinspace g/mol\)

Identify the alkaline earth metal

We have the molar mass of the metal, which is approximately 40.08 g/mol. By comparing this value to the molar masses of alkaline earth metals, we can identify the metal: - Beryllium (Be): 9.012 g/mol - Magnesium (Mg): 24.305 g/mol - Calcium (Ca): 40.078 g/mol - Strontium (Sr): 87.62 g/mol - Barium (Ba): 137.33 g/mol - Radium (Ra): 226 g/mol The molar mass of our metal is closest to Calcium (Ca) with a molar mass of 40.078 g/mol. So, the identity of the alkaline earth metal chloride is Calcium chloride (CaCl2).

Key concepts

Faraday's Law

Understanding the electrolysis process begins with Faraday's Law, which provides a quantitative relationship between the electric charge used in electrolysis and the amount of substance that is deposited or dissolved at an electrode. Faraday's Law states that the amount of a substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity (in coulombs) that passes through the electrolyte.

To calculate the moles of electrons transferred during electrolysis, Faraday's Law formula is applied. It tells us that for every Faraday (96,485 C) of charge passing through, one mole of electrons is transferred. This is the foundational principle that allows us to then determine the amount of metal deposited during electrolysis, by using the charge passed through the circuit, as illustrated in the given problem.

Moles of Electrons

The mole concept is pivotal in chemistry, serving as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure. When we discuss moles of electrons in the context of electrolysis, we are referring to how many electrons are required to deposit or dissolve a certain amount of substance.

In our example, the moles of electrons correspond to the number of electrons that flow through the circuit during electrolysis. By using the charge calculated from the amount of current and the time, we can determine the moles of electrons that were involved in depositing the metal. This is a crucial step in understanding the amount of substance involved in an electrochemical reaction.

Molar Mass Calculation

The molar mass of an element is the mass in grams of one mole of that element. It's an essential concept in chemistry, especially when working with chemical equations and conversions between moles and grams.

The calculation of molar mass is relatively straightforward in the context of our problem. Once you have the moles of the metal deposited, as determined from the moles of electrons, you can then divide the mass of the deposited metal by the moles to find its molar mass. This gives you a precise figure that can be compared against known values of elements to identify the substance, in this case, an alkaline earth metal.

Chemical Stoichiometry

Chemical stoichiometry deals with the quantitative relationships between the reactants and products in a chemical reaction. In the context of electrolysis, stoichiometry helps us understand the 1:1 relationship between the moles of electrons and the moles of metal deposited.

This relationship is crucial when converting the electric charge passed during electrolysis into the amount of metal deposited. For alkaline earth metals, which form divalent cations, two moles of electrons correspond to one mole of metal ions reduced at the cathode. However, in our example, the stoichiometric ratio is 1:1, which simplifies the molar mass calculation.

Identifying Elements by Molar Mass

Once the molar mass of a deposited metal is calculated, we can then compare it with the known molar masses of elements to identify which metal has been deposited. In the given problem, elements from the alkaline earth metals group were considered due to their typical formation of chlorides and presence in electrolysis scenarios.

By comparing the calculated molar mass with the standard molar masses of alkaline earth metals, the element that best matches the value is determined to be the metal in question. This method of identification is direct and universally applicable in chemistry when determining an unknown element or compound based on its molar mass.