Question

Electrolysis of an alkaline earth metal chloride using a current of \(5.00 \mathrm{~A}\) for \(748 \mathrm{~s}\) deposits \(0.471 \mathrm{~g}\) 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 magnesium chloride (MgCl2). This is determined by using Faraday's laws of electrolysis and calculating the molar mass of the deposited metal, which is approximately 24.32 g/mol, close to the molar mass of magnesium (24.305 g/mol).

Step-by-step solution

Gather information from the problem statement

We know the following information: 1. Current, I = 5.00 A 2. Time, t = 748 s 3. Mass of metal deposited, m = 0.471 g

Calculate the charge passed during the electrolysis

We can use the formula \(Q = It\) to find the charge passed during the electrolysis. So, \(Q = 5.00 \mathrm{~A} \times 748 \mathrm{~s} = 3740 \mathrm{~C}\)

Calculate the equivalent weight of the metal

According to Faraday's second law of electrolysis, the weight of a substance deposited during electrolysis is proportional to its equivalent weight, that is: \(W = Ze\) Where: - W is the weight of the substance deposited, - Z is the electrochemical equivalent (ECE), - e is the charge passed. We can calculate the electrochemical equivalent (ECE) using the formula: \(Z = \frac{W}{e}\) Substituting the given values, we get: \(Z = \frac{0.471 \mathrm{~g}}{3740 \mathrm{~C}} = 1.259 \times 10^{-4} \mathrm{\frac{g}{C}}\)

Calculate the molar mass of the metal

Since the alkaline earth metals have a valency of 2, the molar mass of the metal is twice the equivalent weight. So, Molar mass of metal = \(2 \times Z \times Faraday's \,\, constant\), where Faraday's constant (F) is \(96485 \mathrm{\frac{C}{mol}}\). Molar mass of metal = \(2 \times 1.259 \times 10^{-4} \mathrm{\frac{g}{C}} \times 96485 \mathrm{\frac{C}{mol}}\) Molar mass of metal \( = 24.32 \mathrm{~g/mol}\)

Identify the alkaline earth metal

The molar mass of the metal is approximately 24.32 g/mol. This value is very close to the molar mass of magnesium (24.305 g/mol). So, the identity of the alkaline earth metal chloride is magnesium chloride (MgCl2).