Question

Electrolysis of an alkaline earth metal chloride using a current of 5.00 $\mathrm{A}$ for 748 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).

Step-by-step solution

Calculate the total charge passed through the circuit

To calculate the total charge passed through the circuit, we can use the formula: Charge (Q) = Current (I) × Time (t) We are given the current (I) as 5.00 A and the time (t) as 748 s. So, we can substitute these values into the equation: Q = 5.00 A × 748 s = 3740 C (coulombs)

Calculate the number of Faradays used

Now, let's calculate the number of Faradays used in the electrolysis process. We know that one Faraday (F) of charge is equal to 96485 C/mol. Hence, we can find the number of Faradays by dividing the total charge (Q) by the charge of one Faraday (F): Number of Faradays = Q / F = 3740 C / 96485 C/mol ≈ 0.03875 mol

Calculate the amount of metal deposited per Faraday

We are given the mass of metal deposited on the cathode (0.471 g). To find the amount of metal deposited per Faraday, we can divide the mass of metal deposited by the number of Faradays used: Amount of metal deposited per Faraday = Mass of metal / Number of Faradays = 0.471 g / 0.03875 mol ≈ 12.15 g/mol

Determine the equivalent mass of the metal

The equivalent mass of the metal is the mass of the metal deposited per Faraday multiplied by the valence of the metal ion. Since the alkaline earth metals form ions with a +2 charge, the equivalent mass of the metal in this case will be twice the amount of the metal deposited per Faraday: Equivalent mass of metal = 2 × 12.15 g/mol ≈ 24.3 g/mol

Identify the alkaline earth metal based on its equivalent mass

We can now compare the equivalent mass we calculated with the molar masses of the alkaline earth metal to identify the metal. The alkaline earth metals and their molar masses are: - 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): 137.327 g/mol - Radium (Ra): 226 g/mol The equivalent mass we calculated, 24.3 g/mol, is closest to the molar mass of magnesium (Mg), which is 24.305 g/mol. Therefore, the identity of the alkaline earth metal chloride is magnesium chloride (MgCl₂).

Key concepts

Alkaline Earth Metals

Alkaline earth metals are a group of elements found in group 2 of the periodic table. These elements are known for their shiny appearance and good electrical conductivity. They include Beryllium, Magnesium, Calcium, Strontium, Barium, and Radium. Unlike the alkali metals in group 1, alkaline earth metals are less reactive, but they still react with water. They tend to form 2+ ions by losing two electrons, which makes them important in various chemical reactions.

Alkaline earth metals have diverse applications due to their reactivity and abundance. For instance, Magnesium is widely used for structural metal purposes and as a key ingredient in alloys.
Often, these metals form compounds like oxides and halides, like Magnesium Chloride (MgCl₂), which plays a significant role in industrial processes and electrolysis.

Faraday's Constant

Faraday's Constant is a fundamental concept in electrochemistry and defines the amount of electric charge carried by one mole of electrons. This constant is approximately equal to 96485 coulombs per mole (C/mol). Named after Michael Faraday, it is crucial for calculating the charge involved in electrochemical reactions. In electrolysis, it helps us relate the amount of substance formed at an electrode to the total charge passed.

Using Faraday's Constant, we can determine how many moles of electrons have been exchanged in a reaction given the total charge. This is particularly useful when identifying substances deposited during reactions, as seen in the practice of separating elements through electrolysis, such as those from alkaline earth metal chloride solutions.

Coulombs

Coulombs are the unit of electric charge in the International System of Units (SI). Named after Charles-Augustin de Coulomb, this unit quantifies the electric charge transported by a constant current of one ampere in one second. Hence, the formula to calculate the charge is given by $$Q=I\times t$$ where $Q$ is the charge in coulombs, $I$ is the current in amperes, and $t$ is the time in seconds.

In the context of electrolysis, determining the total charge passing through a circuit allows us to estimate the amount of element being deposited. This relationship is vital for industrial processes where precision in the quantity of deposited materials is crucial. For example, when electroplating metals or processing chemical intermediates, accurate charge measurements ensure desired results.

Molar Masses

Molar mass is a fundamental property of chemical compounds and defines the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and is equivalent to the atomic or molecular weight of the substance. For elements and simple compounds, molar mass can be directly referenced from the periodic table.

In electrolysis, molar mass is used to determine the identity of substances based on the amount of deposited substance per unit of charge, such as metals in a cathodic deposition. By calculating the molar mass from experimental data and comparing it to known values, we can identify substances like the alkaline earth metals. For instance, the molar mass for magnesium closely matched the experimentally calculated value in an electrolysis reaction, thereby confirming its identity.