Question

Magnesium is obtained by electrolysis of molten \(\mathrm{MgCl}_{2}\) . (a) Why is an aqueous solution of MgCl_ not used in the electrolysis? (b) Several cells are connected in parallel by very large copper bars that convey current to the cells. Assuming that the cells are 96\(\%\) efficient in producing the desired products in electrolysis, what mass of Mg is formed by passing a current of \(97,000\) A for a period of 24 \(\mathrm{h} ?\)

Short answer

(a) An aqueous solution of \(\mathrm{MgCl}_{2}\) is not used in the electrolysis because water will undergo reactions instead of the Mg ions, producing hydrogen and chlorine gas. (b) The mass of Mg formed by passing a current of 97,000 A for a period of 24 hours with 96% efficiency is 1,018,000 g or 1,018 kg.

Step-by-step solution

Answer for (a)

In the electrolysis of an aqueous solution of \(\mathrm{MgCl}_{2}\), water will also undergo reactions. This is because water can be more easily reduced and oxidized than Mg ions. Therefore, the desired product (Mg metal) will not be formed in an aqueous solution. Instead, hydrogen gas and chlorine gas will be produced at the cathode and anode, respectively.

Formulae needed for calculations

To calculate the mass of Mg formed in part (b), we will use Faraday's law of electrolysis, which states that the mass of a substance formed during electrolysis is proportional to the charge passed through the electrolyte. \(m = \dfrac{Q\times M}{nF}\) Where: - \(m\) is the mass of the substance formed (in this case, Mg) - \(Q\) is the total charge passed through the electrolyte (Coulombs) - \(M\) is the molar mass of the substance (Mg) - \(n\) is the number of electrons involved in the reaction - \(F\) is Faraday's constant (96485 C/mol)

Conversion of current and time to total charge

First, we need to find the total charge passed through the electrolyte (Q). We can do this by multiplying the current (I) and the time (t): \(Q=I\times t\) Current (I) = 97,000 A Time (t) = 24 hours = 86,400 seconds (1 hour = 3600 seconds) \(Q = 97000 A \times 86400 s = 8,378,800,000 C\)

Calculation of mass formed

Now, we can use Faraday's law to find the mass of Mg formed: For Mg, the molar mass (M) is 24.3 g/mol and the number of electrons involved in the reaction (n) is 2 (as \(\mathrm{Mg^{2+}}\) gains 2 electrons to form Mg metal). \(m = \dfrac{Q\times M}{nF} = \dfrac{8,378,800,000 C\times 24.3 g/mol}{2\times 96485 C/mol} = 1060620 g \) Since the cells are 96% efficient, we must multiply the mass by the efficiency factor: Mass of Mg = \(1060620 g \times 0.96 = 1018,000 g\) or 1018 kg

Final answer

(a) An aqueous solution of \(\mathrm{MgCl}_{2}\) is not used in the electrolysis because water will undergo reactions instead of the Mg ions, producing hydrogen and chlorine gas. (b) The mass of Mg formed by passing a current of 97,000 A for a period of 24 hours with 96% efficiency is 1,018,000 g or 1,018 kg.

Key concepts

Faraday's law of electrolysis

Faraday's law of electrolysis is crucial for understanding the chemical changes that occur during electrolysis. It tells us that the amount of substance produced at each electrode is directly related to the amount of charge passed through the electrolyte. This means, in simple terms, that if you increase the charge, more of the desired substance will be created.
Faraday's law is mathematically expressed as:

• \[m = \frac{Q\times M}{nF}\]

Here, \(m\) represents the mass of the substance formed, \(Q\) is the total electrical charge, \(M\) is the molar mass, \(n\) is the number of electrons exchanged per ion, and \(F\) is Faraday's constant which equals approximately 96485 C/mol.
This law is fundamental since it allows chemists and engineers to calculate precisely how much of a material, such as magnesium in this case, can be produced by electrolysis given a specific electrical input.

aqueous solutions

Understanding why an aqueous solution is not suitable for electrolysis in certain cases, like with magnesium chloride, is key. In general, an aqueous solution is a solution where water is the solvent. When electricity is used in this environment, water, being a powerful medium, tends to participate in the reactions instead of the intended ions.
In the case of magnesium chloride (\(\mathrm{MgCl_2}\)), the solution would yield hydrogen and chlorine gas, rather than solid magnesium. This is because water can be more easily reduced and oxidized than magnesium ions. As a result, the production of pure magnesium is compromised when using an aqueous solution. Hence, solid \(\mathrm{MgCl_2}\) is melted and used in its molten state to avoid reactions involving water, ensuring magnesium ions are directly reduced to form the metal.

magnesium production

Electrolysis is a fascinating industrial process for the production of magnesium from its chloride. The process involves passing a large current through molten \(\mathrm{MgCl_2}\) to break the strong ionic bonds, effectively separating the magnesium ions from chlorine ions.
This separation allows for the deposition of magnesium metal at the cathode, while chlorine gas is expelled at the anode. This method is highly efficient and is favored for producing high-purity magnesium. However, because the reaction requires a substantial amount of electrical energy, maintaining cost-efficiency is vital for large-scale production.
The magnesium recovered from this process serves as a lightweight, strong material ideal for applications in industries such as automotive manufacturing and electronics, where reducing weight is a critical factor.

current efficiency

Current efficiency is an important consideration in the process of electrolysis. It refers to the percentage of the electric current that is used effectively to produce the desired chemical change versus the total current supplied.
In the given exercise, the efficiency of the cells is specified as 96%. This means that 96% of the electrical energy contributes to the production of magnesium, while the remainder is lost, typically as heat or due to side reactions. Maximizing current efficiency is important, as it directly impacts production costs and energy consumption.
To calculate the real output of magnesium in this exercise, the initial mass of Mg calculated must be adjusted by this efficiency rate. This adjustment ensures accurate predictions of expected outputs for industrial applications, helping to design processes that minimize waste and maximize resource utilization.