Question

Magnesium is obtained by electrolysis of molten \(\mathrm{MgCl}_{2}\). (a) Why is an aqueous solution of \(\mathrm{MgCl}_{2}\) 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 \(\mathrm{Mg}\) is formed by passing a current of 97,000 A for a period of 24 h?

Short answer

(a) An aqueous solution of \(\mathrm{MgCl}_{2}\) is not used in the electrolysis because H+ ions from the dissociation of water tend to get discharged at the cathode more readily than Mg2+ ions, resulting in the production of hydrogen gas instead of magnesium metal. (b) The mass of magnesium formed during the electrolysis process is approximately 1,029,430 g or 1,029.43 kg when passing a current of 97,000 A for a period of 24 hours with a cell efficiency of 96 %.

Step-by-step solution

Part (a): Explaining the unsuitability of aqueous MgCl2

Aqueous solutions of MgCl2 contain Mg2+ ions and Cl- ions along with the H+ ions from the dissociation of water. On passing current through the aqueous solution, H+ ions from water tend to get discharged at the cathode more readily than Mg2+ ions because of their low ionization potential. Therefore, using an aqueous solution would result in the production of hydrogen gas instead of magnesium metal.

Part (b): Calculating the charge passed

Given, the current is 97,000 A, and the time is 24 h. To calculate the total charge (Q) that passed through the cell, we can use the formula: Q = I × t But first, we need to convert 24 h into seconds: 1 h = 3600 s So, 24 h = 24 × 3600 s Now, we can find the charge: \(Q = 97,000 \: A \times 24 \times 3600 \: s = 8,467,200,000 \: C\)

Part (b): Calculating the moles of Mg formed

We will use Faraday's law of electrolysis to find the moles of magnesium formed: Moles of Mg = (Charge passed × Efficiency) / (n × Faraday's constant) Here, the efficiency of the cells is given as 0.96, and the number of electrons (n) required to reduce one magnesium ion (Mg2+) to magnesium metal is 2. The Faraday's constant (F) is 96,485 C/mol. Let's calculate the moles of Mg formed: Moles of Mg = \((8,467,200,000 \: C \times 0.96) / (2 \times 96,485 \: C/mol) = 42,372 \: mol\)

Part (b): Finding the mass of Mg formed

Now that we have the moles of Mg formed, we can find the mass of Mg using the molar mass of magnesium (24.305 g/mol): Mass of Mg = Moles of Mg × Molar mass of Mg Mass of Mg = \(42,372 \: mol \times 24.305 \: g/mol = 1,029,430 \: g\) So, the mass of magnesium formed during the electrolysis process is approximately 1,029,430 g or 1,029.43 kg.

Key concepts

Faraday's Law of Electrolysis

Understanding electrolysis requires grasping the core principle behind Faraday's Law of Electrolysis. Faraday’s law helps us know how much chemical change occurs when a specific amount of electric charge is passed through a solution. In simple terms, it tells us how many moles of a substance will react as a current flows through it.

Specifically, Faraday’s law states that the amount of substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity that flows through the solution. This means more electricity equals more reaction.

• Each mole of electrons carries a charge of 1 Faraday (96,485 C).
• The number of electrons needed for a reaction is represented by the symbol \( n \).
• Faraday's constant can help convert charge into moles.

As we saw in the problem, to calculate how much magnesium is produced, we first figure out how much charge (Q) flows through the system and use that with Faraday's constant and the efficiency of the reaction. This allows us to accurately determine the moles of magnesium produced by electrolysis.

Magnesium Production

Magnesium is a valuable metal and is commonly produced via electrolysis of magnesium chloride (\( \mathrm{MgCl}_{2} \)). However, this process must be done carefully.

The ideal method for producing magnesium is through molten \( \mathrm{MgCl}_{2} \) rather than its aqueous solution. This is because in water, other reactions are more favorable. When electrolysis is used on aqueous \( \mathrm{MgCl}_{2} \), water molecules can dissociate and prevent magnesium ions from discharging at the cathode.

• Molten \( \mathrm{MgCl}_{2} \) avoids competition with water, directly producing magnesium.
• This yields a more efficient and cleaner production process.
• High current and well-managed systems can produce large amounts, as seen in the calculation of thousands of kilograms of magnesium!

These details emphasize why choosing the correct phase of magnesium chloride is crucial in successfully generating magnesium through electrolysis.

Aqueous Solution

Aqueous solutions are mixtures of substances dissolved in water. They are handy in many chemical reactions, but not always suitable for all processes.

Let's take a deeper look at why an aqueous solution of \( \mathrm{MgCl}_{2} \) isn't ideal for producing magnesium. In water, \( \mathrm{MgCl}_{2} \) dissociates into magnesium ions (\( \mathrm{Mg}^{2+} \)) and chloride ions (\( \mathrm{Cl}^- \)), plus there are ions from water itself, mainly hydrogen ions (\( \mathrm{H}^+ \)). When electrolysis is performed, hydrogen ions are more likely to gain electrons than \( \mathrm{Mg}^{2+} \) ions due to their electrochemical properties.

• If hydrogen ions gain electrons, hydrogen gas is produced instead of magnesium.
• This side reaction can waste power and resources.
• As a result, a molten solution is preferred for magnesium production via electrolysis.

Understanding the behavior of ions in aqueous solutions is key to manipulating and predicting the outcomes of chemical reactions effectively.