Question

(a) Calculate the mass of Li formed by electrolysis of molten LiCl by a current of \(7.5 \times 10^{4}\) A flowing for a period of \(24 \mathrm{~h}\). Assume the electrolytic cell is \(85 \%\) efficient. (b) What is the energy requirement for this electrolysis per mole of Li formed if the applied emf is \(+7.5 \mathrm{~V} ?\)

Short answer

(a) The mass of Li formed by electrolysis is \( 24.82 \mathrm{~kg} \). (b) The energy requirement per mole for this electrolysis is \( 32.46 \mathrm{~kJ/mol} \).

Step-by-step solution

Calculate Equivalent mass of Li using atomic mass and charge of Li ion

First, we need to find the equivalent mass(E) of Li. The equivalent mass of an element can be found by dividing its atomic mass by the charge of its ion. For Lithium: \(Atomic\:mass\:of\:Li\: (A) = 6.939 \:g/mol\), \(Charge\:of\:Li^+\:(Z)=1\) Now, we can calculate the equivalent mass using: \(Equivalent\:mass (E) = \frac{Atomic\:mass (A)}{Charge\:of\:ion (Z)}\)

Calculate charge transferred during the process

The charge transferred during the process can be found by using: \(Charge\: transferred\: (Q) = Current\: (I) \times Time\: (t)\) I = \(7.5 \times 10^{4} A\), t = \(24 \:hours = 24 \times 3600 \:seconds\)

Calculate mass of Li formed considering cell efficiency

Next, we will calculate the mass of Li formed using its equivalent mass and the charge transferred during electrolysis, taking into account the efficiency of the cell. \(Mass\:of\:Li = (\frac{Q}{Faraday's\:constant\: (F)} \times E) \times Efficiency\) \(Efficiency = 85\% = 0.85\)

Calculate energy consumption during electrolysis

Now, we will calculate the total energy consumption for this process using the given applied emf. \(Energy\: Consumption (E_{total}) = Charge\: transferred\: (Q) \times EMF\: (E_{applied})\)

Calculate the energy requirement per mole for this electrolysis

Finally, calculate the energy requirement per mole for this electrolysis using the total energy consumption and the moles of Li formed. \(Energy\:requirement\: per \:mole\:of\:Li\: (E_{per\:mole}) = \frac{E_{total}}{moles \:of \:Li\:formed}\)

Key concepts

Faraday's Laws of Electrolysis

To fully grasp the principles of electrolysis, one must first understand Faraday's laws. These laws, formulated by Michael Faraday in the 19th century, are essential to predict the products and quantities obtained during the electrolysis process.

Faraday's First Law states that the amount of substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity that passes through the electrolyte. Mathematically, this is represented as \(m = (Q/F) \times E\), where \(m\) is the mass of the substance, \(Q\) is the total charge, \(F\) is Faraday's constant (approximately 96,485 coulombs per mole), and \(E\) is the equivalent mass of the substance.

Faraday's Second Law says that when the same quantity of electric charge is passed through multiple electrolytes, the amount of substances liberated at the respective electrodes is directly proportional to their chemical equivalent weights. This, in the exercise, is applied when we determine the mass of lithium produced, leveraging the already calculated equivalent mass of lithium with the charge transferred during the process.

The accurate use of these laws is pivotal in solving electrolysis problems, as seen in our example problem where we use Faraday's laws to calculate the mass of lithium formed from the molten LiCl during electrolysis.

Energy Requirement for Electrolysis

The energy requirement for an electrolysis process is a critical factor to consider, especially when assessing the viability of industrial applications. It refers to the amount of electrical energy needed to drive the electrolytic reaction.

For our electrolysis of molten LiCl, the energy required to produce a given quantity of lithium can be calculated using the formula \(E_{total} = Q \times E_{applied}\), where \(E_{total}\) is the total energy consumed, \(Q\) is the charge transferred, and \(E_{applied}\) is the electromotive force (emf) applied to the system. It is important to note that the energy should be sufficient to overcome the potential difference required for the reaction to occur.

However, it's not just about the total energy consumed; determining the energy per mole of Li produced provides valuable insights into the efficiency and cost-effectiveness of the electrolysis process. To compute this, you divide the total energy consumption by the number of moles of lithium formed, helping you understand the energy expenditure per unit product of lithium.

Electrochemical Cell Efficiency

Efficiency in electrochemistry is a measure of how well an electrochemical cell converts electrical energy into chemical energy, or vice versa, without energy loss through heat or other forms of non-productive energy. Efficiency can be applied to the yield of the desired product or the energy conversion process itself.

In the context of our exercise on the electrolysis of molten LiCl, the cell's efficiency factors into how much of the current actually leads to the formation of lithium versus being lost as heat or in side reactions. The efficiency is given as 85%, which means 15% of the energy is not used for the conversion of lithium ions into lithium metal.

To account for this in calculations, you multiply the theoretically obtained mass of lithium by the efficiency (in decimal form), yielding the actual mass of lithium produced by the electrolysis reaction. Understanding cell efficiency helps in optimizing industrial processes and can guide improvements in electrochemical cell design to minimize waste and cost.