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 minimum voltage required to drive the reaction?

Short answer

The mass of Li formed by the electrolysis of molten LiCl under these conditions is approximately \(395,937.61 g\), and the minimum voltage required to drive the reaction is \(3.04 V\).

Step-by-step solution

Calculate the total charge passed through the cell

Given the current, \(I=7.5 \times 10^4 A\), and the time period, \(t=24h\). The total charge passed through the cell, \(Q\), can be calculated using the formula: \[Q = It\] First, convert the given time to seconds since the unit of current is Amperes (A), which is coulombs per second (C/s). \[t=24h \times 60\frac{min}{h} \times 60\frac{s}{min} = 86400 s\] Now, calculate the total charge \(Q\): \[Q = (7.5 \times 10^4 A)(86400s) = 6.48 \times 10^9 C\]

Determine the number of moles of electrons

To find the number of moles of electrons passed through the cell, we will use Faraday's constant, \(F = 96485 C/mol\). The number of moles of electrons, \(n_e\), can be calculated as follows: \[n_e = \frac{Q}{F}\] So, \[n_e = \frac{6.48 \times 10^9 C}{96485 \frac{C}{mol}} \approx 67149.95 mol\]

Calculate the number of moles of Li produced

Given that the cell is 85% efficient, we can calculate the number of moles of Li produced, \(n_{Li}\), as follows: \[n_{Li} = efficiency \times n_e\] So, \[n_{Li} = (0.85)(67149.95 mol) \approx 57077.46 mol\]

Determine the mass of Li formed

Now that we know the number of moles of Li produced, we can find the mass, \(m_{Li}\), by multiplying it with the molar mass of Li, which is 6.94 g/mol: \[m_{Li} = n_{Li} \times M_{Li}\] So, \[m_{Li} = (57077.46 mol)(6.94 \frac{g}{mol}) \approx 395937.61 g\]

Calculate the minimum voltage required

To find the minimum voltage required to drive the reaction, we can use the standard potential of the Li/Li+ half-cell, \(E^0 = -3.04 V\). Because the reaction involves one mole of electrons, the minimum voltage required for the electrolysis of molten LiCl, \(V_{min}\), is equal to the magnitude of the standard potential: \[V_{min} = |-3.04 V| = 3.04 V\] So, the minimum voltage required to drive the reaction is 3.04 V. In summary, the mass of Li formed by the electrolysis of molten LiCl under these conditions is approximately 395,937.61 g, and the minimum voltage required to drive the reaction is 3.04 V.

Key concepts

Faraday's Law

Faraday's Law is an essential principle in electrochemistry that helps us understand how certain electrical processes will produce chemical changes. In electrolysis, it's crucial to calculate how much material is deposited or dissolved when electricity passes through a substance. Faraday's Law states that the amount of substance transformed at an electrode during electrolysis is directly proportional to the charge passed through the substance.

The mathematical representation of this correlation is given by the formula:

• \( n = \frac{Q}{F} \)

where

• \( n \) is the number of moles of substance.
• \( Q \) is the total charge transferred (in Coulombs).
• \( F \) stands for Faraday's constant, approximately 96485 C/mol.

This equation shows that the number of moles of electrons involved in a reaction corresponds with the total electric charge and Faraday's constant. This relationship allows us to predict the quantity of a chemical substance formed during electrolysis by knowing the current and duration of the electric flow.

Lithium Chloride

Lithium chloride (LiCl) is a chemical compound that consists of lithium and chlorine. It is an important electrochemical substance due to its high solubility and conductivity. In the electrolysis context, molten lithium chloride serves as the material through which electric current is passed to extract the metal lithium.

During electrolysis, lithium ions \((Li^+)\) move toward the cathode, where they gain electrons (are reduced) to form lithium metal \((Li)\). Analogously, chloride ions \((Cl^-)\) travel to the anode, where they lose electrons (are oxidized) to produce chlorine gas \((Cl_2)\). The reaction can be represented as:

• At the cathode: \( Li^+ + e^- \rightarrow Li \)
• At the anode: \( 2Cl^- \rightarrow Cl_2 + 2e^- \)

By leveraging this process, electrolysis of lithium chloride becomes a practical method for obtaining lithium, which is utilized in various applications such as lithium-ion batteries, a crucial technology for many electronic devices.

Electrochemical Cell

An electrochemical cell is a device composed of two different electrodes (an electrolyte and conductive solutions) to convert chemical energy into electrical energy or vice versa. During electrolysis, the cell uses electrical energy to drive a non-spontaneous chemical reaction.

There are two main components in an electrochemical cell:

• Electrodes: These are typically solid materials where the actual reduction and oxidation reactions occur. The cathode is where reduction happens, while the anode is where oxidation occurs.
• Electrolyte: This is the medium that allows the flow of electrical charge between the cathode and anode.

In the case of electrolysis of lithium chloride, the electrochemical cell comprises a molten LiCl acting as the electrolyte, where the input electric current splits the compound into elemental lithium and chlorine gas. Understanding how electrochemical cells function is critical for harnessing electrolysis to form substances from their ionic compounds.

Standard Electrode Potential

Standard electrode potential is a measure of the energy change when a reduction or oxidation reaction occurs. It's crucial in determining the minimum voltage required to drive an electrochemical reaction, such as electrolysis. Each half-reaction has its own standard electrode potential, denoted as \( E^0 \).

Standard electrode potentials are measured under standard conditions:

• 298 K temperature
• 1 atm pressure
• 1 M concentration

For the electrolytic reaction involved in lithium chloride, the relevant standard electrode potential for the lithium ion \((Li^+/Li)\) is \(-3.04 V\), meaning it requires an input of energy to reduce lithium ions into lithium metal. The absolute value of this potential informs us of the minimum voltage needed to make the reduction possible. This metric plays a significant role in designing cells and selecting materials for efficient energy usage.