(a) Calculate the mass of Li formed by electrolysis of molten LiCl by a current of 7.5 × 10⁴ A flowing for a period of 24 h. Assume the electrolytic cell is 85% efficient. (b) What is the minimum voltage required to drive the reaction?

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Step 1: Determine the total charge (Q) passed through the electrolytic cell using the formula Q = I \times t, where I is the current (7.5 \times 10^4 A) and t is the time in seconds (24 hours converted to seconds).

Step 2: Calculate the number of moles of electrons (n_e) using the formula n_e = \frac{Q}{F}, where F is Faraday's constant (approximately 96485 C/mol).

Step 3: Use the stoichiometry of the reaction to find the moles of Li produced. The reaction is Li^+ + e^- \rightarrow Li, indicating a 1:1 mole ratio between electrons and lithium.

Step 4: Calculate the theoretical mass of Li produced using the formula mass = moles \times molar mass of Li (approximately 6.94 g/mol).

Step 5: Adjust for the efficiency of the cell by multiplying the theoretical mass by the efficiency (85%) to find the actual mass of Li produced.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electrolysis

Electrolysis is a chemical process that uses electrical energy to drive a non-spontaneous reaction. In this process, an electric current is passed through an electrolyte, causing the decomposition of the compound. For molten LiCl, electrolysis results in the formation of lithium metal and chlorine gas at the electrodes. Understanding the principles of electrolysis is essential for calculating the mass of lithium produced.

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis quantify the relationship between the amount of substance produced at an electrode and the quantity of electric charge passed through the electrolyte. The first law states that the mass of a substance altered at an electrode is directly proportional to the total electric charge passed. This principle is crucial for calculating the mass of lithium formed in the given electrolysis scenario.

Electrolytic Cell Efficiency

The efficiency of an electrolytic cell refers to the ratio of the actual amount of product formed to the theoretical amount predicted by Faraday's laws. In this case, the cell is stated to be 85% efficient, meaning that only 85% of the theoretical lithium mass calculated from the charge is actually produced. This efficiency factor is vital for accurately determining the mass of lithium formed during the electrolysis process.