Elemental calcium is produced by the electrolysis of molten CaCl2. (a) What mass of calcium can be produced by this process if a current of 7.5 * 10^3 A is applied for 48 h? Assume that the electrolytic cell is 68% efficient. (b) What is the minimum voltage needed to cause the electrolysis?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780137542970

Verified step by step guidance

Step 1: Determine the total charge passed through the electrolytic cell using the formula Q = I \(\times\) t, where Q is the charge in coulombs, I is the current in amperes, and t is the time in seconds. Convert the time from hours to seconds.

Step 2: Calculate the number of moles of electrons transferred using Faraday's constant (F = 96485 C/mol). Use the formula: \(\text{moles of electrons}\) = \(\frac{Q}{F}\).

Step 3: Use the stoichiometry of the reaction to find the moles of calcium produced. The half-reaction for the reduction of calcium is: \(\text{Ca}\)^{2+} + 2e^- \(\rightarrow\) \(\text{Ca}\). This indicates that 2 moles of electrons produce 1 mole of calcium.

Step 4: Calculate the theoretical mass of calcium produced using the molar mass of calcium (40.08 g/mol). Multiply the moles of calcium by its molar mass.

Step 5: Adjust the theoretical mass of calcium for the efficiency of the electrolytic cell. Multiply the theoretical mass by the efficiency (68%) to find the actual mass of calcium produced.

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 the case of molten CaCl2, the application of an electric current causes the compound to dissociate into calcium and chlorine ions, allowing for the production of elemental calcium at the cathode and chlorine gas at the anode.

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis quantify the relationship between the amount of substance produced at an electrode and the electric charge passed through the electrolyte. The first law states that the mass of a substance produced is directly proportional to the quantity of electricity that passes through the cell, which can be calculated using the formula: mass = (current × time × molar mass) / (n × F), where n is the number of moles of electrons and F is Faraday's constant.

Efficiency of Electrolytic Cells

The efficiency of an electrolytic cell refers to the ratio of the actual amount of product obtained to the theoretical amount predicted by Faraday's laws. In this case, the cell's efficiency is given as 68%, meaning that only 68% of the theoretical yield of calcium will be produced under the specified conditions. This efficiency must be factored into calculations to determine the actual mass of calcium produced.

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