Magnesium is obtained by electrolysis of molten MgCl2. (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 Mg is formed by passing a current of 97,000 A for a period of 24 h?

Verified step by step guidance

Calculate the total charge (Q) passed through the cells using the formula Q = I \times t, where I is the current (97,000 A) and t is the time in seconds (24 hours converted to seconds).

Determine the number of moles of electrons (n) using the formula n = \frac{Q}{F}, where F is Faraday's constant (approximately 96,485 C/mol).

Use the stoichiometry of the reaction to find the moles of Mg produced. The balanced equation for the electrolysis of MgCl_2 is MgCl_2 \rightarrow Mg + Cl_2, which shows that 2 moles of electrons produce 1 mole of Mg.

Calculate the theoretical mass of Mg produced using the formula mass = moles \times molar mass of Mg (24.305 g/mol).

Adjust the calculated mass of Mg by the efficiency of the cells (96%) to find the actual mass of Mg 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 this process, an electric current is passed through an electrolyte, causing the decomposition of the compound. For magnesium chloride (MgCl2), electrolysis results in the production of magnesium metal 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 quantity of electric charge passed through the electrolyte. The first law states that the mass of a substance produced is directly proportional to the electric charge. This principle is essential for calculating the mass of magnesium formed in the given electrolysis scenario.

Efficiency in Electrolysis

Efficiency in electrolysis refers to the ratio of the actual amount of product obtained to the theoretical amount predicted by Faraday's laws. In this case, the cells are stated to be 96% efficient, meaning that only 96% of the theoretical yield of magnesium is realized. This efficiency must be factored into calculations to determine the actual mass of magnesium produced from the given current and time.

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