How many hours are required to produce 10.0 kg of magnesium by electrolysis of molten MgCl2 with a constant current of 1.00 * 10^4 A? How many liters of Cl2 at STP will be obtained?

Verified step by step guidance

Step 1: Write the balanced chemical equation for the electrolysis of molten MgCl_2. The reaction is: \[ \text{MgCl}_2 \rightarrow \text{Mg} + \text{Cl}_2 \].

Step 2: Determine the moles of magnesium to be produced. Use the molar mass of magnesium (24.31 g/mol) to convert 10.0 kg of magnesium to moles.

Step 3: Use the stoichiometry of the reaction to find the moles of electrons required. From the balanced equation, 2 moles of electrons are needed to produce 1 mole of Mg.

Step 4: Calculate the total charge required using the formula \( Q = n \times F \), where \( n \) is the moles of electrons and \( F \) is Faraday's constant (96485 C/mol).

Step 5: Determine the time in seconds using the formula \( t = \frac{Q}{I} \), where \( I \) is the current (1.00 \times 10^4 \text{ A} \). Convert the time from seconds to hours.

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 context, it involves the decomposition of molten magnesium chloride (MgCl2) into magnesium and chlorine gas when an electric current is passed through it. The amount of substance produced during electrolysis can be calculated using Faraday's laws, which relate the quantity of electricity used to the amount of substance transformed.

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis state that the amount of substance produced at an electrode during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte. The first law quantifies this relationship, while the second law relates the mass of the substance produced to its molar mass and the number of electrons transferred. These principles are essential for calculating the amount of magnesium produced from a given current over time.

Stoichiometry of Gaseous Products

Stoichiometry involves the calculation of reactants and products in chemical reactions. In this case, it is important to understand the stoichiometric relationships between magnesium and chlorine gas produced during the electrolysis of MgCl2. At standard temperature and pressure (STP), one mole of any gas occupies 22.4 liters, allowing for the conversion of moles of chlorine gas produced into liters, which is crucial for determining the volume of Cl2 generated.