Question

A factory wants to produce \(1.00 \times 10^{3} \mathrm{~kg}\) barium from the electrolysis of molten barium chloride. What current must be applied for \(4.00 \mathrm{~h}\) to accomplish this?

Short answer

To produce \(1.00 \times 10^3 kg\) of Barium through electrolysis of molten barium chloride in 4 hours, first calculate the moles of Barium needed using its molar mass (137.33 g/mol). Then, find the moles of electrons needed for electrolysis, considering that each Barium cation requires 2 electrons. Next, convert the moles of electrons to total charge using the Faraday constant (96485 C/mol). Finally, determine the required current by dividing the total charge by the time (in seconds) for electrolysis. The result will give you the necessary current to achieve this goal.

Step-by-step solution

Determine moles of Barium required

First, we need to find out how many moles of Barium are needed to reach the desired mass of 1000 kg. To do this, we will use the molar mass of Barium (Ba), which is approximately 137.33 g/mol. Given mass of Barium = \(1.00 \times 10^3 kg = 1.00 \times 10^6 g\) Molar mass of Barium (Ba) = 137.33 g/mol Moles of Barium required = \(\frac{Mass}{Molar~mass}\)

Calculate needed electrons for electrolysis

In the electrolysis of molten Barium chloride, the reaction for the production of Barium is given as: Ba^2+ + 2e^- -> Ba From the above reaction, we observe that every Barium cation needs 2 electrons for electrolysis. Therefore, we will multiply the moles of Barium by the number of electrons required for electrolysis (2). Moles of electrons needed = moles of Barium × number of electrons per mole of Barium #-}

Convert moles of electrons to charge

Now, we'll convert the moles of electrons required into total charge using the Faraday constant (F). The Faraday constant represents the amount of charge per mole of electrons and is equal to 96485 C/mol. Total charge, Q = moles of electrons needed × Faraday constant

Determine the time for electrolysis

The given time for electrolysis is 4 hours. We'll convert this time into seconds: Time, t = 4 hours × 3600 seconds/hour

Calculate the required current

Now, we can find the required current using the formula: \(Current, I = \frac{Charge}{Time}\) Substitute the values of total charge (Q) and time (t) to obtain the required current. By following these steps, you'll be able to determine the necessary current to produce the desired amount of Barium through electrolysis in the given time.

Key concepts

Barium

Barium is a chemical element with the symbol Ba and atomic number 56. It is part of the alkali earth metals group on the periodic table. Barium is a soft, silvery metal that is not found as a free element in nature, due to its high reactivity. Instead, it is usually found in combination with other elements in minerals such as barite and witherite.

In industrial applications, barium compounds are used in various ways. One common application is in the production of barium sulfate, which is used in medical imaging due to its opacity to X-rays. Another significant use is the electroplating process where barium's unique properties are utilized.

For this exercise, we focus on pure barium production through electrolysis, a method highlighted by the separation of elements using electric current. In the scenario given, 1000 kg of barium is the target amount to produce. Understanding its molar mass is crucial, as it serves as the bridge between the weight of the substance and the number of atoms or molecules it contains. Knowing that the molar mass of barium is approximately 137.33 g/mol helps in converting mass to moles, a step essential in the process of calculating various electrochemical parameters further used in electrolysis.

Faraday constant

The Faraday constant is a fundamental figure in electrochemistry. Its value is approximately 96485 coulombs per mole of electrons. This constant reflects the total electric charge carried by one mole of electrons, making it a vital component in calculations involving electrolysis.

Understanding the Faraday constant allows us to analyze and convert the moles of electrons involved in a given reaction into the actual electrical charge. For example, when you have determined that a certain amount of moles of electrons is needed for electrolysis, the Faraday constant helps you find out the total charge that these electrons will provide.

This concept is essential because it bridges the gap between chemical reactions, which occur on a molecular level, and electrical engineering, where these reactions are harnessed for practical use. Whether you’re working with barium or any other element, the Faraday constant is a key tool for translating chemical requirements into actionable electrical parameters.

Current calculation

Current, symbolized as I, is defined as the flow of electric charge and is measured in amperes (A). Calculating the current involves understanding the relationship between charge and time. In our electrolysis scenario, where barium is produced from barium chloride, this calculation is crucial for determining how to provide the necessary energy to drive the reaction.

Using the formula \[ I = \frac{Q}{t} \]We can calculate the current. Here, \(Q\) is the total charge calculated using the moles of electrons involved and the Faraday constant, and \(t\) is the time in seconds over which the electrolysis occurs.

For the exercise in question, the time is 4 hours, which must be converted into seconds (14400 seconds) for the formula to work correctly with the charge in coulombs. By substituting the values for charge and time, you derive the current required to achieve the desired chemical transformation in the specified time frame. This concept shows how deep the relationship between chemistry and physics runs, as you translate a chemical process into a controllable physical phenomenon.

Moles of electrons

The concept of moles of electrons is pivotal in understanding how electrolysis works. Electrochemical reactions involve electrons moving from one species to another, and here is where the idea of 'moles' becomes useful.

In simple chemical terms, a mole is just a way to count large numbers of small things, translating to Avogadro’s number, which is approximately \(6.022 \times 10^{23}\). When we talk about a "mole of electrons," we mean this vast number of electrons.

In electrolysis, the stoichiometry of the reaction tells you how many moles of electrons are required to reduce a certain amount of ions. For barium production, the reaction \[ \text{Ba}^{2+} + 2\text{e}^- \rightarrow \text{Ba} \]indicates that each barium ion consumes 2 moles of electrons for reduction to metallic barium. These moles of electrons need to be converted into charge using the Faraday constant to determine the electrical charge necessary to drive the reaction forward.

Understanding moles of electrons allows chemists and engineers to design processes that efficiently use electricity as a reagent to carry out significant chemical transformations.