What Is The Initial Mass Of Iron(II) Chloride (FeCl₂) In A Mixture After Electrolysis, Given Specific Cathode Mass Increase And Anode Gas Production?

In the realm of chemistry, electrolysis stands as a cornerstone technique for driving non-spontaneous chemical reactions using electrical energy. This process finds extensive applications in various industrial and scientific domains, including metal refining, electroplating, and the production of essential chemicals. In this comprehensive exploration, we delve into the intricate electrolysis of a mixture containing both iron(II) chloride (FeCl₂) and iron(III) chloride (FeCl₃) dissolved in water. Our focus will be on meticulously analyzing the electrochemical reactions transpiring at both the cathode and anode, quantifying the mass changes, and unraveling the stoichiometric relationships governing the entire process. Through a step-by-step approach, we aim to elucidate the underlying principles and provide a clear understanding of the chemical transformations involved.

Electrolysis is a fascinating process where an electric current is used to drive a non-spontaneous chemical reaction. When a mixture of iron(II) chloride (FeCl₂) and iron(III) chloride (FeCl₃) is dissolved in water and subjected to electrolysis, a series of redox reactions occur at the electrodes. At the cathode, reduction takes place, where metal ions gain electrons and deposit as a solid metal. Conversely, at the anode, oxidation occurs, where ions lose electrons and form gaseous products or undergo other oxidative transformations. Understanding these reactions is crucial for determining the quantitative aspects of the electrolysis, such as the mass changes at the electrodes and the amount of gases evolved. Stoichiometry, the study of the quantitative relationships between reactants and products in chemical reactions, plays a pivotal role in deciphering these transformations. By carefully analyzing the mass changes and gas evolution, we can determine the initial composition of the iron chloride mixture.

Consider a scenario where a mixture of iron(II) chloride (FeCl₂) and iron(III) chloride (FeCl₃) undergoes electrolysis in an aqueous solution. During this process, the cathode witnesses an increase in mass of 33.6 grams due to the deposition of metallic iron. Simultaneously, at the anode, 1 mole of gas is liberated, exhibiting a combined mass of 59.3 grams. The electrolysis continues until only pure water remains in the solution. The central objective is to determine the initial mass of iron(II) chloride (FeCl₂) present in the mixture before the commencement of electrolysis. This problem encapsulates several key electrochemical concepts and requires a methodical approach to unravel the underlying reactions and stoichiometric relationships. By systematically analyzing the given data and applying the principles of electrolysis, we can deduce the initial composition of the iron chloride mixture.

Electrolysis involves the use of electrical energy to drive non-spontaneous chemical reactions. In this specific problem, the electrolysis of a mixture of FeCl₂ and FeCl₃ in water results in the deposition of iron at the cathode and the evolution of gases at the anode. The mass increase at the cathode (33.6 g) directly corresponds to the amount of iron deposited, while the 1 mole of gas evolved at the anode with a mass of 59.3 g provides crucial information about the oxidation reactions occurring there. The fact that only pure water remains after electrolysis implies that all iron ions have been reduced and all chloride ions have been oxidized. The challenge lies in using these pieces of information to quantitatively determine the initial mass of FeCl₂. This requires a deep understanding of electrolysis principles, including half-cell reactions, Faraday's laws, and stoichiometry.

To comprehensively understand the electrolysis process, we must dissect the electrochemical reactions transpiring at both the cathode and the anode. At the cathode, the reduction of iron ions (Fe²⁺ and Fe³⁺) takes place, leading to the deposition of solid iron (Fe). The specific reactions are as follows:

Fe²⁺(aq) + 2e⁻ → Fe(s)

Fe³⁺(aq) + 3e⁻ → Fe(s)

These reactions dictate the increase in mass observed at the cathode. Conversely, at the anode, the oxidation of chloride ions (Cl⁻) occurs, resulting in the evolution of chlorine gas (Cl₂): 2Cl⁻(aq) → Cl₂(g) + 2e⁻

However, the problem statement indicates the evolution of 1 mole of gas with a mass of 59.3 g, which cannot be solely attributed to chlorine gas (Cl₂, molar mass ≈ 71 g/mol). This discrepancy suggests the involvement of another gas, which is oxygen (O₂), produced from the oxidation of water: 2H₂O(l) → O₂(g) + 4H⁺(aq) + 4e⁻

Therefore, the gas evolved at the anode is a mixture of chlorine (Cl₂) and oxygen (O₂). Understanding these half-cell reactions is paramount for quantifying the amounts of reactants consumed and products formed during electrolysis. The stoichiometry of these reactions, combined with the given data, will allow us to calculate the initial mass of FeCl₂.

The electrolysis of a mixture of FeCl₂ and FeCl₃ involves several redox reactions at the electrodes. The reduction of iron ions at the cathode is the primary process leading to the mass increase. Both Fe²⁺ and Fe³⁺ ions can be reduced to solid iron, contributing to the overall mass gain. The stoichiometry of these reactions is critical; each Fe²⁺ ion requires 2 electrons, while each Fe³⁺ ion requires 3 electrons to be reduced to Fe. At the anode, the oxidation of chloride ions to chlorine gas is a key reaction. However, the evolution of 1 mole of gas with a mass less than that of pure chlorine suggests that another gas is also being produced. The oxidation of water to oxygen gas is a likely secondary reaction, especially in solutions with lower chloride concentrations. The balance between chlorine and oxygen evolution depends on various factors, including the ion concentrations and the applied potential. By carefully considering these reactions and their stoichiometry, we can build a framework for calculating the initial amount of FeCl₂.

To determine the initial mass of iron(II) chloride, a meticulous quantitative analysis is essential. The mass increase at the cathode (33.6 g) allows us to calculate the total moles of iron deposited: Moles of Fe = Mass of Fe / Molar mass of Fe = 33.6 g / 55.845 g/mol ≈ 0.602 mol

Let's denote the moles of FeCl₂ as 'x' and the moles of FeCl₃ as 'y'. From the reduction reactions at the cathode, we can infer: Moles of Fe from FeCl₂ = x Moles of Fe from FeCl₃ = y

Therefore, x + y = 0.602 mol (Equation 1)

At the anode, let's denote the moles of Cl₂ as 'a' and the moles of O₂ as 'b'. We are given that: a + b = 1 mol (Equation 2)

The mass of the gas mixture is 59.3 g: (a × 70.906 g/mol) + (b × 32 g/mol) = 59.3 g (Equation 3)

Solving Equations 2 and 3 simultaneously yields: a ≈ 0.705 mol b ≈ 0.295 mol

The moles of Cl₂ produced are related to the moles of FeCl₂ and FeCl₃ oxidized: 2x + 3y = 2a (Equation 4)

Substituting the value of 'a' into Equation 4: 2x + 3y = 2 × 0.705 ≈ 1.41 mol (Equation 5)

Now, we solve Equations 1 and 5 simultaneously: From Equation 1, y = 0.602 - x

Substituting 'y' in Equation 5: 2x + 3(0.602 - x) = 1.41 2x + 1.806 - 3x = 1.41 -x = -0.396 x ≈ 0.396 mol

Therefore, the moles of FeCl₂ = 0.396 mol Initial mass of FeCl₂ = Moles of FeCl₂ × Molar mass of FeCl₂ = 0.396 mol × 126.751 g/mol ≈ 50.2 g

This quantitative analysis provides a clear and methodical approach to determine the initial mass of FeCl₂ in the mixture. The steps involve applying stoichiometry, Faraday's laws, and solving simultaneous equations to correlate the mass changes and gas evolution with the amounts of reactants and products involved in the electrolysis process. The careful balancing of equations and the systematic approach to solving for unknowns are critical for obtaining an accurate result. The result indicates that approximately 50.2 grams of FeCl₂ were initially present in the mixture, demonstrating the power of quantitative analysis in electrochemistry.

The quantitative analysis of electrolysis involves several steps, each crucial for accurately determining the initial mass of FeCl₂. The starting point is the mass increase at the cathode, which allows us to calculate the total moles of iron deposited. This is a direct application of Faraday's laws of electrolysis, which relate the amount of substance produced at an electrode to the quantity of electricity passed through the electrolytic cell. The next step involves setting up stoichiometric equations based on the half-cell reactions. These equations relate the moles of iron deposited to the initial moles of FeCl₂ and FeCl₃. Similarly, the moles of gases evolved at the anode are related to the moles of Cl₂ and O₂ produced. The simultaneous solution of these equations provides the key to unlocking the initial composition of the mixture. The mass of the gas mixture and the total moles of gas evolved provide additional constraints that allow us to determine the individual moles of Cl₂ and O₂. By carefully combining these pieces of information, we can solve for the moles of FeCl₂ and, consequently, its initial mass. The accuracy of this calculation hinges on the precision of the experimental data and the correct application of electrochemical principles.

In conclusion, through a detailed analysis of the electrolysis process involving a mixture of iron(II) chloride and iron(III) chloride, we have successfully determined the initial mass of iron(II) chloride to be approximately 50.2 grams. This determination involved a systematic approach, including the identification of electrochemical reactions at both electrodes, the application of stoichiometric principles, and the quantitative analysis of mass changes and gas evolution. The electrolysis of iron chloride mixtures is a complex process involving multiple redox reactions. The ability to quantitatively analyze such processes is crucial in various applications, including industrial electrochemistry and chemical analysis. The approach used in this analysis can be extended to other electrolysis problems, demonstrating the power of electrochemical principles in solving practical chemical challenges.

The determination of the initial mass of FeCl₂ through electrolysis highlights the importance of understanding electrochemical reactions and their stoichiometry. The analysis involved several critical steps, starting from the identification of the reactions occurring at the cathode and anode, to the quantitative assessment of the products formed. The mass increase at the cathode provided a direct measure of the total iron deposited, while the gas evolution at the anode offered insights into the oxidation processes. The key to solving this problem was the careful application of stoichiometry and Faraday's laws, combined with the constraints provided by the total moles and mass of the gases evolved. The result, approximately 50.2 grams of initial FeCl₂, is a testament to the power of electrochemical analysis in quantitatively determining the composition of mixtures. The methodology employed here serves as a valuable framework for tackling similar problems in electrolysis and electrochemistry, showcasing the relevance of these principles in both theoretical and practical contexts.

6. Keywords:

• Electrolysis
• Iron(II) Chloride
• Iron(III) Chloride
• Stoichiometry
• Electrochemical Reactions
• Quantitative Analysis
• Cathode
• Anode
• Gas Evolution
• Faraday's Laws

7. Repair Input Keyword:

What is the initial mass of iron(II) chloride when a mixture of iron(II) chloride and iron(III) chloride is dissolved in water and electrolyzed, given that the cathode mass increases by 33.6 g, the anode produces 1 mol of gases with a mass of 59.3 g, and only pure water remains after electrolysis?