Question

The element indium is to be obtained by electrolysis of a molten halide of the element. Passage of a current of \(3.20\) A for a period of \(40.0\) min results in formation of \(3.05 \mathrm{~g}\) of \(\mathrm{In}\). What is the oxidation state of indium in the halide melt? (Atomic weight: \(\quad \operatorname{In}=114.8\) ) (a) 3 (b) 2 (c) 5 (d) 1

Short answer

(d) 1

Step-by-step solution

Calculate total charge passed during electrolysis

To find the total charge passed through the electrolyte, use the relation Q = current (I) x time (t). Convert the time from minutes to seconds for compatibility with the current measured in amperes (A).

Calculate moles of electrons used

Using the formula Q = n x F, where Q is the total charge, n is the number of moles of electrons, and F is Faraday's constant (96485 C/mol), calculate the moles of electrons that have passed through the electrolyte.

Calculate moles of Indium deposited

Now, calculate the moles of Indium deposited by dividing the mass of Indium by its atomic weight.

Determine the oxidation state of Indium

To find the oxidation state of Indium, divide the moles of electrons by the moles of Indium deposited. This gives the charge of the Indium ion in the halide before reduction, which is its oxidation state.

Key concepts

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis are pivotal to understanding electrodeposition and the interconversion of chemical and electrical energy in electrochemical cells. The first law states that the amount of chemical change (or the mass of substance deposited) at an electrode during electrolysis is directly proportional to the total electric charge passed through the substance. Mathematically, it is expressed as \( m = (Q/F) \times M/e \) where \( m \) is the mass of the substance deposited, \( Q \) is the electric charge, \( F \) is Faraday's constant, \( M \) is the molar mass of the substance, and \( e \) is the valence number of ions.
Faraday's second law states that when the same amount of electric charge is passed through different electrolytes, the mass of substances produced at the electrodes is directly proportional to their equivalent weights (which is the molar mass divided by the valence number).

These laws are crucial for calculating the quantity of a substance produced during electrolysis, as seen in the exercise where one has to determine the number of moles of electrons to find out the amount of indium deposited.

Oxidation States

Oxidation states, also referred to as oxidation numbers, represent the degree of oxidation of an atom in a chemical compound. Understanding the concept of oxidation states is essential when dealing with electrochemical reactions.
An oxidation state is a hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic. Electrolysis involves the transfer of electrons, and during this process, the oxidation state of an element changes. For example, a metal ion in a molten halide will reduce to a metal during electrolysis, changing its oxidation state to zero.

In the given exercise, the oxidation state of indium in the halide is the charge that indium ion had before being reduced. This information is necessary to establish the relationship between the amount of electricity passed through the cell and the number of indium atoms deposited as the metal.

Mole Concept

The mole concept is a fundamental aspect of chemistry that provides a bridge between the atomic world and the macroscopic world we experience daily. A mole represents Avogadro's number, approximately \(6.022 \times 10^{23}\), of particles, which could be atoms, molecules, ions, or electrons.
For electrolytic processes, the mole concept is used to connect the number of moles of electrons transferred in the reaction to the quantity of substance produced or consumed. The mass of indium obtained in the exercise is converted to moles by dividing by its molar mass so that it can be related to the moles of electrons transferred during the electrolysis.

It's important in electrochemistry exercises like these to understand that the charge passed, measured in coulombs, corresponds to a certain number of moles of electrons, and it is this number that determines the chemical change observed.

Electrochemical Calculations

Electrochemical calculations are at the heart of solving problems related to electrolysis and other electrochemical processes. These calculations often include converting physical quantities like current and time into an electrical charge, using Faraday's laws to relate the electrical charge to chemical quantities, and applying the mole concept to understand the material change.
In the context of our exercise, an understanding of electrochemical calculations enables us to determine the mass of indium produced at the cathode as a result of electrolysis. By calculating the total electric charge and using Faraday's constant, we find the moles of electrons, and subsequently, the moles of indium deposited. Finally, applying the concept of oxidation states, we deduce the ratio of moles of electrons per mole of indium to find the oxidation state of indium in the original halide melt.

This methodical approach to electrochemical calculations is an excellent example of the interplay between physical measurements and chemical realities, two domains bridged by the theories and laws of electrochemistry.