Three Faraday of electricity is passed through three electrolytic cells connected in series having \(\mathrm{Ag}^{+}, \mathrm{Ca}^{+2}\) and \(\mathrm{Al}^{3+}\) ions respectively. The molar ratio in which these are liberated at electrodes can be given as? (a) \(3: 2: 1\) (b) \(1: 2: 3\) (c) \(6: 3: 2\) (d) \(1: 2: 1\)

An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or facilitating chemical reactions through the introduction of electrical energy. There are two main types of electrochemical cells: galvanic cells, also known as voltaic cells, which convert chemical energy into electrical energy, and electrolytic cells, which do the opposite.

Electrochemical cells are made up of electrodes - the anode and the cathode - immersed in an electrolyte solution containing ions. When a chemical reaction occurs at the electrodes, electrons flow through an external circuit, generating an electric current.

In the context of Faraday's laws of electrolysis, the electrochemical cell in question is an electrolytic cell, where electricity is used to drive non-spontaneous chemical reactions. Understanding the function and components of electrochemical cells is crucial for interpreting electrolytic processes and calculating the outcomes of such reactions.

Connecting electrolytic cells in series means that the same electric current passes sequentially through multiple cells. The amount of electricity, measured in Faradays, is consistent across all the cells. This is an important consideration in electrolysis because Faraday's laws state the quantity of substance liberated at an electrode is directly proportional to the quantity of electricity.

When cells are in series, any variable that depends on the electric current, such as the amount of substance deposited or liberated at the electrode, will be affected equally. In our example, the three electrolytic cells each contain different metal ions, but since they are connected in series, they all receive the same amount of electricity, which is proportional to the mass of ions deposited at the cathode.

The molar ratio electrolysis relates to the proportions of substances produced at the electrodes during the electrolytic process, based on the number of moles of electrons (or Faradays of electricity) that have transferred. One Faraday of electricity is equivalent to the charge carried by one mole of electrons.

When calculating the molar ratio, Faraday's second law comes into play: it allows us to predict the amount of each substance liberated at the electrodes based on its equivalent weight and the total charge passed through the electrolyte. In our example, the molar ratio between silver (Ag), calcium (Ca), and aluminum (Al) ions results from the specific charge (valency) of each ion and the total charge (in Faradays) passed through each cell.

The chemical equivalent weight of a substance is a crucial concept in electrolysis, as it helps determine the mass of a substance that is liberated or deposited at an electrode. It is defined as the molar mass of a substance divided by its valence number (the number of electrons it can donate or accept).

Faraday's second law comes into force here, stating that different substances deposited or liberated by an equal amount of electric charge will be in proportion to their respective chemical equivalent weights.

For example, the valence of \( \mathrm{Ag}^{+} \) is 1, \( \mathrm{Ca}^{+2} \) is 2, and \( \mathrm{Al}^{3+} \) is 3. So their chemical equivalent weights would be their atomic masses divided by 1, 2, and 3, respectively. This relationship allows us to calculate the mass of each element released during electrolysis, which leads us to solve the molar ratio problem presented in the exercise.