Question

The amounts of metals deposited when \(965 \mathrm{C}\) of electricity is passed through \(\mathrm{NaCl}\) and \(\mathrm{AgNO}_{3}\) solutions are ___ and ___ respectively. (a) \(23 \mathrm{~g}, 108 \mathrm{~g}\) (b) \(11.5 \mathrm{~g}, 54 \mathrm{~g}\) (c) \(0.23 \mathrm{~g}, 1.08 \mathrm{~g}\) (d) \(2.3 \mathrm{~g}, 10.8 \mathrm{~g}\)

Short answer

Answer: The amounts of metals deposited are 23 g for Na and 108 g for Ag.

Step-by-step solution

Identify the chemical reactions

In the NaCl solution, Na+ ions are reduced to Na metal, and in the AgNO3 solution, Ag+ ions are reduced to Ag metal. Write down the half-reactions: Na+ + e- -> Na Ag+ + e- -> Ag

Use Faraday’s law of electrolysis

We can use Faraday’s law of electrolysis to determine the amount of each substance deposited. Faraday's law states that: m = (Q * n * M) / (z * F) where: m = mass of deposited substance Q = charge passed (in coulombs) n = number of moles of electrons exchanged (1 mole for both reactions) M = molar mass of the substance z = number of electrons exchanged (1 for both reactions) F = Faraday's constant (96485 C/mol)

Calculate the amount of Na deposited

Using the given values and the equation for Faraday's law, calculate the mass of Na deposited: m = (965C * 1 mol * 22.99 g/mol) / (1 * 96485 C/mol) m ≈ 23 g

Calculate the amount of Ag deposited

Using the given values and the equation for Faraday's law, calculate the mass of Ag deposited: m = (965C * 1 mol * 107.87 g/mol) / (1 * 96485 C/mol) m ≈ 108 g

Match the answer with the given options

We found that the amounts of metals deposited when 965C of electricity is passed through NaCl and AgNO3 solutions are 23g and 108g, respectively. This matches option (a). So, the correct answer is (a) \(23 \mathrm{~g}, 108 \mathrm{~g}\).

Key concepts

Electrochemical Reaction

At the heart of understanding Faraday's law of electrolysis is grasping the concept of electrochemical reactions, which lie at the intersection of chemistry and electricity. An electrochemical reaction involves the movement of electrons from one substance to another through an electrical circuit. In the context of our exercise, when electricity is passed through solutions of NaCl (sodium chloride) and AgNO₃ (silver nitrate), electrochemical reactions take place. In these reactions, metal ions in solution gain electrons and are 'reduced' to form solid metals.

In simpler terms, Na⁺ ions gain an electron to become sodium (Na) metal, and Ag⁺ ions gain an electron to become silver (Ag) metal. This is achieved by applying an electrical current, which forces the electrons to flow in a specific direction, thereby transforming the ions into their metallic forms. Understanding the underlying electrochemical processes is essential for comprehending how the amount of metal deposited is directly proportional to the amount of electricity used, which is the essence of Faraday's law.

Molar Mass

The concept of molar mass is a cornerstone in chemistry, especially when dealing with the quantitative aspects of reactions, such as those in electrolysis. The molar mass represents the mass of one mole of a substance, usually measured in grams per mole (g/mol). In this electrochemical context, it determines the mass of the metal that will be deposited during the reaction.

For example, in our textbook exercise, the molar mass of sodium (Na) is 22.99 g/mol, and that of silver (Ag) is 107.87 g/mol. When combining these values with the known amount of charge in coulombs and Faraday's constant, we can calculate the actual mass of each element that will be deposited from the solution. It's crucial to note that the higher the molar mass, the greater the mass of the substance that will be deposited for the same amount of charge passed through the solution.

Coulombs

The concept of coulombs is foundational in the realm of electricity, named after the physicist Charles-Augustin de Coulomb. A coulomb, symbolized as C, is the unit of electrical charge. To put it in perspective, one coulomb is roughly the amount of charge that passes through a common incandescent light bulb in one second at a current of one ampere.

In our exercise involving Faraday's law, the charge passed through the solutions is given as 965 C. This quantity allows us to calculate the mass of metal deposited by linking the charge to the molar mass and the number of electrons transferred. Understanding how coulombs relate to the processes of electrolytic deposition is vital, as it defines the relationship between electric charge and the chemical changes observed during electrolysis, illustrating the practical application of Faraday's law.