Problem 105 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The same current was passed successively through solution of zinc-ammonium sulphate and nickel-ammonium sulphate rendered alkaline with ammonia. The weights of zinc and nickel deposited in a certain time were found to be \(22.89 \mathrm{~g}\) and \(20.55 \mathrm{~g}\), respectively. Given that the chemical equivalent weight of zinc is \(32.7\), what is the chemical equivalent weight of nickel? (a) \(58.71\) (b) \(29.36\) (c) \(14.39\) (d) \(36.42\)

Step-by-Step Solution

Answer

The chemical equivalent weight of nickel is approximately 29.36.

Step 1: Understand the Problem

In an electrolysis experiment, the same current deposits 22.89 g of zinc and 20.55 g of nickel. The chemical equivalent weight of zinc (Zn) is given as 32.7. We need to find the chemical equivalent weight of nickel (Ni) using the data provided.

Step 2: State the Law of Electrolysis

Faraday's Second Law of Electrolysis states that when the same quantity of electricity is passed through different electrolytes, the weights of the substances deposited are proportional to their chemical equivalent weights. Mathematically, it can be written as \( W_1 / W_2 = E_1 / E_2 \), where \(W_1\) and \(W_2\) are the weights of the substances deposited and \(E_1\) and \(E_2\) are their corresponding chemical equivalent weights.

Step 3: Set Up the Proportion

Using the law and the given data, we can create a proportion: \( 22.89 / 20.55 = 32.7 / E_{Ni} \) where \(E_{Ni}\) is the chemical equivalent weight of nickel.

Step 4: Solve for the Chemical Equivalent Weight of Nickel

Cross-multiply and solve for \(E_{Ni}\): \((22.89 \cdot E_{Ni} = 32.7 \cdot 20.55\)). Now compute \(E_{Ni}\): \((E_{Ni} = (32.7 \cdot 20.55) / 22.89\)).

Step 5: Calculate the Answer

Perform the division to find \(E_{Ni}\): \(E_{Ni} = (32.7 \cdot 20.55) / 22.89 ≈ 29.36\).

Key Concepts

Electrolysis

Electrolysis is the process by which ionic substances are decomposed into simpler substances when an electric current is passed through them. It occurs in an electrochemical cell where the substance to be decomposed, called the electrolyte, is dissolved in a suitable solvent or melted in its molten form.

During electrolysis, positively charged ions (cations) move towards the negative electrode (cathode), where they gain electrons in a process known as reduction. Similarly, negatively charged ions (anions) move towards the positive electrode (anode) and lose electrons, undergoing oxidation. This movement of ions and the subsequent chemical reactions result in the deposition of substances at the electrodes.

By applying this knowledge to our exercise, we considered the deposition of zinc and nickel from their salts solutions when an electric current is passed. The weights of the metals deposited provided a practical application of electrolysis in determining chemical equivalent weights.

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis are fundamental to understanding the quantitative aspects of electrolysis. There are two laws, but in the context of our exercise, Faraday's Second Law is particularly relevant. It states that the amount of substance deposited at an electrode during electrolysis is proportional to its chemical equivalent weight when the same amount of electric charge is passed through different electrolytes.

Mathematically, Faraday's Second Law can be represented as \( W_1 / E_1 = W_2 / E_2 \) where \( W_1 \) and \( W_2 \) are the weights of different substances deposited, and \( E_1 \) and \( E_2 \) are their respective chemical equivalent weights. This law provides the relationship required to solve for the unknown in our given exercise, the chemical equivalent weight of nickel, based on the known equivalent weight of zinc and the weights of both metals deposited.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It provides the calculations concerning the masses of reactants and products, based on the principle that matter is conserved in a chemical reaction.

Calculations in stoichiometry are often based on the balanced chemical equation for the reaction involved. In the context of electrolysis, stoichiometry is important because it allows us to calculate the amounts of substances involved in the electrochemical changes occurring at the electrodes. In our exercise, stoichiometry helps us understand the relationship between the mass of metal deposited during electrolysis and the amount of electric charge passed through the electrolyte.

By utilizing stoichiometry, we can easily relate the physical change (deposition of metal) with the chemical property (chemical equivalent weight) using the quantitative data given in the exercise. This illustrates the practical application of stoichiometry in solving real-world chemical problems.