Problem 76 - Chemistry: The Central Science

Question

In an electrolytic process nickel sulfide is oxidized in a two-step reaction: $$ \begin{aligned} \mathrm{Ni}_{3} \mathrm{~S}_{2}(\mathrm{~s}) & \longrightarrow \mathrm{Ni}^{2+}(a q)+2 \mathrm{NiS}(s)+2 \mathrm{e}^{-} \\ \mathrm{NiS}(s) & \longrightarrow \mathrm{Ni}^{2+}(a q)+\mathrm{S}(s)+2 \mathrm{e}^{-} \end{aligned} $$ What mass of \(\mathrm{Ni}^{2+}\) is produced in solution by passing a current of 67 A for a period of \(11.0 \mathrm{hr}\), assuming the cell is \(90 \%\) efficient?

Step-by-Step Solution

Answer

The mass of Ni²⁺ produced in solution after passing a current of 67 A for 11.0 hours with 90% efficiency is \(727.04 \ \text{g}\).

Step 1: Calculate the total charge passed through the cell

To find the total charge passed through the cell, we can use the formula: $$ Q = I \times t $$ where Q is the charge (in Coulombs), I is the current (in Amperes), and t is the time (in seconds). First, we need to convert the time given (11.0 hours) into seconds: $$ 11.0 \ \text{hours} \times \frac{3600 \ \text{seconds}}{1 \ \text{hour}} = 39600 \ \text{seconds} $$ Now we can calculate the charge: $$ Q = 67 \ \text{A} \times 39600 \ \text{s} = 2659200 \ \text{C} $$

Step 2: Consider the efficiency of the cell

Since the cell is 90% efficient, we need to consider only 90% of the total charge calculated above: $$ Q_{\text{effective}}= 0.9 \times 2659200 \ \text{C} = 2393280 \ \text{C} $$

Step 3: Determine the moles of Ni²⁺ produced

Using Faraday's Laws of electrolysis, we can calculate the moles of Ni²⁺ produced. Note that for both reactions, 2 moles of electrons are needed to produce 1 mole of Ni²⁺. The Faraday constant (F) is approximately 96485 C/mol. Therefore, we can find the moles of Ni²⁺ produced as follows: $$ \text{moles of Ni}^{2+} = \frac{Q_{\text{effective}}}{2 \times F} = \frac{2393280 \ \text{C}}{2 \times 96485 \ \text{C/mol}} = 12.391 \ \text{mol} $$

Step 4: Calculate the mass of Ni²⁺ produced

To find the mass of Ni²⁺ produced, we can multiply the moles calculated above by the molar mass of nickel (Ni), which is approximately 58.69 g/mol: $$ \text{mass of Ni}^{2+} = 12.391 \ \text{mol} \times 58.69 \ \frac{\text{g}}{\text{mol}} = 727.04 \ \text{g} $$ The mass of Ni²⁺ produced in solution is 727.04 g.

Key Concepts

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis are critical to understanding how the mass of substances produced at the electrodes in an electrolysis cell is related to the amount of electric charge passed through the cell. There are two laws introduced by Michael Faraday:

• Faraday's First Law states that the mass of a substance altered at an electrode during electrolysis is directly proportional to the amount of electricity that passes through the cell.
• Faraday's Second Law declares that the masses of different substances liberated by the same quantity of electricity are proportional to their respective molar masses (more specifically, equivalent weights).

To put it simply, if you pass an electric current through an electrolytic solution, the amount of chemical change that occurs is proportional to the amount of electricity used. This relationship is quantified using the Faraday constant (approximately 96485 Coulombs/mol), which represents the charge per mole of electrons. In our problem, we applied the first law to determine the moles of Ni²⁺ by dividing the effective charge by two times the Faraday constant, as each nickel ion requires two electrons to form.

Electrochemical Reaction

An electrochemical reaction involves the conversion between chemical energy and electrical energy. In the case of the electrolytic process described, we are looking at a redox reaction, where nickel sulfide (Ni₃S₂) is oxidized to produce nickel ions (Ni²⁺) and solid sulfur (S) as the half-reactions when an external current is applied. In the context of our problem, two electrons are involved in the reaction for each atom of nickel that is oxidized. In electrolysis, the flow of electrons is provided by an external power source, which is what causes the redox reaction to occur in the electrolytic cell. The overall chemical change is a composition of two linked half-reactions occurring at different electrodes. Understanding the electrochemical reactions is crucial for calculating the yield of the desired product in an electrolysis setup.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance (usually in grams per mole), and it plays a vital role in stoichiometry when it comes to electrolysis calculations. It links the macroscopic world, where we measure mass in grams to the microscopic world of atoms and molecules, quantified in moles. Knowing the molar mass of the element in question allows us to convert between mass and moles, a crucial step in chemistry problems. In Faraday's laws, once we calculate the moles of substance produced or consumed in electrolysis, we can determine the mass by multiplying the moles by the substance's molar mass. This is exactly what we did in our calculations for Ni²⁺. With nickel's molar mass being approximately 58.69 g/mol, we were able to calculate the mass of nickel ions produced during the electrolysis.