Question

An electrolysis experiment is performed to determine the value of the Faraday constant (number of coulombs per mole of electrons). In this experiment, \(28.8 \mathrm{~g}\) of gold is plated out from a AuCN solution by running an electrolytic cell for two hours with a current of \(2.00 \mathrm{~A}\). What is the experimental value obtained for the Faraday constant?

Short answer

Answer: The experimental value obtained for the Faraday constant in this electrolysis experiment is approximately \(32,850 \mathrm{~C/mol}\).

Step-by-step solution

Calculate the number of moles of gold plated out

We are given that \(28.8 \mathrm{~g}\) of gold was plated out during the experiment. We can calculate the number of moles of gold by using the molar mass of gold, which is \(197.0 \mathrm{~g/mol}\): $$\text{Number of moles of gold} = \frac{28.8 \mathrm{~g}}{197.0 \mathrm{~g/mol}} \approx 0.146 \mathrm{~mol}.$$

Calculate the total charge passed through the cell

We are given that the cell had a current of \(2.00 \mathrm{~A}\) running through it for two hours. Since \(1 \mathrm{~A}\) is equivalent to \(1 \mathrm{~C/s}\), we can find the total charge (in coulombs) that was passed through the cell by multiplying the current by the time in seconds: $$\text{Total charge} = 2.00 \mathrm{~A} \times 2 \mathrm{~hour} \times \frac{3600 \mathrm{~s}}{1 \mathrm{~hour}} = 14400 \mathrm{~C}.$$

Calculate the experimental value for the Faraday constant

To calculate the experimental value for the Faraday constant, we will divide the total charge (in coulombs) by the number of moles of electrons that were transferred. Since one mole of gold atoms (Au) requires 3 moles of electrons to be fully reduced (Au\(^{3+}\) + 3e\(^-\) → Au), we will first determine the number of moles of electrons transferred. The number of moles of electrons transferred is three times the number of moles of gold: $$\text{Number of moles of electrons} = 3 \times 0.146 \mathrm{~mol} \approx 0.438 \mathrm{~mol}.$$ Now, we can find the experimental value for the Faraday constant by dividing the total charge by the number of moles of electrons: $$\text{Faraday constant} = \frac{14400 \mathrm{~C}}{0.438 \text{~mol}} \approx 32850 \mathrm{~C/mol}.$$ The experimental value obtained for the Faraday constant in this electrolysis experiment is approximately \(32,850 \mathrm{~C/mol}\).

Key concepts

Electrochemical Reaction

An electrochemical reaction is a process that converts chemical energy into electrical energy or vice versa. These reactions occur in electrochemical cells, which comprise two electrodes and an electrolyte. During an electrolysis experiment, like the one to determine the Faraday constant, an electric current is passed through an electrolytic cell, causing a chemical change. This specific type of electrochemical reaction is known as electrolysis.

Electrolysis involves the movement of ions in the electrolyte between the electrodes. When electricity is applied, positively charged ions (cations) migrate to the cathode, where reduction occurs, and negatively charged ions (anions) migrate to the anode, where oxidation happens. For instance, in the gold plating electrolysis experiment, gold ions in the AuCN solution are reduced to solid gold at the cathode. Understanding electrochemical reactions is critical in the context of the Faraday constant, as it relates to the charge needed for reducing or oxidizing a certain amount of substance.

Molar Mass of Gold

The molar mass of an element is the mass of one mole of that element's atoms and is expressed in grams per mole (g/mol). For gold (Au), the molar mass is approximately 197.0 g/mol. The concept of molar mass is essential when working with chemical quantities in laboratories or industries.

In our textbook example, the molar mass of gold enables us to determine how much gold in moles can be plated out during electrolysis when given the mass in grams. Using the molar mass of gold, we can convert from mass to moles, which is a crucial step for subsequent calculations in the determination of the Faraday constant. Knowing the accurate molar mass allows for precise stoichiometric conversions that form the basis of many chemical calculations.

Calculating Moles

The concept of moles connects the microscopic world of atoms and molecules to the macroscopic quantities that we can measure. One mole corresponds to Avogadro's number (approximately \(6.022 \times 10^{23}\)) of particles, whether they are atoms, molecules, ions, or electrons.

In the context of our electrolysis experiment, calculating moles involves using the mass of gold (expressed in grams) and dividing it by the molar mass of gold. The formula looks like this: \[\text{Number of moles} = \frac{\text{Given mass in grams}}{\text{Molar mass of element (g/mol)}}\].

By doing this, we can link the physical mass plated in the experiment to the amount of substance in terms of moles. This step is crucial for understanding the stoichiometry of the electrochemical reaction and for calculating the Faraday constant.

Electric Current and Charge

In electrochemistry, the relationship between electric current and charge is fundamental. Electric current, measured in Amperes (A), quantifies the flow of electric charge. One Ampere of current represents the flow of one Coulomb (C) of charge passing through a point in one second. The total charge passed in an experiment can be calculated by multiplying the current by the time during which the current flows.

In our example, we determine the total charge conveyed through the electrolytic cell over two hours of constant current using the formula: \[\text{Total charge (C)} = \text{Current (A)} \times \text{Time (s)}\].

Understanding the direct relationship between current, charge, and time enables students to connect quantities in an electrolysis experiment to the fundamental concept of the Faraday constant, which represents the total charge required to reduce or oxidize a mole of substance.