Question

Describe a laboratory experiment that you could perform to evaluate the Faraday constant, \(F,\) and then show how you could use this value to determine the Avogadro constant.

Short answer

The laboratory experiment will involve the electrolysis of a copper sulphate solution with copper electrodes, with the electric current and time being precisely measured. The Faraday constant, representing the total charge per mole of electrons, is calculated from the measurements taken during the experiment. This constant can subsequently be used to compute the Avogadro constant, which represents the number of particles in one mole of a substance, by dividing the Faraday constant by the charge of one electron.

Step-by-step solution

Design an Experiment to determine the Faraday Constant

An experiment can be set up where electrolysis is performed on a solution of Copper Sulphate using copper electrodes. The electric current and the time are precisely measured and controlled. The electrode where the reduction reaction takes place will increase in mass due to the deposition of copper. The increase in mass is measured precisely.

Calculation of Faraday Constant

Faraday's law of electrolysis tells us that the amount of a substance deposited during electrolysis is directly proportional to the amount of charge passed. We know the molar mass of copper, the charge of one mole of electrons, and from the experiment the increase in mass of copper article, and the total charge passed. Thus, we can calculate the Faraday constant \(F\) using the formula: \[F= \frac{I \times t}{(w/M) \times n}\] where \(I\) is the current, \(t\) is the time, \(w\) is the increase in mass of the copper electrode, \(M\) is the molar mass of copper and \(n\) is the number of electrons involved in the redox reaction.

Use Faraday Constant to find Avogadro Constant

As mentioned earlier, Faraday constant \(F\) is the total charge carried by one mole of electrons. Therefore, we can use the formula \[F = e \times N_A\] where \(e\) is the charge of one electron (1.60218 x 10^-19 C) and \(N_A\) is the Avogadro constant. So, \[N_A = \frac{F}{e}\] By substituting the value of \(F\) (calculated in previous step), we can find the Avogadro constant.

Key concepts

Exploring the Electrolysis of Copper Sulfate

The electrolysis of copper sulfate is a classic chemistry lab experiment used to demonstrate the principles of electrolysis. During this process, an electrical current is passed through an aqueous solution of copper (II) sulfate, which results in the decomposition of the solution into its component elements.

At the cathode, the reduction reaction occurs, and copper ions gain electrons to form copper metal, which can be observed as an increase in mass of the copper electrode. Conversely, at the anode, oxidation takes place, and copper metal is converted into copper ions, which enter the solution, potentially reducing the mass of the electrode.\[Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\] at the cathode, and \[Cu(s) \rightarrow Cu^{2+}(aq) + 2e^-\] at the anode.

In this experiment, it is important to control variables such as the concentration of the copper sulfate solution, temperature, and the surface area of the electrodes. To improve the results, the electrodes should be cleaned thoroughly before the experiment to remove any oxide layers, and the same electric current should be maintained throughout the process. The increase in mass at the copper cathode can then be used to determine the Faraday constant, a measure of electric charge per mole of electrons.

Calculating Avogadro's Number

Avogadro's number, denoted as \(N_A\), is a fundamental constant in chemistry, representing the number of particles (usually atoms or molecules) in one mole of a substance. The value of Avogadro's number is approximately \(6.022 \times 10^{23}\) particles per mole, providing a link between macroscopic measurements and the atomic scale.

To calculate Avogadro's number, we can use the Faraday constant obtained from the electrolysis experiment. This calculation relies on the fact that one mole of electrons carries one Faraday of charge. Since we previously established the Faraday constant, we can now apply it to determine Avogadro's number by the relationship \(F = e \times N_A\), where \(e\) is the elementary charge. By rearranging the formula as \(N_A = \frac{F}{e}\), and substituting in our measured value of \(F\) and known value of \(e\), we obtain Avogadro's number.

To ensure accurate calculation, it's paramount to have precise measurements of the charge passed during the electrolysis, alongside a highly accurate value for the charge of one electron. Students should be reminded that proper units must be maintained throughout the calculation to establish a correct value for Avogadro's number.

Understanding Faraday's Laws of Electrolysis

Faraday's laws of electrolysis are two scientific principles that govern the relationship between the amount of substance deposited at an electrode during electrolysis and the quantity of electricity passed through the electrolyte. The first law states that the mass of the substance altered at an electrode is directly proportional to the amount of electricity that passes through the electrolyte. The second law indicates that the masses of different substances liberated by the same quantity of electricity are directly proportional to their chemical equivalent weights.

The Faraday constant connects these laws quantitatively to the experiment. It represents the charge of one mole of electrons, named after Michael Faraday who first described these laws. The constant, approximately \(96485\) coulombs per mole, is essential for making calculations in electrochemistry. When we determine the Faraday constant via copper sulfate electrolysis, we use the direct relationship between electric charge and substance deposition.\[F= \frac{I \times t}{(w/M) \times n}\] Here, \(I\) is the current in amperes, \(t\) is the time in seconds, \(w\) is the mass of copper deposited, \(M\) is the molar mass of copper, and \(n\) is the number of electrons transferred per ion of copper. By ensuring the precision of these measurements, we can accurately calculate the Faraday constant and deepen our understanding of electrolysis principles. This in-depth comprehension can further facilitate the understanding of electrolysis applications in various fields such as metallurgy, energy storage, and electroplating.