Understanding Charge and Faradays

The question asks for the number of electrons that constitute a given amount of charge, specifically 1.5 Faradays. To solve this, we need to understand what a Faraday represents in terms of electric charge and the number of particles carrying that charge.

Defining Faraday's Constant

Faraday's constant (\(F\)) is a fundamental physical constant that represents the magnitude of electric charge per mole of electrons. It is approximately equal to the charge of \(6.022 \times 10^{23}\) electrons (Avogadro's number) or other elementary entities per mole.

The accepted value of Faraday's constant is approximately \(96485 \text{ coulombs per mole } (\text{C/mol})\). This means:

• 1 Faraday of charge is equivalent to the charge of 1 mole of electrons.
• 1 mole of electrons contains Avogadro's number (\(N_A\)) of electrons.
• Avogadro's number (\(N_A\)) is approximately \(6.022 \times 10^{23}\) particles per mole.

Therefore, 1 Faraday of charge corresponds to \(N_A\) electrons.

Calculating Number of Electrons for 1.5 Faradays

We are given a charge of 1.5 Faradays. Since 1 Faraday corresponds to \(N_A\) electrons, 1.5 Faradays will correspond to 1.5 times the number of electrons in 1 Faraday.

Number of electrons = Given charge in Faradays \(\times\) Number of electrons per Faraday

Number of electrons = \(1.5 \text{ Faradays} \times N_A \text{ electrons/Faraday}\)

Using the approximate value of \(N_A = 6.022 \times 10^{23}\) electrons/mol (which is the number of electrons per Faraday):

Number of electrons = \(1.5 \times 6.022 \times 10^{23}\)

Let's perform the multiplication:

\(1.5 \times 6.022\)

\(1.5 \times 6 = 9.0\)

\(1.5 \times 0.022 = 0.033\)

So, \(1.5 \times 6.022 = 9.0 + 0.033 = 9.033\)

Therefore, the number of electrons is \(9.033 \times 10^{23}\).

Comparing with Options

Let's look at the given options:

• \(9.03 \times 10^{23}\)
• \(9.03 \times 10^{22}\)
• \(9.03 \times 10^{24}\)
• \(9.03 \times 10^{25}\)

Our calculated value \(9.033 \times 10^{23}\) is very close to the first option, \(9.03 \times 10^{23}\), considering possible rounding in the provided value of \(N_A\) or the options.

The number of electrons constituting 1.5 Faradays of charge is approximately \(9.03 \times 10^{23}\).

Revision Table: Faraday's Constant and Electrons

Additional Information: Faraday's Laws of Electrolysis

Faraday's constant is crucial in electrochemistry, particularly in Faraday's laws of electrolysis. These laws relate the amount of substance produced or consumed during electrolysis to the quantity of electric charge passed through the electrolytic cell.

The first law states that the mass of a substance deposited or liberated at any electrode is directly proportional to the quantity of electricity (charge) passed. The second law states that the masses of different substances produced by the same quantity of electricity are proportional to their equivalent weights.

Understanding the relationship between charge (measured in Coulombs or Faradays) and the number of electrons or moles of substances is fundamental for solving problems in electrolysis.

For example, depositing 1 mole of a monovalent ion (like Na\(\text{}^+\) or Ag\(\text{}^+\)) requires 1 mole of electrons, which is 1 Faraday of charge. Depositing 1 mole of a divalent ion (like Cu\(\text{}^{2+}\) or Zn\(\text{}^{2+}\)) requires 2 moles of electrons, which is 2 Faradays of charge.