Calculate the value of the Faraday constant, F, from the charge of 1 electron, 1.602×10-19 C. (Show all work to receive karma) (Hint: what are the units of the faraday constant and Avogadro
The correct answer and explanation is :
To calculate the value of the Faraday constant ( F ) from the charge of a single electron, we can use the relationship between the charge of an electron and the Faraday constant. Here’s the step-by-step process:
Step 1: Definition of Faraday Constant
The Faraday constant ( F ) represents the charge per mole of electrons, and its units are Coulombs per mole (C/mol). The value of ( F ) is related to the charge of a single electron (( e )) and Avogadro’s number (( N_A )):
[
F = e \times N_A
]
Where:
- ( e ) is the charge of a single electron in Coulombs (C).
- ( N_A ) is Avogadro’s number, which represents the number of particles (in this case, electrons) per mole.
Step 2: Known Values
- The charge of a single electron, ( e = 1.602 \times 10^{-19} ) C.
- Avogadro’s number, ( N_A = 6.022 \times 10^{23} ) mol(^{-1}).
Step 3: Calculate Faraday Constant
Now, we can plug these values into the formula:
[
F = (1.602 \times 10^{-19} \, \text{C}) \times (6.022 \times 10^{23} \, \text{mol}^{-1})
]
Let’s compute this:
[
F = (1.602 \times 10^{-19}) \times (6.022 \times 10^{23}) = 9.649 \times 10^{4} \, \text{C/mol}
]
Step 4: Result
The value of the Faraday constant is approximately:
[
F \approx 9.649 \times 10^{4} \, \text{C/mol}
]
This is the value of the Faraday constant.
Explanation:
The Faraday constant, ( F ), is a fundamental constant in electrochemistry that represents the amount of electric charge in one mole of electrons. Since electrons are the charge carriers in most electrochemical reactions, this constant is crucial in understanding processes such as the charging and discharging of batteries, as well as the efficiency of electrolysis.
The calculation above shows how the charge of a single electron and Avogadro’s number are used to determine the total charge per mole of electrons. The Faraday constant is significant because it allows chemists and physicists to relate macroscopic quantities (such as moles) to microscopic quantities (such as individual charges on electrons), making it a key parameter in stoichiometry and energy calculations in electrochemical reactions.