What is the numerical value of one Faraday in Coulombs?
96487
Understanding the Faraday Constant
The question asks for the numerical value of one Faraday in Coulombs. The Faraday constant, denoted by \(F\), is a fundamental physical constant widely used in electrochemistry. It represents the magnitude of electric charge per mole of electrons or singly charged ions.
Calculating the Faraday Constant
The Faraday constant is defined as the product of the elementary charge, \(e\), and the Avogadro constant, \(N_A\). The elementary charge is the charge of a single proton or electron, and the Avogadro constant is the number of particles (like atoms, molecules, or electrons) in one mole of a substance.
The formula is:
\(F = e \times N_A\)
Where:
- \(e\) is the elementary charge, approximately \(1.602176634 \times 10^{-19}\) Coulombs (C).
- \(N_A\) is the Avogadro constant, approximately \(6.02214076 \times 10^{23}\) mol\(^{-1}\).
Multiplying these values gives the charge of one mole of electrons:
\(F \approx (1.602176634 \times 10^{-19} \text{ C}) \times (6.02214076 \times 10^{23} \text{ mol}^{-1})\)
\(F \approx 96485.33212 \text{ C/mol}\)
Historically, the value was determined experimentally and has been refined over time. A commonly used and accepted value for the Faraday constant is approximately 96485 C/mol.
Analyzing the Options
Let's look at the provided options for the numerical value of one Faraday in Coulombs:
- Option 1: 96587
- Option 2: 99500
- Option 3: 96487
- Option 4: 6.023
Comparing these options to the calculated and standard value of the Faraday constant (approximately 96485 C/mol), Option 3, which is 96487, is the closest and most commonly used value in many contexts, often rounded from the more precise value.
Option 4 (6.023) is close to the Avogadro number divided by \(10^{20}\), not the Faraday constant itself.
Identifying the Correct Faraday Value
Based on the definition and calculation of the Faraday constant, the value representing the charge of one mole of electrons is approximately 96485 Coulombs. Among the given choices, 96487 is the closest and most widely accepted numerical value for one Faraday in Coulombs in many standard references.
| Constant | Symbol | Value (approximate) | Units |
|---|---|---|---|
| Elementary Charge | \(e\) | \(1.602 \times 10^{-19}\) | Coulombs (C) |
| Avogadro Constant | \(N_A\) | \(6.022 \times 10^{23}\) | mol\(^{-1}\) |
| Faraday Constant | \(F\) | \(96485\) | C/mol (or just C for 1 Faraday) |
Revision Table: Faraday Constant
| Concept | Description | Numerical Value (Coulombs) |
|---|---|---|
| One Faraday | Charge of one mole of electrons or singly charged ions. | \(\approx 96485\) to \(96487\) C |
Additional Information on Faraday's Laws and Constant
The Faraday constant is named after Michael Faraday, whose work on electrolysis established the relationship between the amount of electricity passed through an electrolytic cell and the amount of substance deposited or liberated. Faraday's laws of electrolysis are directly related to the Faraday constant.
Faraday's First Law of Electrolysis:
The mass of a substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity (charge) transferred at that electrode.
Faraday's Second Law of Electrolysis:
For a given quantity of electricity, the mass of an element deposited or liberated at an electrode is directly proportional to the element's equivalent weight.
These laws demonstrate that the charge required to deposit or liberate one equivalent weight of a substance is constant, and this constant quantity of charge is equal to one Faraday. The Faraday constant serves as a crucial link between electrical quantities (charge) and chemical quantities (moles, mass) in electrochemical reactions.
96487
1 Faraday = Charge of 1 mole of electrons
Avogadro's number \( N_A = 6.022 \times 10^{23} \)
Charge on one electron \( e = 1.602 \times 10^{-19} \, \text{C} \)
Multiply: \( 1 \, \text{F} = N_A \times e = (6.022 \times 10^{23}) \times (1.602 \times 10^{-19}) = 96485 \, \text{C} \)
Therefore, the numerical value of 1 Faraday = 96487 C (rounded value)
Answer:
96487
96487
Definition:
One Faraday (F) is the magnitude of electric charge per mole of electrons.
Calculation:
\[ F = N_A \times e \]
Where:
- \( N_A \) = Avogadro's number = \( 6.02214076 \times 10^{23} \) mol⁻¹
- \( e \) = elementary charge = \( 1.602176634 \times 10^{-19} \) C
\[ F = (6.02214076 \times 10^{23}) \times (1.602176634 \times 10^{-19}) \]
\[ F \approx 96485.33212\ \text{C mol}^{-1} \]
Standard Value:
The accepted value of the Faraday constant is: \[ F = 96485.33289(59)\ \text{C mol}^{-1} \] which is typically rounded to 96,485 C for most calculations.
Final Answer:
The numerical value of one Faraday is \[ \boxed{96487} \] Coulombs (closest option).
Note: While the exact modern value is 96,485 C, among the given options, 96487 is the closest correct value.
Important Questions from Electrochemistry
Identify transition metal complexes which are not octahedral in shape.
(A) [Co(NH₃)₆]³⁺
(B) [Ni(CO)₄]
(C) [CoCl(NH₃)₅]²⁺
(D) [CoCl₂(NH₃)₄]⁺
(E) [PtCl₄]²⁻
Choose the correct answer from the options given below:
The product of complete hydrolysis of XeF₆ in the following reaction is:
XeF₆ + H₂O → ? HF
In a reaction A and B react to form product. The initial rate of reaction (ro) was determined using different initial concentrations of A and B as shown below:
A/mol L-1 B/mol L-1 ro/mol L-1 s-1 0.10 0.30 6.81 × 10-4 0.10 0.10 2.27 × 10-4 0.20 0.30 13.62 × 10-4 What is the initial rate of reaction (ro) when the critical concentration of A and B is 0.50 mol/L and 0.50 mol/L, respectively?
In which of the following actinoid elements 6d subshell is vacant?
Which of the following shows both, Frenkel and Schottky defect?
