Electric Elementary Charge Given Tafel Slope Calculator

Elementary Charge Formula:

\[ e = \frac{\ln(10) \times [BoltZ] \times T}{A_{slope} \times \alpha} \]

Elementary Charge (e):

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1. What is the Elementary Charge Formula?

The elementary charge formula calculates the fundamental electric charge carried by a single proton or electron using temperature, Tafel slope, and charge transfer coefficient parameters from electrochemical kinetics.

2. How Does the Calculator Work?

The calculator uses the elementary charge formula:

\[ e = \frac{\ln(10) \times [BoltZ] \times T}{A_{slope} \times \alpha} \]

Where:

\( [BoltZ] \) — Boltzmann constant (1.38064852 × 10⁻²³ J/K)
\( T \) — Temperature in Kelvin
\( A_{slope} \) — Tafel slope in Volts
\( \alpha \) — Charge transfer coefficient (dimensionless)
\( \ln(10) \) — Natural logarithm of 10 (approximately 2.302585)

Explanation: This formula derives the elementary charge from electrochemical measurements using the relationship between Tafel slope and charge transfer kinetics.

3. Importance of Elementary Charge Calculation

Details: Calculating the elementary charge is fundamental in electrochemistry and physics for understanding charge transfer processes, electrode kinetics, and fundamental physical constants.

4. Using the Calculator

Tips: Enter temperature in Kelvin, Tafel slope in Volts, and charge transfer coefficient (typically between 0.3-0.7 for most electrochemical reactions). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the accepted value of elementary charge?
A: The accepted value is approximately 1.60217662 × 10⁻¹⁹ Coulombs, which represents the electric charge carried by a single proton.

Q2: Why use natural logarithm in the formula?
A: The natural logarithm appears due to the exponential relationship between current and voltage in electrode kinetics described by the Butler-Volmer equation.

Q3: What is the typical range for charge transfer coefficient?
A: The charge transfer coefficient typically ranges from 0.3 to 0.7 for most electrochemical reactions, with 0.5 being common for symmetric reactions.

Q4: How does temperature affect the calculation?
A: Temperature appears in the numerator, so higher temperatures generally result in higher calculated elementary charge values, reflecting increased thermal energy.

Q5: What are common Tafel slope values?
A: Tafel slopes typically range from 0.03 to 0.12 V/decade, depending on the electrochemical reaction and electrode material.