The Relationship Between Faraday Constant ($F$), Avogadro Constant ($L$), and Electron Charge ($e$)
In physical chemistry and electrochemistry, a fundamental relationship connects the macroscopic world of measurable chemistry to the microscopic world of subatomic particles. This relationship is defined by the equation:
$$F = L \times e$$
Defining the Components
To understand why this relationship holds true, we must look at what each constant represents:
| Symbol | Constant Name | Physical Meaning | Standard Value |
|---|---|---|---|
| $F$ | Faraday Constant | The total electric charge carried by one mole of electrons. | $\approx 96,500 \text{ C mol}^{-1}$ |
| $L$ (or $N_A$) | Avogadro Constant | The number of constituent particles (electrons) in one mole of a substance. | $\approx 6.02 \times 10^{23} \text{ mol}^{-1}$ |
| $e$ | Charge on an Electron | The fundamental elementary electrical charge of a single electron. | $\approx 1.60 \times 10^{-19} \text{ C}$ |
Derivation & Logical Proof
The derivation of this formula is straightforward and frequently asked in structural exam questions:
- The charge of exactly one single electron is $e$ Coulombs ($\text{C}$).
- One mole of any substance contains exactly $L$ number of particles. Therefore, one mole of electrons contains $L$ electrons.
- To find the total charge of one mole of electrons ($F$), we multiply the charge of one electron by the total number of electrons in a mole:
$$\text{Total Charge per Mole } (F) = \text{Number of Electrons per Mole } (L) \times \text{Charge per Electron } (e)$$
$$F = L \times e$$
Sample Calculation Verification
Let's verify the relationship using standard data booklet values:
$$F = (6.02 \times 10^{23} \text{ mol}^{-1}) \times (1.60 \times 10^{-19} \text{ C})$$
$$F = 96,320 \text{ C mol}^{-1}$$
(Note: In most A-Level and IB syllabi, this value is rounded to $96,500 \text{ C mol}^{-1}$ for ease of calculation in exam problems.)
💡 Singapore H2 / IB Exam Tip: Questions on this topic often ask you to calculate the Avogadro constant ($L$) or the charge of an electron ($e$) using experimental data from an electrolysis experiment. Always remember that the value of $F$ is a constant given in your Data Booklet, allowing you to rearrange the formula easily:
$L = \frac{F}{e}$ or $e = \frac{F}{L}$