Faraday's laws Knowledge-Based Study

Study notes

1. Fundamental Principle

   Faraday's first law states that the mass of a substance liberated, deposited, or dissolved at an electrode during electrolysis is directly proportional to the total electric charge that passes through the electrolyte solution or molten salt.

   Mathematically, the relationship is expressed as:

   $$m \propto Q$$

   Because electric charge ($Q$) in coulombs is the product of electric current ($I$) in amperes and time ($t$) in seconds:

   $$Q = I \times t$$

   Consequently, doubling the duration of electrolysis or doubling the current doubles the mass of the substance formed at the electrode, provided all other operating conditions remain constant.

   Equivalent Mass and Charge Relationship

   Faraday's second law states that when the same quantity of electric charge passes through different electrolytes, the masses of substances produced or consumed at the electrodes are directly proportional to their equivalent masses (chemical equivalents).

   The equivalent mass of an element is defined as its molar mass ($M$) divided by the number of electrons ($z$) transferred per ion in the half-reaction:

   $$\text{Equivalent mass} = \frac{M}{z}$$

   The charge carried by one mole of electrons is known as the Faraday constant ($F$), which has an approximate value of:

   $$F \approx 96500\text{ C/mol}$$

   Therefore, delivering $1\text{ F}$ (96500 C) of charge reduces or oxidizes 1 mole of electrons, liberating 1 mole of univalent ions (such as $\text{Ag}^+$), 0.5 mole of divalent ions (such as $\text{Cu}^{2+}$), or 0.33 mole of trivalent ions (such as $\text{Al}^{3+}$).

   Combined Mathematical Formulation

   Combining both laws yields the general equation for the mass ($m$) of substance deposited or liberated at an electrode:

   $$m = \frac{M \times I \times t}{z \times F}$$

   where:

   • $m$: Mass of substance deposited or dissolved (g)
   • $M$: Molar mass of the substance (g/mol)
   • $I$: Electric current (A)
   • $t$: Time (s)
   • $z$: Number of electrons transferred per atom or molecule (valence number)
   • $F$: Faraday constant ($96500\text{ C/mol}$)

   Key Problem-Solving Steps

   1. Identify the relevant half-reaction at the electrode to determine the value of $z$.
   2. Convert the time to seconds (s) and determine the total charge using $Q = I \times t$.
   3. Calculate the moles of electrons transferred using $n_{e^-} = \frac{Q}{F}$.
   4. Use the stoichiometric mole ratio between electrons and the product to find moles of product, then convert to grams or gas volume at STP if required.