When an ionic compound such as table salt (NaCl), which consists of a combination of sodium and chlorine, is dissolved in water, the compounds split into positively and negatively charged ions. This process is called dissociation. In the case of table salt, an aqueous solution containing positively charged sodium ions and negatively charged chloride ions is formed. Such a solution is called an electrolyte, because the presence of ions allows it to conduct electricity.
If two electrodes are placed at a certain distance within this solution and a voltage is applied, an electric current flows between them, which is initially larger the more ions are dissolved.
As long as the concentration is not too high, a linear relationship between concentration and current is observed. However, if the concentration becomes too high, the oppositely charged ions are no longer spatially separated, and the attraction between them dominates. This ultimately leads to a decrease in current. The conductivity of the electrolyte also depends on the viscosity of the solvent (in this case, water) and the temperature of the solution. The more viscous the solvent, the lower the current. Since the viscosity of a liquid decreases with increasing temperature, molecular mobility and thus conductivity increase. A higher temperature also means higher thermal energy, which reduces the energy required to overcome the electric field of the ions. Thus, overall, a higher temperature improves the conductivity of the solution.
During current flow in the electrolyte, electrons are transferred to the positively charged \( \text{Na}^+ \) ions at the negatively charged electrode (cathode), while electrons are removed from the \( \text{Cl}^- \) ions at the positively charged electrode (anode). As a result, the respective elements—sodium and chlorine in this case—are deposited in their pure forms at the electrodes. However, sodium cannot be collected in its elemental form because sodium atoms immediately react with water to form sodium hydroxide. This reaction also produces hydrogen, which escapes together with chlorine as a gas. The overall reaction for the electrolysis of sodium chloride is therefore:
\[
2 \mathrm{NaCl} + 2 \mathrm{H_2O} \rightarrow 2 \mathrm{NaOH} + \mathrm{H_2} + \mathrm{Cl_2}
\]
In general, for ions with charge number \( z \), \( z \) electrons must be gained or lost in order to obtain the elements in their pure form. The total charge for \( N \) atoms is then:
\[
q = zNe
\]
To calculate the current, this must be divided by the time \( t \), according to the definition of current:
\[
I = \frac{q}{t} = \frac{zNe}{t}
\]
Using Avogadro’s constant, the number of particles \( N \) can be related to the amount of substance \( m \):
\[
I = \frac{zmN_A e}{M t}
\]
If one wants to calculate the mass instead of the amount of substance, the molar mass \( M \) of the atoms must be taken into account. Rearranging for time gives:
\[
t = \frac{m z N_A e}{M I}
\]
With this formula, the time required to deposit an element with mass \( m \) by electrolysis can be calculated. In honor of Michael Faraday, who was the first to study electrolysis scientifically, the product \( N_A e \) is defined as the Faraday constant:
\[
\boxed{F = N_A e}
\]
with the accurately known value:
\[
F = 9.64853321233100184 \cdot 10^4 \, \frac{\mathrm{A \, s}}{\mathrm{mol}}
\]
Thus, the above relationship can be written as:
\[
\boxed{t = \frac{m z F}{M I}}
\]
If the electrolysis is to be carried out within a specific time, the formula can be rearranged to calculate the required current.