Electrolysis

If ordinary salt, which consists of sodium chloride, is placed in water, it immediately starts to dissolve, creating positively charged sodium ions and negatively charged chloride ions. This process is called dissociation in chemistry. The solution is then called electrolyte because the available ions act as a conductor for electricity. If two electrodes are placed into this electrolyte and a voltage is applied to them, the sodium ions drift towards the negatively charged electrode which is called the cathode, whereas the chloride ions drift towards the anode. After reaching there, the sodium ions are reduced and take one electron from the cathode. The chloride ions give away one electron to the anode. This results in the creation of elementary chlorine and sodium. This method is called electrolysis. The sodium is, however, immediately reacting with the water creating a sodium hydroxide solution which makes the water soapy. The chlorine, that escapes the electrolysis setup, can be observed by its aggressive smell. We want to quantify this reaction and derive the so-called Faraday's law of electrolysis. For that purpose, we take a look at the cathode, where positive ions with the charge number $z$ are reduced by taking electrons from the cathode. Considering $N$ ions, the total transferred charge can be calculated according to $$Q = zNe$$ In order to calculate the current from that, this equation has to be divided by $I$ which leads to $$I = \frac{Q}{t} = \frac{zNe}{t}$$ In the next step, the Avogadro constant is used to convert the number $N$ of ions to the amount of substance $n$: $$I = \frac{zNN_\mathrm{A}e}{t}$$ It is usually easier to do calculations with the mass which is directly measurable. With the help of the molar mass, this equation can be rewritten to $$I = \frac{zmN_\mathrm{A}e}{nMt}$$ Solving this equation for the $t$ finally leads to $$t = \frac{mzN_\mathrm{A}e}{MI}$$ Sometimes the product of $N_\mathrm{A}$ and $e$ is called Faraday's constant. It is therefore defined as $$\boxed{F=N_\mathrm{A}e}$$ One can easily calculate the value $$F = 9.64853\dots\cdot 10^4\,\frac{\mathrm{A}\,\mathrm{s}}{\mathrm{mol}}$$ With the help of this constant, the above-mentioned relation can be written as $$\boxed{t = \frac{mzF}{MI}}$$ This formula can be used to estimate the time which is required to receive a certain amount of a specific material via the method of electrolysis.