When zinc is refined by electrolysis, the desired halfreaction at the sathnde is $$\mathrm{Zn}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn}(s)$$ A competing reaction, which lowers the yield, is the formation of hydrogen gas: $$2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g)$$ If \(91.50 \%\) of the current flowing results in zinc being deposited, while \(8.50 \%\) produces hydrogen gas, how many liters of \(\mathrm{H}_{2},\) measured at STP, form per kilogram of zinc?

Faraday's laws of electrolysis help us understand how much substance is decomposed or deposited during electrolysis. The first law states that the amount of substance deposited or liberated at an electrode is directly proportional to the quantity of electricity (charge) passed through the electrolyte. This can be represented as \[ m = Z \times Q \] where **m** is the mass of the substance, **Z** is the electrochemical equivalent, and **Q** is the total electric charge passed. The second law states that when the same quantity of electricity is passed through different electrolytes, the amounts of substances deposited or liberated at the electrodes are proportional to their equivalent weights. Equivalent weight can be calculated by dividing the molar mass by the valence (number of electrons required to liberate one mole of the substance). This means that knowing the valence and molar mass of a substance, we can predict the mass or volume produced by a specific charge.

Current efficiency in electrolysis measures how effectively the electric current is used for a desired reaction versus side reactions. It is calculated by dividing the current that successfully contributes to the desired reaction by the total current supplied. In the provided exercise, 91.50% of the current is used to deposit zinc, while 8.50% drives the side reaction producing hydrogen gas. High current efficiency means most of the electric energy contributes to the main reaction, leading to better yields and lower energy costs. To express as a formula:
\[ \text{Current Efficiency} = \frac{\text{Effective current for desired products}}{\text{Total current supplied}} \times 100\] Understanding current efficiency is essential in optimizing processes like metal refining, where minimizing side reactions like hydrogen formation can significantly enhance yield and efficiency.

Mass to moles conversion is a fundamental concept in chemistry. It helps translate the macroscopic mass of a substance into the number of atoms or molecules, which is crucial for stoichiometry. The conversion is done using the formula \[ n = \frac{m}{M} \]
where **n** represents the number of moles, **m** is the mass in grams, and **M** is the molar mass in grams per mole (g/mol). In the example of zinc electrolysis: First, we find the molar mass of zinc, which is 65.38 g/mol. For 1000 grams (or 1 kilogram) of zinc, we use: \[ n(\text{Zn}) = \frac{1000 \text{ grams}}{65.38 \text{ grams/mol}} = 15.29 \text{ moles}\]
This conversion allows us to work with quantities in consistent units to further analyze and predict reaction outcomes like calculating the charge required in electrolysis or the volume of gas produced.