On electrolysis of acidified water, if volume of hydrogen liberated is \(5.6 \mathrm{~cm}^{3}\), then the volume of oxygen liberated equal to: (a) \(1.4 \mathrm{~cm}^{3}\) (b) \(2.8 \mathrm{~cm}^{3}\) (c) \(8.2 \mathrm{~cm}^{3}\) (d) \(5.6 \mathrm{~cm}^{3}\)

Stoichiometry is akin to a recipe for chemists. It involves using balanced chemical equations to calculate the quantities of reactants and products involved in chemical reactions. When solving problems related to the electrolysis of water, stoichiometry allows us to predict the amount of hydrogen and oxygen gas that will be produced.

In the electrolysis of water, the stoichiometric coefficients in the balanced chemical equation indicate the proportions of water (reactant) that decompose into hydrogen and oxygen gases (products). The balanced equation shows a 2:1 ratio, meaning two hydrogen molecules (or two volumes) are produced for every one oxygen molecule (or one volume).

This relationship can be applied whether we are measuring in moles, molecules, or—as in this exercise—volumes. Knowing how to use the stoichiometric ratios from the balanced equation is crucial in accurately determining the quantities of each substance produced or required.

Chemical equations represent the shorthand of chemistry, conveying the transformation of reactants to products during a chemical process. A well-balanced equation is essential because it follows the law of conservation of mass—matter is neither created nor destroyed.

The equation for the electrolysis of water, \(2H_2O (l) \rightarrow 2H_2 (g) + O_2 (g)\),is balanced. This means that the number of atoms for each element is the same on both the reactant and product sides. Such equations also inform us about the phase of matter, with '(l)' denoting liquid for water and '(g)' denoting gas for hydrogen and oxygen. By mastering the interpretation of chemical equations, students can contextualize the changes occurring during a reaction and predict the outcomes effectively.

When gases are produced or consumed in a chemical reaction, they occupy volumes that can be related through stoichiometric principles. In ideal conditions, at a constant temperature and pressure, Avogadro's law states that equal volumes of gases contain an equal number of molecules. This allows us to relate the volumes of gases directly to the coefficients in the balanced chemical equation.

In our exercise, the 2:1 volume ratio of hydrogen to oxygen reflects this stoichiometric relationship. For every two parts of hydrogen, one part of oxygen is produced during the electrolysis. It's a direct and essential relation that comes from the stoichiometry of the chemical equation involved—practical knowledge for handling problems about the gaseous products in electrolysis.