Question

Explain why the volumes of \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) obtained in the electrolysis of water are not the same.

Short answer

The volumes of H2(g) and O2(g) obtained from the electrolysis of water are not the same because of the stoichiometry of the chemical reaction. It shows that from 2 volumes of water, we produce 2 volumes of hydrogen gas and 1 volume of oxygen gas, hence resulting in differing volumes of hydrogen and oxygen.

Step-by-step solution

State the Reactants and Products

Determine the reaction taking place in the process. For the electrolysis of water, we have water (H2O) as the reactant, and hydrogen gas (H2) and oxygen gas (O2) as the products. This gives us the chemical reaction: 2H2O(l) → 2H2(g) + O2(g).

Understand Stoichiometric Ratios

Notice the stoichiometric coefficients (the numbers in front of the molecules in the chemical reaction). They provide the ratio of the molecules involved. Essentially, for every 2 molecules of water, we produce 2 molecules of Hydrogen and 1 molecule of Oxygen. So, the ratio is 2:1.

Apply Gas Laws

Knowing that the laws of gases tells us that equal volumes of gases, at the same temperature and pressure conditions, contain the same number of gas particles (Avogadro's Law), we can conclude that, in this reaction, for every 2 volumes of water, we produce 2 volumes of Hydrogen and 1 volume of Oxygen. Hence, the volumes of Hydrogen and Oxygen gases aren't the same.

Key concepts

Stoichiometric Ratios

Understanding stoichiometric ratios is fundamental when dealing with chemical reactions, like the electrolysis of water. These ratios are derived from the balanced chemical equation. For the reaction \(2\text{H}_2\text{O (l)} \rightarrow 2\text{H}_2\text{(g)} + \text{O}_2\text{(g)}\), stoichiometry tells us how molecules convert and relate to each other in terms of amounts. For example, the coefficient '2' in front of \(\text{H}_2\text{O}\) and \(\text{H}_2\) in the equation means that two molecules of water produce two molecules of hydrogen gas. In contrast, only one molecule of oxygen gas is produced, as indicated by the coefficient '1' in front of \(\text{O}_2\). Thus, the ratio of hydrogen to oxygen is 2:1.Knowing these ratios helps us predict the amounts of products formed from given reactants. Proper grasp of this concept is crucial for many applications in chemistry, such as predicting yields and designing chemical processes.

Avogadro's Law

Avogadro's Law is a key concept in understanding gas behavior, especially in reactions such as the electrolysis of water. It states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This is quite handy because it simplifies how we measure gases without needing to count each molecule. In our case of water electrolysis, Avogadro's Law explains why the volumes of hydrogen and oxygen gases produced are different. Despite having twice as many hydrogen molecules compared to oxygen molecules according to the stoichiometric ratio, both gases are compared in terms of their volumes. The law helps in imagining gas reactions because it links volumes directly to the number of gas particles, making calculations straightforward. It is essential for predicting the volumes of gases produced or consumed in a chemical reaction.

Gas Laws

The behavior of gases in chemical reactions is greatly influenced by the gas laws, particularly when discussing gases like hydrogen and oxygen in the electrolysis process. Gas laws include principles like Boyle's Law, Charles's Law, and Avogadro's Law, each contributing to understanding different aspects of gas behavior under various conditions. The significant takeaway from these laws, especially Avogadro's Law in this context, is that the relation between volumes, pressures, temperatures, and the amount of gas matter because they maintain equilibrium in chemical reactions. For instance, when electrolysis occurs at constant temperature and pressure, the produced gases expand and contract in predictable ways. These laws help simplify and unify the theoretical understanding of gases, enabling chemists to make accurate predictions about reactions like those occurring in the electrolysis of water. Applying these laws ensures that the calculated volumes of products fit accurately with the stoichiometric predictions, which is vital in scientific and industrial applications.