Question

In the electrolysis of aqueous \(\mathrm{NaCl}\), what volume of \(\mathrm{Cl}_{2}(g)\) is produced in the time that it takes to liberate \(5.0\) liter of \(\mathrm{H}_{2}(\mathrm{~g})\) ? Assume that both gases are measured at STP. (a) \(5.0\) (b) \(2.50\) (c) \(7.50\) (d) \(10.0\)

Short answer

5.0 liters of \(\mathrm{Cl}_2\) gas are produced.

Step-by-step solution

Identify the Electrolysis Reaction

In the electrolysis of aqueous \(\mathrm{NaCl}\), the chemical reaction taking place at the electrodes can be represented as: \[2\mathrm{NaCl} (aq) + 2\mathrm{H}_2\mathrm{O} (l) \rightarrow 2\mathrm{NaOH} (aq) + \mathrm{H}_2 (g) + \mathrm{Cl}_2 (g)\] At the anode, chlorine gas \(\mathrm{Cl}_2\) is liberated, and at the cathode, hydrogen gas \(\mathrm{H}_2\) is liberated.

Understand the Stoichiometry

Based on the balanced chemical equation: \[2\mathrm{NaCl} (aq) + 2\mathrm{H}_2\mathrm{O} (l) \rightarrow 2\mathrm{NaOH} (aq) + \mathrm{H}_2 (g) + \mathrm{Cl}_2 (g)\] For every 2 moles of \(\mathrm{NaCl}\) that react, 1 mole of \(\mathrm{H}_2\) and 1 mole of \(\mathrm{Cl}_2\) are produced. This implies that \(\mathrm{H}_2\) and \(\mathrm{Cl}_2\) are produced in a 1:1 molar ratio.

Apply Avogadro's Law

Avogadro's law states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules. At STP, this means that the volume of \(\mathrm{H}_2\) gas produced will be equal to the volume of \(\mathrm{Cl}_2\) gas produced since they are in a 1:1 molar ratio.

Calculate the Volume of Chlorine Gas Produced

Given that 5.0 liters of \(\mathrm{H}_2\) gas are produced, and because of the 1:1 molar ratio with \(\mathrm{Cl}_2\), the volume of \(\mathrm{Cl}_2\) gas produced will also be 5.0 liters. Therefore, the answer is 5.0 liters.

Key concepts

Stoichiometry

Stoichiometry is the mathematical relationship between the amounts of reactants and products in a chemical reaction. It's vital for predicting the quantities of substances consumed and produced in a reaction.

In the context of the electrolysis of aqueous NaCl, stoichiometry allows us to understand the proportions at which chemical species react and are produced. As we've seen in the exercise, for every 2 molecules of NaCl that break down, we get 1 molecule each of H₂ and Cl₂ gas.

Understanding the 1:1 Ratio

Through stoichiometric analysis, we can deduce that if the same number of moles of hydrogen is produced, the same number of moles of chlorine will be produced as well. This is crucial when trying to determine the amount of product formed from a given quantity of reactant, in this case, NaCl. Knowing that these two products are generated in equal amounts leads us directly to the answer to our problem.

Avogadro's Law

Avogadro's Law is a principle stating that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules. This is fundamental to problems involving gas volumes, such as the one described.

At Standard Temperature and Pressure (STP), one mole of any gas occupies approximately 22.4 liters. When we know that one gas volume corresponds to a certain amount, Avogadro's Law allows us to infer the same volume for any other gas under the same conditions.

Application in Electrolysis

For the electrolysis of aqueous NaCl, applying Avogadro's Law means that since we have 5 liters of H₂ produced, we should expect the same volume of Cl₂, a direct consequence of the stoichiometry and Avogadro's Law working hand in hand. This is a principle that can simplify the handling of gas volumes in chemical reaction problems immensely.

Chemical Reactions in Electrolysis

Electrolysis is a chemical process by which electric current is used to drive a non-spontaneous chemical reaction. It's widely applied in various industrial processes, like the extraction of metals and the decomposition of compounds into simpler substances.

In the case of aqueous NaCl, the electrolysis process involves the movement of ions to their respective electrodes where they are either oxidized or reduced, leading to the formation of gas and aqueous products.

Understanding the Electrode Reactions

At the cathode, water reduction occurs, producing hydrogen gas (H₂) and hydroxide ions (OH^-). Meanwhile, at the anode, chloride ions (Cl^-) are oxidized to chlorine gas (Cl₂). By understanding this redox process and the stoichiometry of the involved electrolysis reaction, one can predict the products and their volumes, as seen in the textbook exercise. Chemical reactions in electrolysis, such as the production and liberation of gases, are predictable when combining knowledge on reaction stoichiometry and gas laws like Avogadro's Law.