Problem 31 - Chemistry

Question

When mixtures of gaseous \(\mathrm{H}_{2}\) and gaseous \(\mathrm{Cl}_{2}\) react, a product forms that has the same properties regardless of the relative amounts of \(\mathrm{H}_{2}\) and \(\mathrm{Cl}_{2}\) used. a. How is this result interpreted in terms of the law of definite proportion? b. When a volume of \(\mathrm{H}_{2}\) reacts with an equal volume of \(\mathrm{Cl}_{2}\) at the same temperature and pressure, what volume of product having the formula \(\mathrm{HCl}\) is formed?

Step-by-Step Solution

Answer

a. The reaction between $\mathrm{H}_{2}$ and $\mathrm{Cl}_{2}$ to form $\mathrm{HCl}$ abides by the law of definite proportion as the product always contains the same elements, H and Cl, in the same proportion, 1:1, regardless of the relative amounts of $\mathrm{H}_{2}$ and $\mathrm{Cl}_{2}$. b. When an equal volume of $\mathrm{H}_{2}$ reacts with $\mathrm{Cl}_{2}$ at the same temperature and pressure, double the volume of product $\mathrm{HCl}$ is formed. If the volume of $\mathrm{H}_{2}$ is V (liters) and the volume of $\mathrm{Cl}_{2}$ is also V (liters), they react to form a volume of $\mathrm{HCl}$ equal to 2V (liters).

Step 1: Understand the Law of Definite Proportion

The Law of Definite Proportion states that a chemical compound always contains the same elements in the same proportions, regardless of the method of preparation or the source of the material. In this case, we need to explain the given result in terms of the Law of Definite Proportion.

Step 2: Interpretation of the reaction

According to the problem, the product formed (HCl) has the same properties regardless of the relative amounts of H2 and Cl2. This indicates that the product formed always contains the same elements, hydrogen (H) and chlorine (Cl), in the same proportions, 1:1 in this case. Thus, the reaction abides by the law of definite proportion.

Step 3: Reaction between gaseous H2 and Cl2

Let's analyze the balanced chemical equation of the reaction between gaseous hydrogen (H2) and gaseous chlorine (Cl2) to form hydrogen chloride (HCl): \[H_{2(g)} + Cl_{2(g)} \rightarrow 2 HCl_{(g)}\]

Step 4: Volume relationship of gases in the reaction

By reaction stoichiometry, we can determine the mole relationship of H2, Cl2, and HCl. According to the balanced equation, one mole of H2 reacts with one mole of Cl2 to form two moles of HCl. At the same temperature and pressure, one mole of any gas occupies the same volume. Hence, if the volume of H2 is V (liters) and the volume of Cl2 is also V (liters), they react to form double the volume of HCl, which is 2V (liters).

Step 5: Answer the questions

a. The fact that a product with the same properties is formed regardless of the relative amounts of H2 and Cl2 supports the Law of Definite Proportion. It indicates that the product formed (HCl) always contains the same elements, H and Cl, in the same proportion, 1:1. b. When an equal volume of H2 reacts with Cl2 at the same temperature and pressure, double the volume of product HCl is formed. If the volume of H2 is V (liters) and the volume of Cl2 is also V (liters), they react to form a volume of HCl equal to 2V (liters).