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 HCl is formed?

The law of definite proportions states that a given chemical compound always contains its component elements in a fixed proportion by mass. In other words, the ratio of the masses of the elements in a compound is always the same, regardless of the amount or source of the compound.

According to the problem, the product formed from the reaction between gaseous H2 and gaseous Cl2 has the same properties regardless of the relative amounts of H2 and Cl2 used. This means that no matter how much H2 or Cl2 we use, the product will always be the same compound with the same proportions of hydrogen and chlorine. This behavior is consistent with the law of definite proportions, which states that the ratio of the masses of elements in a compound is always the same. Therefore, the reaction can be interpreted as a confirmation of this law.

Before we can determine the volume of the product formed, we need to write the balanced chemical equation for the reaction. The reaction between hydrogen (H2) and chlorine (Cl2) produces hydrogen chloride (HCl): \(H_2 + Cl_2 \rightarrow 2HCl\) This balanced equation tells us that one molecule of H2 reacts with one molecule of Cl2 to form two molecules of HCl.

The problem states that we start with equal volumes of H2 and Cl2 reacting at the same temperature and pressure. According to Avogadro's law, equal volumes of gases at the same temperature and pressure have the same number of molecules. Therefore, the number of moles of H2 and Cl2 used in the reaction is the same. From the balanced equation in Step 3, we know that one mole of H2 reacts with one mole of Cl2 to produce two moles of HCl. Therefore, when equal volumes of H2 and Cl2 react, two moles of HCl are formed per mole of H2 (or Cl2). In terms of volume, this means that the volume of HCl produced will be twice the volume of H2 (or Cl2) used. To summarize, when a volume of H2 reacts with an equal volume of Cl2 at the same temperature and pressure, double the volume of HCl is formed.