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 HCl is formed?

Short answer

When equal volumes of gaseous H2 and Cl2 react at the same temperature and pressure, the product formed is consistent with the law of definite proportions, confirming that the ratio of the masses of elements in a compound is always the same. The balanced chemical equation for the reaction is \(H_2 + Cl_2 \rightarrow 2HCl\). According to this equation, the volume of HCl formed will be twice the volume of H2 (or Cl2) used. Thus, when a volume of H2 reacts with an equal volume of Cl2, double the volume of HCl is formed.

Step-by-step solution

Review the Law of Definite Proportions

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.

Interpret the Result

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.

Write the Balanced Chemical Reaction

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.

Determine the Volume of HCl Formed

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.

Key concepts

Chemical Reaction

A chemical reaction occurs when substances interact to form new substances with different properties. In the problem given, the chemical reaction takes place between gaseous hydrogen (\(\mathrm{H}_2\)) and chlorine (\(\mathrm{Cl}_2\)) to produce hydrogen chloride (\(\mathrm{HCl}\)). This transformation involves the rearrangement of atoms. It's crucial to understand that while the number of atoms must be conserved,the bonds between them change creating new substances.

• Reactants: The starting substances (\(\mathrm{H}_2\) and \(\mathrm{Cl}_2\)).
• Products: The substances formed (\(\mathrm{HCl}\)).

Recognizing such reactions helps in predicting the products formed and understanding their properties.

Avogadro's Law

Avogadro's Law is a principle in chemistry that states equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This concept is pivotal in understanding gaseous reactions like the one between hydrogen and chlorine.
In our problem, because the volumes of \(\mathrm{H}_2\) and \(\mathrm{Cl}_2\) are equal, each contains the same number of molecules. This understanding simplifies analyzing the reaction's outcome about volumes,because it allows us to determine the molar relationship between the reactants and products.

• The volume relationship is directly related to the mole relationship.
• This law assists in predicting the volumes of products formed from reactant gases.

This law is key to calculations involving gases in chemical reactions.

Balanced Chemical Equation

A balanced chemical equation ensures that the number of atoms for each element is the same on both sides of the reaction. For the reaction between hydrogen and chlorine, the balanced equation is:\[\mathrm{H}_2 + \mathrm{Cl}_2 \rightarrow 2\,\mathrm{HCl}\]This equation confirms that one molecule of \(\mathrm{H}_2\) reacts with one molecule of \(\mathrm{Cl}_2\) to produce two molecules of \(\mathrm{HCl}\). Balancing chemical equations is essential for understanding the stoichiometry of a reaction, whereby the proportions of reactants and products can be accurately calculated.

• Atoms are conserved in reactions - none are lost or gained.
• Provides the stoichiometric ratio necessary for calculations.

This concept is fundamental in applying the Law of Definite Proportions effectively.

Volume Ratio in Gaseous Reactions

In gaseous reactions, understanding the volume ratios is vital. Owing to Avogadro's Law, the ratio of the volumes of reactants and products is equal to the ratio of their coefficients in the balanced equation.Here, from the balanced chemical equation:\[\mathrm{H}_2 + \mathrm{Cl}_2 \rightarrow 2\,\mathrm{HCl}\]the volume ratio between \(\mathrm{H}_2\) and \(\mathrm{HCl}\) product is 1:2 under identical conditions of temperature and pressure.
This means that reacting equal volumes of \(\mathrm{H}_2\) and \(\mathrm{Cl}_2\) yields a volume of \(\mathrm{HCl}\) double the initial volume of hydrogen or chlorine.

• Relies on the assumption of ideal gas behavior.
• Simplifies prediction of product volumes from given reactant volumes.

Volume ratios in gaseous reactions bring practical insights into laboratory or industrial chemical production.