Question

Assuming all gases are at the same temperature and pressure, how many milliliters of iodine vapor react with \(125 \mathrm{~mL}\) of hydrogen gas? $$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{HI}(g)$$

Short answer

125 mL of iodine vapor is needed.

Step-by-step solution

Review the Reaction Equation

The given reaction is \(\mathrm{H}_{2}(g) + \mathrm{I}_{2}(g) \rightarrow 2\mathrm{HI}(g)\). This equation indicates that 1 molecule of hydrogen gas reacts with 1 molecule of iodine vapor to form 2 molecules of hydrogen iodide gas.

Use the Concept of Stoichiometry

Since the equation is balanced as \(1:1\) for \(\mathrm{H}_{2}\) to \(\mathrm{I}_{2}\), we know that 1 volume of hydrogen gas reacts with 1 volume of iodine vapor when the gases are at the same temperature and pressure.

Determine Volume of Iodine Vapor Needed

Given that \(125 \mathrm{~mL}\) of hydrogen gas is used, the stoichiometric ratio tells us that \(125 \mathrm{~mL}\) of iodine vapor is required to completely react with that hydrogen.

Key concepts

Understanding a Balanced Chemical Equation

In chemistry, a balanced chemical equation is essential for understanding how substances react with each other. It tells us which reactants (starting materials) turn into which products (end materials), ensuring the same number of each type of atom on both sides of the equation. This balance is key because it respects the Law of Conservation of Mass, meaning mass is neither created nor destroyed in a chemical reaction.

The given reaction, \( \mathrm{H}_{2}(g) + \mathrm{I}_{2}(g) \rightarrow 2\mathrm{HI}(g) \), is balanced. This indicates that one molecule of hydrogen gas reacts with one molecule of iodine gas to produce two molecules of hydrogen iodide gas. In essence, the coefficients in front of the chemical formulas represent the smallest whole number ratio of the molecules involved in the reaction.

• For \( \mathrm{H}_{2} \) and \( \mathrm{I}_{2} \), the coefficient is 1, meaning there is one hydrogen and one iodine needed for the reaction.
• For \( \mathrm{HI} \), the coefficient is 2, indicating that two molecules of hydrogen iodide are produced from the reaction of each pair of reactant gases.

This balance ensures precise calculations for predicting the amounts of reactants needed and products formed.

Volume Ratio in Gases

When dealing with gases, particularly in stoichiometric calculations, the volume ratio between them is an important concept. According to Avogadro's Law, equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules. This means that the ratio of volumes is directly related to the ratio of molecules.

For our balanced equation \( \mathrm{H}_{2}(g) + \mathrm{I}_{2}(g) \rightarrow 2\mathrm{HI}(g) \), the coefficients indicate a 1:1 ratio for \( \mathrm{H}_{2} \) to \( \mathrm{I}_{2} \). This says that one volume of hydrogen reacts with one volume of iodine gas. Hence, if we have 125 mL of hydrogen, we need 125 mL of iodine vapor under the same conditions of temperature and pressure. This is not just a coincidence but a precise application of Avogadro's principle, making such stoichiometric calculations straightforward and intuitively simple.

• For gases, the coefficient equals the volume ratio when conditions (temperature and pressure) are the same.
• This direct relationship simplifies the process of determining required reactants and expected products in gaseous reactions.

Significance of Gas Reactions

Gas reactions, like the one between hydrogen and iodine to form hydrogen iodide, are common and highly significant in both industrial and laboratory settings. These reactions can be influenced by factors like temperature, pressure, and the nature of the gases involved. Understanding gas reactions helps chemists to manipulate conditions to optimize yields and minimize waste.

In the reaction \( \mathrm{H}_{2}(g) + \mathrm{I}_{2}(g) \rightarrow 2\mathrm{HI}(g) \), both reactants and products are in the gaseous state. Conducting such a reaction is typically easier compared to solid or liquid reactions as gases mix well and react more easily due to their high kinetic energy and diffusibility.

• Gas reactions allow detailed study of reaction kinetics and mechanisms.
• The ability to control the reaction environment (e.g., temperature and pressure) can dramatically affect the rate and outcome.

In addition, many gases are environmentally friendly. Using gases reduces the need for solvents and makes purification of products easier.