Question

Calculate the mass in grams of hydrogen chloride produced when \(5.6 \mathrm{~L}\) of molecular hydrogen measured at STP react with an excess of molecular chlorine gas.

Short answer

18.23 grams of HCl are produced.

Step-by-step solution

Understand the Reaction

The reaction between molecular hydrogen (\(\text{H}_2\)) and molecular chlorine \((\text{Cl}_2)\) to produce hydrogen chloride \((\text{HCl})\) is given by the balanced equation: \(\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}\). This tells us that one mole of hydrogen reacts with one mole of chlorine to produce two moles of hydrogen chloride.

Use STP Conditions to Determine Moles of Hydrogen

At standard temperature and pressure (STP), one mole of an ideal gas occupies \(22.4\text{ L}\). With \(5.6 \text{ L}\) of \(\text{H}_2\), the number of moles is calculated by: \(\text{moles of } \text{H}_2 = \frac{5.6 \text{ L}}{22.4 \text{ L/mol}} = 0.25 \text{ moles}\).

Calculate Moles of Hydrogen Chloride Produced

From the balanced equation: \(\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}\), we see that each mole of \(\text{H}_2\) produces 2 moles of \(\text{HCl}\). Therefore, \(0.25\) moles of \(\text{H}_2\) will produce: \(0.25 \times 2 = 0.5 \text{ moles of HCl}\).

Convert Moles of HCl to Grams

The molar mass of \(\text{HCl}\) is calculated as \(1.01\text{ g/mol (H)} + 35.45\text{ g/mol (Cl)} = 36.46\text{ g/mol}\). The mass of \(0.5 \text{ moles of HCl}\) is \(0.5 \times 36.46 \text{ g/mol} \approx 18.23 \text{ g}\).

Key concepts

Chemical Reactions

A chemical reaction involves the transformation of one or more substances into different substances. In this exercise, hydrogen gas (\( \text{H}_2 \)) and chlorine gas (\( \text{Cl}_2 \)) react to form hydrogen chloride (\( \text{HCl} \)). This is represented by the balanced chemical equation: \( \text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl} \).

Balancing an equation ensures the same number of each type of atom on both sides. Here, one mole of \( \text{H}_2 \) reacts with one mole of \( \text{Cl}_2 \) to produce two moles of \( \text{HCl} \). This process follows the law of conservation of mass, indicating no atoms are lost or gained during the reaction. Understanding this helps identify how reactants convert to products.

Mole Concept

The mole concept is a fundamental idea in chemistry that helps quantify amounts in a chemical reaction. A mole is a unit that represents \( 6.022 \times 10^{23} \) particles, such as atoms or molecules.

In this problem, we calculate the number of moles of hydrogen gas based on its volume at standard temperature and pressure (STP), where 1 mole of gas occupies \( 22.4 \text{ L} \). With \( 5.6 \text{ L} \) of \( \text{H}_2 \), we find it corresponds to \( 0.25 \) moles. This value helps us determine how much product, \( \text{HCl} \), can be formed. Moles allow us to connect mass and volume to the particles involved in the reaction.

Ideal Gas Law

The ideal gas law is a useful tool to connect pressure, volume, and temperature of gases. The simple form used at STP (standard temperature and pressure) states that \( 1 \text{ mole} \) of an ideal gas occupies \( 22.4 \text{ L} \).

This principle helps us convert the given volume of hydrogen gas (\( 5.6 \text{ L} \)) to moles. It simplifies many stoichiometry problems involving gases, especially under standard conditions, by correlating the physical characteristics of gases with their chemical properties through the equation \( PV = nRT \). This allows for straightforward calculations when given volumes.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, often expressed in grams per mole. Calculating molar masses involves adding the atomic masses of all elements in a compound.

For \( \text{HCl} \), the molar mass is calculated by adding the atomic mass of hydrogen (\( 1.01 \text{ g/mol} \)) and chlorine (\( 35.45 \text{ g/mol} \)), resulting in \( 36.46 \text{ g/mol} \).

In the exercise, \( 0.5 \text{ moles} \) of \( \text{HCl} \) are produced. By multiplying by its molar mass, we find that the reaction yields approximately \( 18.23 \text{ g} \) of \( \text{HCl} \). Understanding molar mass connects the concept of moles with measurable quantities, such as mass.