Problem 46 - Chemistry and Chemical Reactivity

Question

The reaction of \(\mathrm{SO}_{2}\) with \(\mathrm{Cl}_{2}\) gives dichlorine oxide, which is used to bleach wood pulp and to treat wastewater: $$ \mathrm{SO}_{2}(\mathrm{g})+2 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{OSCl}_{2}(\mathrm{g})+\mathrm{Cl}_{2} \mathrm{O}(\mathrm{g}) $$ All of the compounds involved in the reaction are gases. List them in order of increasing average speed.

Step-by-Step Solution

Answer

The order is \( \mathrm{OSCl}_2 \), \( \mathrm{Cl}_2 \), \( \mathrm{Cl}_2 \mathrm{O} \), \( \mathrm{SO}_2 \).

Step 1: Understand Root Concept

The average speed of gas molecules is determined by their molar mass. Lighter gas molecules move faster, while heavier ones move slower.

Step 2: Identify Chemicals

List the compounds in the reaction: \( \mathrm{SO}_2 \), \( \mathrm{Cl}_2 \), \( \mathrm{OSCl}_2 \), and \( \mathrm{Cl}_2 \mathrm{O} \).

Step 3: Calculate Molar Masses

Calculate the molar mass of each compound using the atomic masses from the periodic table: - \( \mathrm{SO}_2 \) has a molar mass of 64 g/mol (Sulfur: 32.07 g/mol, Oxygen: 16.00 g/mol × 2).- \( \mathrm{Cl}_2 \) has a molar mass of 70.9 g/mol (Chlorine: 35.45 g/mol × 2).- \( \mathrm{OSCl}_2 \) has a molar mass of 102.5 g/mol (Oxygen: 16.00 g/mol, Sulfur: 32.07 g/mol, Chlorine: 35.45 g/mol × 2).- \( \mathrm{Cl}_2 \mathrm{O} \) has a molar mass of 86.9 g/mol (Chlorine: 35.45 g/mol × 2, Oxygen: 16.00 g/mol).

Step 4: Arrange Compounds by Molar Mass

Order the compounds by their molar masses from lightest to heaviest: \( \mathrm{SO}_2 \) (64 g/mol), \( \mathrm{Cl}_2 \mathrm{O} \) (86.9 g/mol), \( \mathrm{Cl}_2 \) (70.9 g/mol), \( \mathrm{OSCl}_2 \) (102.5 g/mol).

Step 5: List Compounds by Average Speed

Since lighter gases move faster, the order of increasing average speed (from slowest to fastest) is: \( \mathrm{OSCl}_2 \), \( \mathrm{Cl}_2 \), \( \mathrm{Cl}_2 \mathrm{O} \), \( \mathrm{SO}_2 \).

Key Concepts

Molar Mass Calculation

Understanding how to calculate the molar mass of a chemical compound is crucial for determining the behavior of gases. Molar mass refers to the mass of one mole of a substance, usually expressed in grams per mole (g/mol). Calculating molar mass involves combining the atomic masses of all the atoms in a molecule.

• First, identify the atomic masses of each element from the periodic table.
• Next, multiply the atomic mass by the number of atoms of that element in the molecule.
• Finally, sum these values to obtain the total molar mass of the compound.

For example, when calculating the molar mass of sulfur dioxide (\(\mathrm{SO}_2\)), you add the mass of one sulfur atom (32.07 g/mol) and the mass of two oxygen atoms (16.00 g/mol each). Thus, the molar mass of \(\mathrm{SO}_2\) is 64.07 g/mol.

• More complex molecules, like \(\mathrm{OSCl}_2\), require the aggregation of sulfur, oxygen, and chlorine atoms' masses, resulting in a molar mass of 102.5 g/mol.

Chemical Compound Identification

Identifying chemical compounds is essential for understanding any chemical reaction. Every compound has a distinct formula that indicates which elements and how many atoms of each are present in the molecule.In the reaction provided, we start by identifying the molecules involved:

• \(\mathrm{SO}_2\) - Sulfur dioxide, composed of one sulfur and two oxygen atoms.
• \(\mathrm{Cl}_2\) - Chlorine gas, made up of two chlorine atoms.
• \(\mathrm{OSCl}_2\) - A compound with one oxygen, one sulfur, and two chlorine atoms, known as thionyl chloride.
• \(\mathrm{Cl}_2\mathrm{O}\) - Dichlorine monoxide, comprising two chlorine and one oxygen atom.

Understanding these chemical formulas helps predict and analyze the products and reactants in reactions. It also assists in recognizing properties such as reactivity and physical states.

Reaction Product Analysis

Analyzing the products of a chemical reaction gives insights into the chemical process and the energy changes involved. For the reaction given:\(\mathrm{SO}_{2} + 2\mathrm{Cl}_{2} \rightarrow \mathrm{OSCl}_{2} + \mathrm{Cl}_{2} \mathrm{O}\)We focus on the products, \(\mathrm{OSCl}_2\) and \(\mathrm{Cl}_2\mathrm{O}\). It is essential to confirm whether the balance of atoms is preserved and if the reaction follows the laws of conservation of mass:

• The reaction should demonstrate that all sulfur, chlorine, and oxygen atoms in the reactants are accounted for in the products.
• The reactants and products must maintain mass and moles, ensuring neither atoms nor mass is lost or gained.

This analysis shows the transformation from reactants to products and involves understanding aspects such as reaction yield and energetics. Furthermore, knowing the speed order helps in illustrating kinetic properties related to molar mass and gas speed, as lighter molecules generally travel faster. As demonstrated, \(\mathrm{SO}_2\) is the fastest due to its lower molar mass compared to other compounds in this reaction.