Molar Mass as a Conversion Factor

Chapter 3: Molecules and Compounds

Introduction

This section introduces the concepts of molecules and compounds, focusing on how to use molar mass as a conversion factor to relate mass, moles, and number of molecules. These skills are fundamental in general chemistry for quantifying substances and performing stoichiometric calculations.

Using Molar Mass as a Conversion Factor

Definition and Purpose

• Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol).

• It serves as a bridge between the mass of a sample and the number of particles (atoms, molecules) it contains.

• Avogadro's number ($6.022 \times 10^{23}$) is the number of particles in one mole of a substance.

By using molar mass and Avogadro's number, you can convert between grams, moles, and number of molecules or atoms.

Conversion Pathways

• To find molecules from mass:

  1. Convert grams to moles using molar mass.

  2. Convert moles to molecules using Avogadro's number.

• To find mass from molecules:

  1. Convert molecules to moles using Avogadro's number.

  2. Convert moles to grams using molar mass.

Key Formulas

• Moles from mass: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

• Number of molecules from moles: $\text{number of molecules} = \text{moles} \times 6.022 \times 10^{23}$

• Mass from number of molecules: $\text{mass (g)} = \frac{\text{number of molecules}}{6.022 \times 10^{23}} \times \text{molar mass (g/mol)}$

Example: CO2 in Dry Ice

• Problem: Calculate the number of CO2 molecules in a sample of dry ice (solid CO2) with a mass of 10.8 g.

• Given: 10.8 g CO2

• Find: Number of CO2 molecules

• Strategy: Grams → Moles → Molecules

Step 1: Convert grams to moles:

$\text{moles CO}_2 = \frac{10.8\ \text{g CO}_2}{44.01\ \text{g/mol}} = 0.2454\ \text{mol CO}_2$

Step 2: Convert moles to molecules:

$\text{molecules CO}_2 = 0.2454\ \text{mol} \times 6.022 \times 10^{23}\ \text{molecules/mol} = 1.48 \times 10^{23}\ \text{molecules}$

Final Answer: $1.48 \times 10^{23}$ CO2 molecules

Practice Problem: Aspirin Tablet

• Problem: An aspirin tablet contains 325 mg of acetylsalicylic acid (C9H8O4). How many acetylsalicylic acid molecules does it contain?

• Hint: Convert mg to g, then use the molar mass of C9H8O4 to find moles, and finally use Avogadro's number to find molecules.

Practice Problem: Mass from Number of Molecules

• Problem: Determine the mass of a sample that contains $3.55 \times 10^{22}$ H2O molecules.

• Hint: Convert molecules to moles, then moles to grams using the molar mass of H2O.

Summary Table: Mass, Moles, and Molecules Conversion

Given	Conversion Factor	Find
Mass (g)	Divide by molar mass (g/mol)	Moles
Moles	Multiply by Avogadro's number ($6.022 \times 10^{23}$)	Number of molecules
Number of molecules	Divide by Avogadro's number	Moles
Moles	Multiply by molar mass (g/mol)	Mass (g)

Key Terms

• Molar mass: The mass of one mole of a substance, in grams per mole (g/mol).

• Avogadro's number: $6.022 \times 10^{23}$, the number of particles in one mole.

• Mole: The SI unit for amount of substance, representing Avogadro's number of particles.

Reflection

Understanding how to use molar mass and Avogadro's number to convert between mass, moles, and number of molecules is essential for solving quantitative problems in chemistry. Mastery of these conversions enables you to analyze chemical reactions, determine empirical formulas, and calculate yields.