Chemical Quantities and Reactions: Study Notes

Chemical Quantities and Reactions

Introduction

Chemical quantities and reactions are foundational concepts in general chemistry, enabling the calculation and prediction of the amounts of substances involved in chemical changes. This chapter covers the mole concept, Avogadro’s number, molar mass, and the principles of writing and balancing chemical equations.

The Mole and Avogadro’s Number

Counting Particles: The Mole

The mole is a counting unit used to express amounts of a chemical substance. Just as a dozen means 12 items, a mole represents a specific number of particles—Avogadro’s number.

• Avogadro’s Number: $6.022 \times 10^{23}$ particles (atoms, molecules, or ions) per mole.

• Application: Used to count extremely small entities such as atoms and molecules.

Using Avogadro’s Number in Calculations

Avogadro’s number allows conversion between moles and the number of particles.

• Equality: $1\ \text{mol} = 6.022 \times 10^{23}$ particles

• Conversion Factors:

  • From moles to particles: $\text{moles} \times \frac{6.022 \times 10^{23}\ \text{particles}}{1\ \text{mol}}$

  • From particles to moles: $\text{particles} \times \frac{1\ \text{mol}}{6.022 \times 10^{23}\ \text{particles}}$

Example: Converting Moles to Atoms

To find the number of atoms in 2.0 moles of aluminum (Al):

• Given: 2.0 moles of Al

• Needed: Number of atoms of Al

• Calculation: $2.0\ \text{mol} \times \frac{6.022 \times 10^{23}\ \text{atoms}}{1\ \text{mol}} = 1.2 \times 10^{24}\ \text{atoms}$

Moles of Elements in a Formula

Interpreting Chemical Formulas

The subscripts in a chemical formula indicate the number of atoms of each element in one molecule and the number of moles of each element in one mole of the compound.

• For aspirin, C9H8O4:

  • 1 molecule contains 9 C, 8 H, and 4 O atoms.

  • 1 mole contains 9 moles C, 8 moles H, 4 moles O.

Example: Atoms in a Given Amount of Compound

To find the number of O atoms in 0.150 mole of aspirin (C9H8O4):

• Step 1: 0.150 mol C9H8O4

• Step 2: Use the subscript (4 mol O per 1 mol aspirin)

• Step 3: Multiply by Avogadro’s number

• Calculation: $0.150\ \text{mol} \times \frac{4\ \text{mol O}}{1\ \text{mol C}_9\text{H}_8\text{O}_4} \times \frac{6.022 \times 10^{23}\ \text{atoms}}{1\ \text{mol O}}$

Molar Mass

Definition and Calculation

The molar mass of an element or compound is the mass in grams of one mole of that substance. For elements, it is numerically equal to the atomic mass from the periodic table, expressed in grams per mole (g/mol).

• Example: 1 mole of Na = 22.99 g

• Example: 1 mole of C = 12.01 g

Calculating Molar Mass of Compounds

To calculate the molar mass of a compound, sum the molar masses of all atoms in the formula, each multiplied by its subscript.

• Example: Lithium carbonate (Li2CO3)

• Calculation: $2 \times \text{Li} + 1 \times \text{C} + 3 \times \text{O}$

Visualizing 1-Mole Quantities

One mole of different substances contains the same number of particles but has different masses and volumes.

Calculations Using Molar Mass

Conversions Between Mass and Moles

Molar mass is used as a conversion factor to relate the mass of a substance to the number of moles, and vice versa.

• From grams to moles: $\text{grams} \times \frac{1\ \text{mol}}{\text{molar mass (g)}}$

• From moles to grams: $\text{moles} \times \text{molar mass (g)}$

Example: Converting Mass to Moles

To find the number of moles in 737 g of NaCl:

• Step 1: Given mass = 737 g NaCl

• Step 2: Molar mass of NaCl = 58.44 g/mol

• Step 3: $737\ \text{g} \times \frac{1\ \text{mol}}{58.44\ \text{g}} = 12.6\ \text{mol}$

Summary Map: Mass, Moles, and Particles

The following diagram summarizes the relationships between mass, moles, and particles for elements and compounds:

Equations for Chemical Reactions

Writing and Balancing Chemical Equations

A chemical equation represents a chemical reaction, showing the substances involved (reactants and products) and their quantities. Equations must be balanced to obey the law of conservation of mass.

• Reactants: Substances present before the reaction (left side).

• Products: Substances formed by the reaction (right side).

• Arrow (→): Separates reactants from products.

• Physical states: (s) solid, (l) liquid, (g) gas, (aq) aqueous.

• Delta (Δ): Indicates heat is used.

Symbols Used in Chemical Equations

Symbol	Meaning
+	Separates two or more reactants or products
→	Separates reactants from products
(s)	Solid state
(l)	Liquid state
(g)	Gaseous state
(aq)	Aqueous (dissolved in water)
Δ	Heat is added

Balancing Chemical Equations

To balance a chemical equation, adjust the coefficients (not subscripts) so that the number of atoms of each element is the same on both sides.

• Step 1: Write correct formulas for all reactants and products.

• Step 2: Count the number of atoms of each element on both sides.

• Step 3: Use coefficients to balance each element.

• Step 4: Check that all elements are balanced and coefficients are in the lowest ratio.

Balancing Equations with Polyatomic Ions

When polyatomic ions appear unchanged on both sides of the equation, balance them as units to simplify the process.

Summary Table: Key Concepts

Concept	Definition/Key Point
Mole	Counting unit for particles; 1 mole = $6.022 \times 10^{23}$ particles
Molar Mass	Mass of 1 mole of substance (g/mol)
Balanced Equation	Same number of each atom on both sides
Conversion Factors	Used to convert between grams, moles, and particles