Unit 2: Mole-cular Cookbook – Quantitative Chemistry and Chemical Calculations

Global Context and Key Concepts

Scientific and Technical Innovation in Chemistry

This unit explores how quantitative logic and evidence-based reasoning allow scientists to interpret chemical evidence, construct molecular models, and manage resource transformation, fueling scientific and technical innovation.

• Logic: The foundation for quantitative analysis in chemistry.

• Evidence: Data and observations used to support chemical models and reactions.

• Transformation: Chemical changes and conversions of matter.

ATL Skills Focused On

• Information Literacy: Finding, interpreting, judging, and creating information.

• Communication: Verbal and written communication of scientific ideas.

Core Concepts

• Empirical and Molecular Formulae: Calculating the simplest whole-number ratio and the actual number of atoms of each element in a compound.

• Stoichiometry: The quantitative relationship between reactants and products in a chemical reaction.

• Redox Reactions: Analysis of chemical reactions involving electron transfer and changes in oxidation states.

• Limiting Reactants: Determining which reactant restricts the amount of product formed.

Learning Objectives

• State the formulae of elements and compounds.

• Define molecular and empirical formulae.

• Deduce formulas from atomic composition.

• Construct word and symbol equations, including state symbols.

• Deduce formulas for ionic compounds and assign charges.

• Balance chemical equations and write ionic equations.

Atoms, Elements, and Chemical Equations

Reactants and Products

Chemical reactions involve the transformation of reactants into products. These can be represented in word form, diagram form, or as chemical equations.

• Example: Carbon + Oxygen → Carbon Dioxide

• Example: Hydrogen + Oxygen → Water

Symbol Equations and Coefficients

Symbol equations use chemical formulas and coefficients to represent the number of molecules or moles involved.

• Coefficients: Indicate the number of units (molecules/moles) of each substance.

• Example: $2H_2(g) + O_2(g) \rightarrow 2H_2O(g)$

State Symbols

State symbols indicate the physical state of each substance:

• (s) = solid

• (l) = liquid

• (g) = gas

• (aq) = aqueous (dissolved in water)

Balancing Chemical Equations

Equations must be balanced so that the number of atoms of each element is the same on both sides.

• Only coefficients can be changed, not subscripts in formulas.

• Steps: List atoms, count on both sides, multiply if necessary, add coefficients.

Relative Atomic Mass ($A_r$) and Isotopes

Definition and Calculation

Relative atomic mass ($A_r$) is the weighted average mass of the isotopes of an element compared to $^{12}C$.

• Isotopes: Atoms of the same element with different numbers of neutrons.

Name	Protons	Neutrons	Nucleon Number	% of chlorine atoms
chlorine-35	17	18	35	75%
chlorine-37	17	20	37	25%

Calculating $A_r$ from isotopes:

• $A_r = (\% \times \text{nucleon number for isotope 1}) + (\% \times \text{nucleon number for isotope 2})$

• Example for chlorine: $A_r = 0.75 \times 35 + 0.25 \times 37 = 35.5$

Relative Molecular Mass ($M_r$) and Molar Mass ($M$)

Definitions

• Relative molecular mass ($M_r$): The sum of the relative atomic masses of all atoms in a molecule.

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

Examples:

• Water: $M_r = 2 \times 1.01 + 16.00 = 18.02$ g/mol

• Methane: $M_r = 12.01 + 4 \times 1.01 = 16.05$ g/mol

• Sodium chloride: $M_r = 22.99 + 35.45 = 58.44$ g/mol

The Mole and Avogadro's Constant

Definition of a Mole

The mole (n) is a unit for measuring the amount of substance. One mole contains $6.02 \times 10^{23}$ particles (Avogadro's constant).

• 1 mole of $^{12}C$ = 12.00 g = $6.02 \times 10^{23}$ atoms

• 1 mole of $H_2O$ = $6.02 \times 10^{23}$ molecules

Calculations with Moles

Converting Between Mass, Moles, and Molar Mass

• $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

• $\text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)}$

Example: Calculate the mass of 0.5 moles of $Br_2$ (Molar mass = 159.8 g/mol): $0.5 \times 159.8 = 79.9$ g

Stoichiometry and Chemical Equations

Interpreting Chemical Equations

Chemical equations show the mole ratio between reactants and products using coefficients.

• Example: $2Fe_2O_3 \rightarrow 4Fe + 3O_2$

• Coefficients represent the ratio: 2 moles of $Fe_2O_3$ produce 4 moles of Fe and 3 moles of $O_2$.

Percentage Composition and Purity

Calculating Percentage Composition

• $\% \text{composition of element} = \frac{\text{mass of element in 1 mole}}{\text{molar mass of compound}} \times 100$

Example: In $CuO$, $\%$ composition of Cu = $\frac{64}{80} \times 100 = 80\%$

Calculating Percentage Purity

• $\% \text{purity} = \frac{\text{mass of pure compound in sample}}{\text{total mass of impure sample}} \times 100$

• Example: $\frac{87.3}{150.0} \times 100 = 58.2\%$

Dimensional Analysis

Unit Conversion in Chemistry

Dimensional analysis is used to convert between units, such as grams to moles, or cm3 to dm3.

• Conversion factors are written as fractions equal to 1 (e.g., $\frac{100\,cm}{1\,m}$ or $\frac{1\,m}{100\,cm}$).

• Units cancel appropriately to yield the desired unit.

Practice Problems and Worked Examples

• Calculate the molar mass of $NH_3$ and $Mg(NO_3)_2$.

• Balance chemical equations using coefficients.

• Calculate the mass of a substance from moles and molar mass.

• Determine percentage composition and purity in a sample.

Summary Table: Key Quantities and Formulas

Quantity	Symbol	Unit	Formula
Mole	n	mol	$n = \frac{m}{M}$
Mass	m	g	$m = n \times M$
Molar Mass	M	g/mol	$M = \frac{m}{n}$
Relative Atomic Mass	$A_r$	-	Weighted average from isotopes
Relative Molecular Mass	$M_r$	-	Sum of $A_r$ for all atoms in molecule
Avogadro's Constant	L	$6.02 \times 10^{23}$	Particles per mole

Additional info:

• These notes cover foundational quantitative chemistry topics, including chemical equations, mole concept, atomic and molecular masses, stoichiometry, and dimensional analysis, all essential for General Chemistry.