Introductory Chemistry: Essential Calculation and Concept Review

Chapter 2: Measurement and Problem Solving

Scientific Notation

Scientific notation is a method for expressing very large or very small numbers in a compact form. It is commonly used in chemistry to handle measurements efficiently.

• How to Convert: Move the decimal point so that only one nonzero digit remains to the left of the decimal. Count the number of moves to determine the exponent.

• Rule: If the original number is less than 1, the exponent is negative; if greater than 1, the exponent is positive.

• Example: 0.00045 = $4.5 \times 10^{-4}$

Significant Figures

Significant figures (sig figs) indicate the precision of a measured or calculated quantity.

• Counting Sig Figs: Ignore leading zeros; count all other digits, including zeros between or after nonzero digits.

• Example: 0.00450 has 3 significant figures (4, 5, 0).

Significant Figures in Calculations

• Addition/Subtraction: Round the result to the least number of decimal places among the numbers used.

• Example: 12.11 + 3.2 = 15.3

• Multiplication/Division: Round the result to the least number of significant figures among the numbers used.

• Example: 4.56 × 1.2 = 5.5

Metric Conversions

Metric prefixes are used to convert between units. Common prefixes include kilo (k), centi (c), and milli (m).

• Example: 2.5 km to meters: $2.5 \times 1000 = 2500$ m

Multi-Step Conversions

Complex conversions may require several steps, using conversion factors to cancel units sequentially.

• Example: Convert 5.0 miles to centimeters:

  • 1 mile = 1.609 km

  • 1 km = 1000 m

  • 1 m = 100 cm

  Method: Multiply across and cancel units at each step.

Density

Density relates the mass of a substance to its volume and is a key property in chemistry.

• Formula: $d = \frac{m}{v}$

• Example: Mass = 20 g, Volume = 5 mL; $d = \frac{20}{5} = 4$ g/mL

Using Density as a Conversion Factor

• Formula: $m = d \times v$

• Example: Density = 2 g/mL, Volume = 10 mL; $m = 2 \times 10 = 20$ g

Chapter 3: Matter and Energy

Temperature Conversion

Temperature can be measured in Celsius (°C) or Kelvin (K). The Kelvin scale is the SI unit for temperature.

• Formula: $T_K = T_C + 273.15$

• Example: 25°C = $25 + 273.15 = 298.15$ K

Specific Heat

Specific heat is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

• Formula: $q = m C \Delta T$

• Example: $q = 10 \times 4.184 \times 5 = 209.2$ J (where m = 10 g, C = 4.184 J/g°C, ΔT = 5°C)

Physical vs Chemical Change

Understanding the difference between physical and chemical changes is fundamental in chemistry.

• Physical Change: The substance remains the same (e.g., ice melting).

• Chemical Change: A new substance is formed (e.g., burning wood).

Exothermic vs Endothermic Processes

• Exothermic: Releases heat (e.g., fire).

• Endothermic: Absorbs heat (e.g., ice melting).

Chapter 4: Atoms and Elements

Protons, Neutrons, and Electrons

Atoms are composed of protons, neutrons, and electrons. The atomic number equals the number of protons and electrons in a neutral atom.

• Example: Carbon-14: Atomic number = 6; Protons = 6; Electrons = 6; Neutrons = 14 - 6 = 8

Ions

Ions are atoms or molecules that have gained or lost electrons, resulting in a net charge.

• Metals: Lose electrons to form positive ions (cations), e.g., Na → Na⁺

• Nonmetals: Gain electrons to form negative ions (anions), e.g., Cl → Cl⁻

Predicting Ion Charge

The periodic table helps predict the charges of ions formed by elements.

• Group 1: +1

• Group 2: +2

• Group 16: -2

• Group 17: -1

• Example: Oxygen (Group 16) forms O²⁻

Isotope Average Mass

The average atomic mass of an element is calculated using the relative abundance and mass of each isotope.

• Formula: $\text{Average mass} = (\text{fraction}_1 \times \text{mass}_1) + (\text{fraction}_2 \times \text{mass}_2) + \ldots$

• Example: 50% at 10 amu, 50% at 12 amu: $(0.5 \times 10) + (0.5 \times 12) = 11$ amu

Chapter 9: Electrons in Atoms and the Periodic Table

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals.

• Example: Oxygen (8 electrons): 1s² 2s² 2p⁴

Noble Gas Shortcut

The noble gas notation simplifies electron configurations by using the symbol of the previous noble gas.

• Example: Sodium (Na): [Ne] 3s¹

Valence Electrons

Valence electrons are the outermost electrons and determine chemical reactivity.

• Example: Oxygen (Group 16): 6 valence electrons

Periodic Trends

• Atomic Size: Increases down a group and to the left across a period.

• Ionization Energy: Increases up a group and to the right across a period.

Chapter 10: Chemical Bonding

Ionic vs Covalent Bonds

Chemical bonds form between atoms to achieve stability. The two main types are ionic and covalent bonds.

• Ionic: Metal + nonmetal (e.g., NaCl)

• Covalent: Nonmetal + nonmetal (e.g., CO₂)

Lewis Structures (Covalent)

Lewis structures represent the arrangement of electrons in molecules.

• Example: H₂O: Oxygen in the center, two bonds, two lone pairs

Lewis Structures (Ionic)

• Example: NaCl: Show Na⁺ and Cl⁻ with charges, no lines

VSEPR Shape

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts molecular shapes based on electron pairs around the central atom.

• Example: CO₂: linear; H₂O: bent

Electronegativity

Electronegativity is the ability of an atom to attract electrons in a bond. Fluorine is the most electronegative element.

Bond Type by Electronegativity Difference

• Large difference: Ionic bond

• Medium difference: Polar covalent bond

• Small difference: Nonpolar covalent bond

Polarity

Molecular polarity depends on both bond polarity and molecular shape.

• Symmetrical molecules: Nonpolar (e.g., CO₂)

• Bent/uneven molecules: Polar (e.g., H₂O)

Summary Table: Key Concepts and Examples

Topic	Key Rule/Formula	Example
Scientific Notation	Move decimal, count exponent	0.00045 = $4.5 \times 10^{-4}$
Sig Figs (Addition)	Least decimal places	12.11 + 3.2 = 15.3
Sig Figs (Multiplication)	Least sig figs	4.56 × 1.2 = 5.5
Density	$d = \frac{m}{v}$	20 g / 5 mL = 4 g/mL
Temperature	$T_K = T_C + 273.15$	25°C = 298.15 K
Specific Heat	$q = m C \Delta T$	10 × 4.184 × 5 = 209.2 J
Electron Config	Fill orbitals by energy	O: 1s² 2s² 2p⁴
Lewis Structure (H₂O)	2 bonds, 2 lone pairs	H–O–H (with lone pairs on O)
Ionic vs Covalent	Metal + nonmetal = ionic	NaCl (ionic), CO₂ (covalent)

Additional info: This guide focuses on the most tested calculation and concept areas for introductory chemistry, including significant figures, conversions, density, temperature, specific heat, electron configuration, Lewis structures, and bonding types. For exam preparation, practice active recall by covering answers, rewriting problems, and solving from memory.