General Chemistry Exam Review: Concepts, Calculations, and Dimensional Analysis

Measurement, Units, and Dimensional Analysis

Unit Conversions and Dimensional Analysis

Dimensional analysis is a systematic method used to convert between units and solve problems involving measurements. It is essential in chemistry for ensuring that calculations are accurate and that units are consistent.

• Key Point: Always include units in calculations and use conversion factors to move between units.

• Example: Converting fluid ounces to cubic inches using multiple conversion factors.

• Formula: $\text{Quantity in new units} = \text{Original quantity} \times \frac{\text{Conversion factor 1}}{\text{Conversion factor 2}} \times \cdots$

Significant Figures: The number of significant digits in a calculated answer should reflect the precision of the measurements used.

• Example: $3.11 \times (7.5 - 3.31)$

Atoms, Elements, and Isotopes

Atomic Structure

Atoms consist of protons, neutrons, and electrons. The number of protons defines the element, while the number of neutrons determines the isotope.

• Atomic Number (Z): Number of protons in the nucleus.

• Mass Number (A): Sum of protons and neutrons.

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

• Example: Gold with atomic number 79 has 79 protons and, if neutral, 79 electrons.

• Example: For $^{134}_{56}Y^{2+}$, protons = 56, neutrons = 78, electrons = 54.

Atomic Mass and Weighted Average

The atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes.

• Formula: $\text{Atomic mass} = \sum (\text{isotope mass} \times \text{fractional abundance})$

• Example: Calculating atomic mass of magnesium from Mg-24, Mg-25, and Mg-26.

Moles, Molar Mass, and Avogadro's Number

The Mole Concept

The mole is a fundamental unit in chemistry representing $6.022 \times 10^{23}$ entities (Avogadro's number).

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

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

• Example: How many moles in 6.50 g of H2O?

Counting Atoms and Molecules

• Number of Atoms: $\text{Number of atoms} = \text{moles} \times 6.022 \times 10^{23}$

• Example: Calculating number of oxygen atoms in a given mass of K2Cr2O7.

Chemical Compounds, Mixtures, and Classification

Compounds vs. Mixtures

Chemical substances can be classified as elements, compounds, or mixtures.

• Compound: Substance composed of two or more elements chemically bonded (e.g., CO(g), H2(g)).

• Mixture: Physical combination of two or more substances (e.g., milk).

• Element: Pure substance consisting of only one type of atom.

Physical and Chemical Changes

• Physical Change: Change in state or appearance without altering composition (e.g., ice melting).

• Chemical Change: Change that produces new substances (e.g., wood burning, carbon and oxygen forming CO2).

Stoichiometry and Chemical Equations

Balancing Chemical Equations

Balancing equations ensures the conservation of mass and atoms in a chemical reaction.

• Example: $\text{Fe(s)} + \text{H}_2\text{O(l)} \rightarrow \text{Fe}_3\text{O}_4(s) + \text{H}_2(g)$

• Sum of coefficients: Add up all coefficients after balancing.

Stoichiometric Calculations

• Mass-Mole Relationships: Use molar mass to convert between mass and moles.

• Mole-Molecule Relationships: Use Avogadro's number to convert between moles and number of molecules.

• Example: Calculating molecules of CO2 in a given mass.

Density, Volume, and Mass Calculations

Density

Density is the mass per unit volume of a substance.

• Formula: $\text{Density} = \frac{\text{mass}}{\text{volume}}$

• Example: Given density and mass, calculate volume: $\text{Volume} = \frac{\text{mass}}{\text{density}}$

Classification of Elements

Groups and Periodic Table

• Alkali Metals: Group 1 elements (e.g., hydrogen is not an alkali metal, but lithium is).

• Halogens: Group 17 elements (e.g., iodine).

• Alkaline Earth Metals: Group 2 elements (e.g., calcium).

Visual Representation of Matter

Particle Diagrams

Diagrams can be used to represent mixtures and pure substances.

Image	Description
1	Mixture (different types of particles not bonded)
2	Mixture (different molecules and atoms)
3	Pure substance (all particles identical)

Additional Info

• Some questions require careful attention to units and significant figures for full credit.

• Dimensional analysis problems reward neat, orderly solutions with correct units.