General Chemistry Practice Exam 1: Key Concepts and Explanations

Chapter E Essentials

Units and Measurement

Understanding units and measurement is fundamental in chemistry, as it allows for accurate communication of quantities and comparison of data.

• Mass Measurements: Four different mass measurements are compared: 0.750 kg, 775 g, 7.75 × 102 g, and 7.5 × 101 mg.

• Largest Mass: IV – 7.75 × 102 g

• Smallest Mass: III – 7.5 × 101 mg

• Conversion Example: To compare, convert all masses to grams:

  • I. 0.750 kg = 750 g

  • II. 775 g = 775 g

  • III. 7.5 × 101 mg = 0.075 g

  • IV. 7.75 × 102 g = 775 g

Precision and Accuracy

Precision refers to how close repeated measurements are to each other, while accuracy refers to how close a measurement is to the true value.

• Student Measurements:

  • Student 1: 7.80, 7.81, 7.82 g/cm3

  • Student 2: 7.60, 7.89, 7.87 g/cm3

• Accuracy: Student 2 is more accurate (average is closer to the reported value).

• Precision: Student 1 is more precise (measurements are closer together).

Significant Figures

Significant figures reflect the precision of a measurement. When performing calculations, the number of significant figures in the result should reflect the least precise measurement.

• Example Calculation: $(39.546 - 2.457) / 38.21 = 0.969$ (rounded to three significant figures).

• Rules:

  • For addition/subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places.

  • For multiplication/division, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Density and Volume Measurement

Density is defined as mass per unit volume. It is commonly used to identify substances and solve problems involving mass and volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Example: If the mass of an ore is 47.3 g and the volume is 52.2 mL, then $\text{Density} = \frac{47.3}{52.2} = 0.906$ g/mL.

Classification of Matter

Elements, Compounds, and Mixtures

Matter can be classified as elements, compounds, or mixtures based on its composition.

• Element: Pure substance made of only one type of atom (e.g., Substance A in the diagram).

• Homogeneous Mixture: Uniform composition throughout (e.g., Substance B).

• Heterogeneous Mixture: Non-uniform composition (e.g., Substance C and D).

Atomic Structure and Isotopes

Atomic Particles

Atoms are composed of protons, neutrons, and electrons. The number of each determines the identity and properties of the atom.

• Protons: Define the element.

• Neutrons: Affect the isotope.

• Electrons: Affect the charge (ions).

Isotopes and Atomic Mass

Isotopes are atoms of the same element with different numbers of neutrons. The atomic mass is a weighted average of all naturally occurring isotopes.

• Example Calculation:

  • Isotope 1: 65.32 amu, abundance 23%

  • Isotope 2: 77.55 amu, abundance 77%

  • Average atomic mass: $(65.32 \times 0.23) + (77.55 \times 0.77) = 75.07$ amu

Ions and Their Symbols

Ions are atoms that have gained or lost electrons. The charge is indicated as a superscript.

• Example: An iron ion with 26 protons, 29 neutrons, and 23 electrons is $\text{Fe}^{3+}$.

• Calculation: $26 - 23 = +3$ (charge)

Waves and Light

Frequency, Wavelength, and Energy

Light behaves as both a wave and a particle. The frequency and wavelength are related to the energy of photons.

• Key Equations:

  • $c = \lambda \nu$ (speed of light = wavelength × frequency)

  • $E = h \nu$ (energy of a photon = Planck's constant × frequency)

• Example: To find the frequency from wavelength:

  • $\nu = \frac{c}{\lambda}$

  • For $\lambda = 96.8 \text{ nm}$, $\nu = \frac{2.998 \times 10^8}{96.8 \times 10^{-9}} = 3.10 \times 10^{15}$ Hz

Photoelectric Effect

The photoelectric effect demonstrates that light can eject electrons from a metal surface if the energy of the photons exceeds the threshold energy.

• Threshold Frequency: $\nu_0 = \frac{E_0}{h}$

• Energy of Ejected Electrons: $E_{\text{kinetic}} = h\nu - E_0$

Electron Configuration and Orbitals

Degeneracy of Orbitals

Orbitals in the same subshell (e.g., all p orbitals in a given shell) have the same energy, a property known as degeneracy.

• Example: The 2px, 2py, and 2pz orbitals all have the same energy.

Tables

Sample Table: Classification of Matter

Substance	Classification
A	Element
B	Homogeneous Mixture
C	Heterogeneous Mixture
D	Heterogeneous Mixture

Sample Table: Atomic Changes

Change	Result
Add 2 neutrons	Different isotope
Take away 8 protons	Different element
Take away 4 electrons	Cation
Add 4 electrons	Anion

Additional info:

• Some explanations and calculations have been expanded for clarity and completeness.

• All equations are provided in LaTeX format for clarity.