AP Chem

The mole is a fundamental counting unit in chemistry, analogous to how a dozen always represents $12$ items.
Molar Mass (Molecular Weight / Molecular Mass): The total mass of one mole of a substance, expressed in units of $\text{g/mol}$ .
Conversions between mass, moles, and number of molecules: $\text{\# of moles} = \frac{\text{weight in grams}}{\text{molar mass}}$ $\text{\# of molecules of substance} = (\text{\# of moles of substance}) \times (\text{Avogadro's number})$
Procedure to find the number of molecules from a given mass:
1. Obtain the atomic/molar mass of the substance using the periodic table.
2. Calculate the number of moles present by dividing the given mass in grams by the molar mass.
3. Multiply the calculated number of moles by Avogadro's number ( $6.022 \times 10^{23}$ ).

Mass spectroscopy is an analytical technique used to measure the relative abundance of different isotopes or atoms within a chemical sample.
Operation of a mass spectrometer:
1. Ionization: The sample is bombarded with high-energy electrons to impart a positive charge onto the particles.
2. Deflection / Separation: Magnetic fields deflect the charged ions based on their charge and weight (mass). Ions of differing masses require different magnetic field strengths to reach the detector.
3. Detection: A detector reads the relative abundance of each ion striking it.
Data Plotting: Results are graphed with the mass-to-charge ratio ( $m/z$ ) plotted on the x-axis and the relative abundance of each atom/isotope type plotted on the y-axis.

Pure Substances: Materials composed of a single type of substance with uniform and consistent characteristics throughout that cannot be separated or broken down further via physical processes.
- Element: A pure substance composed of only one type of atom.
- Compound: A pure substance composed of only one type of molecule.
Law of Definite Proportions: A pure chemical compound, when broken down into its constituent elements, always contains those elements in a fixed, definite mass ratio regardless of the source or method of preparation. For example, pure water ( $\text{H}_2\text{O}$ ) always maintains the exact same proportion of hydrogen to oxygen by mass anywhere it is found.

Mixture: A physical combination of more than one type of element or compound where components can exist in variable proportions.
- Example: Saline solution can be prepared as a $20\%$ saline solution ( $20\%$ sodium chloride and $80\%$ water) or a $5\%$ saline solution ( $5\%$ sodium chloride and $95\%$ water).
Physical Separation: Because no chemical reactions occur during mixture formation, individual components retain their chemical identities and can be recovered back into pure forms through physical methods (e.g., evaporating water away from saline to yield solid sodium chloride and water vapor).
Mixture Types:
- Homogenous Mixture: A mixture in which all parts are uniform and identical due to an even distribution of compounds (e.g., well-mixed saline solution).
- Heterogenous Mixture: A mixture exhibiting a non-uniform distribution of compounds throughout.

Atoms consist of three main subatomic particles:
- Protons: Positively charged particles located in the nucleus.
- Neutrons: Uncharged (neutral) particles located in the nucleus.
- Electrons: Negatively charged particles orbiting outside the nucleus within electron shells.
Particle Characteristics:
- Mass of Proton $\approx 1.67 \times 10^{-27}\,\text{kg}$ ( $1\,\text{amu}$ ).
- Mass of Neutron $\approx 1.67 \times 10^{-27}\,\text{kg}$ ( $1\,\text{amu}$ ).
- Mass of Electron is negligible (approximately $\frac{1}{1800}$ the mass of a proton or neutron) and is ignored when estimating atomic mass.

Atomic Structure Diagram showing electron shells, nucleus, protons, and neutrons

Atomic Symbol Notation: ${}_{Z}^{A}X$
- $X$ : Element symbol.
- $A$ : Mass number (total whole number of protons and neutrons in the nucleus).
- $Z$ : Atomic number (total number of protons in the nucleus).
Element Identity: Defined strictly by the atomic number ( $Z$ ). Adding or removing a proton alters the element's identity (e.g., Carbon has $Z = 6$ ; adding one proton transforms it into Nitrogen with $Z = 7$ ).
Isotopes: Atoms of the same element containing equal numbers of protons ( $Z$ ) but differing numbers of neutrons. The number of neutrons is calculated as: $\text{\# of neutrons} = A - Z$
Atomic Mass: The weighted average mass number of all naturally occurring isotopes of an element. For example, Lithium (Li) has an atomic number of $3$ and an average atomic mass of $6.941\,\text{amu}$ , indicating that most lithium atoms on Earth contain more than $3$ neutrons ( $A = 7$ ).
Atomic Charge and Ions:
- Neutral atom: Number of protons equals number of electrons.
- Ion: Atom possessing a non-zero net charge due to electron gain or loss.
- Anion: Negatively charged ion created by gaining electron(s).
- Cation: Positively charged ion created by losing electron(s).

Shells ( $n$ ): Discrete distances and energy levels outside the nucleus ( $n = 1, 2, 3, \dots$ ). Energy levels increase with distance from the nucleus.
Subshells ( $l$ ): Energy sub-levels within a main shell, designated by letters corresponding to quantum numbers:
- $0 = s$
- $1 = p$
- $2 = d$
- $3 = f$
- $4 = g$
- $5 = h$
Orbitals: Regions of space within a subshell where the probability of finding an electron is highest. Each orbital holds a maximum of $2$ electrons.
Subshell and Shell Capacity Formulas:
- Number of orbitals in a subshell ( $l$ ) $= 2l + 1$
- Subshell $d$ ( $l = 2$ ): $2(2) + 1 = 5$ orbitals $$\rightarrow