Principles of Chemistry I - Core Concepts & Principles

Total points in course: $500\,pt$
Course grade components: $3$ Exams at $100\,pt$ each ( $300\,pt$ total), $5$ Quizzes at $10\,pt$ each ( $50\,pt$ total), Homework ( $50\,pt$ total), and a standardized departmental Final Exam ( $100\,pt$ ).
Lowest exam score out of $4$ and lowest quiz score out of $6$ are dropped.
Tokens handle unforeseen circumstances (e.g., late submissions, quiz corrections), and remaining tokens convert to up to $25\,pt$ of bonus grade points at the end of the semester.

Measured numbers carry uncertainty from instruments; exact numbers come from counting or definitions and never limit significant figures.
Significant Figure Rules:
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Leading zeros never count.
- Trailing zeros count only if a decimal point is explicitly written.
- In scientific notation ( $a \times 10^n$ ), rules apply only to $a$
Calculations with Significant Figures:
- Multiplication and Division: Answer is rounded to the same number of significant figures as the measurement with the fewest significant figures.
- Addition and Subtraction: Answer is rounded to the same number of decimal places as the measurement with the fewest decimal places.

SI Base Units: Standard units for fundamental quantities, including kilogram ( $\text{kg}$ ), meter ( $\text{m}$ ), second ( $\text{s}$ ), kelvin ( $\text{K}$ ), mole ( $\text{mol}$ ), ampere ( $\text{A}$ ), and candela ( $\text{cd}$ ).
Derived Units: Units created from mathematical combinations of base units, such as volume ( $\text{cm}^3$ or $\text{mL}$ ) and energy ( $\text{J} = \text{kg} \times (\text{m/s})^2$ ).
Metric Prefixes:
- Kilo ( $\text{k}$ ): $10^3$
- Deci ( $\text{d}$ ): $10^{-1}$
- Centi ( $\text{c}$ ): $10^{-2}$
- Milli ( $\text{m}$ ): $10^{-3}$
- Micro ( $\mu$ ): $10^{-6}$
- Nano ( $\text{n}$ ): $10^{-9}$
Temperature Conversions: Temperature scales have different zero points and require equations rather than simple conversion factors:
- Celsius from Fahrenheit: $T_{\text{C}} = \frac{T_{\text{F}} - 32}{1.8}$
- Kelvin from Celsius: $T_{\text{K}} = T_{\text{C}} + 273$

States of Matter: Solid, liquid, gas, and plasma. During phase transitions, temperature remains constant as energy is added or removed.

Classification of Matter:
- Pure Substances: Composed of elements (e.g., $\text{O}_2$ , $\text{Au}$ ) or compounds (e.g., $\text{H}_2\text{O}$ , $\text{NaCl}$ ).
- Mixtures: Homogeneous / Solutions (uniform composition throughout, e.g., salt water, rum) or Heterogeneous (non-uniform composition, e.g., oil and water, fermented mash).
Properties of Matter:
- Physical Property: Can be observed without changing chemical identity (e.g., color, density, boiling point).
- Chemical Property: Can only be observed during a chemical reaction (e.g., flammability, toxicity, acidity).
- Intensive Property: Independent of the amount of substance (e.g., density, melting point, specific heat capacity).
- Extensive Property: Depends directly on the amount of substance present (e.g., mass, volume, heat capacity).
Changes in Matter:
- Physical Change: Form or appearance changes, but chemical composition remains the same.
- Chemical Change: One or more new chemical substances are formed.

Distillation: A physical separation technique that utilizes differences in boiling points (e.g., methanol boils at $64.7\,^\circ\text{C}$ , ethanol at $78.4\,^\circ\text{C}$ , and water at $100\,^\circ\text{C}$ ).
Concentration Expressions:
- Percent by Mass ( $\%\,\text{m/m}$ ): $\%\text{ by mass } (\text{m/m}) = \left(\frac{\text{mass solute}}{\text{mass solution}}\right) \times 100$
- Percent by Volume ( $\%\,\text{v/v}$ ): $\%\text{ by volume } (\text{v/v}) = \left(\frac{\text{vol solute}}{\text{vol solution}}\right) \times 100$
- Percent Mass/Volume ( $\%\,\text{m/v}$ ): $\%\text{ mass/vol } (\text{m/v}) = \left(\frac{\text{mass solute}}{\text{vol solution}}\right) \times 100$

Heat Capacity ( $C$ ): Extensive property defining heat required to change an object's temperature by $1\,^\circ\text{C}$ or $1\,\text{K}$ ( $\text{J}/^\circ\text{C}$ ): $C = \frac{q}{\Delta T} = c \times m$
Specific Heat Capacity ( $c$ ): Intensive property defining heat required to raise $1\,\text{g}$ of a substance by $1\,^\circ\text{C}$ or $1\,\text{K}$ ( $\text{J}/(\text{g}\cdot^\circ\text{C})$ ): $c = \frac{q}{m \cdot \Delta T}$
Thermal Energy Calculation: $q = m \cdot c \cdot \Delta T$ $\Delta T = T_{\text{final}} - T_{\text{initial}}$

Precision: Measures consistency among repeated measurements without requiring a known accepted value: $\text{Deviation} = |\text{measurement} - \text{mean}|$ $\%\text{ deviation} = \left(\frac{\text{avg dev}}{\text{mean}}\right) \times 100$
Accuracy: Measures correctness relative to a true or accepted reference standard: $\text{Error} = |\text{mean} - \text{true value}|$ $\%\text{ error} = \left(\frac{|\text{mean} - \text{true value}|}{\text{true value}}\right) \times 100$
Historical Forensic Context:
- Charles Norris and Alexander Gettler established standardized forensic testing methods in New York City beginning in 1918.
- Falsifying or ignoring scientific standards (such as Annie Dookhan's misconduct at the William A. Hinton State Laboratory Institute) leads to massive systemic failures, including 21,587 dismissed drug convictions.