Chapter 1 Lecture

Matter Defined: Matter is defined as anything that has mass and occupies space. It encompasses everything around us.
Subcategories of Matter: Matter is primarily divided into two categories: mixtures and substances.
Mixtures: A mixture is formed when two or more substances are combined without a fixed proportion or specific amount requirement.
- Homogeneous Mixtures: These are mixtures where the final product is completely uniform throughout.
  - Example: Sodium chloride ( $NaCl$ ) dissolved in water creates a uniform salt-water mixture.
- Heterogeneous Mixtures: These are mixtures that are non-uniform, meaning the individual components that make up the mix can be clearly seen.
  - Example 1: A salad containing lettuce, cucumber, and tomato.
  - Example 2: "Tremex" (Trail mix) containing a mixture of peanuts, raisins, and various nuts like almonds.

Elements:
- Elements are unique substances represented by specific symbols.
- No two elements share the same symbol.
- Symbols can consist of one letter (e.g., Carbon is represented by the symbol $C$ ) or two letters (e.g., Sodium is represented by the symbol $Na$ ).
- Case sensitivity is vital; the second letter of a two-letter symbol must be lowercase (e.g., $Na$ vs. $NA$ ).
Compounds:
- A compound is formed when elements combine in a fixed ratio or fixed proportion.
- The Law of Definite Proportions: If the ratio of elements in a compound is changed, the identity of the compound changes entirely.
  - Example 1 (Water vs. Hydrogen Peroxide): In water ( $H_2O$ ), the ratio of hydrogen to oxygen is $2:1$ . If the ratio changes to $2:2$ , it becomes hydrogen peroxide ( $H_2O_2$ ), a completely different substance.
  - Example 2 (Carbon Oxides): Carbon monoxide ( $CO$ ) and carbon dioxide ( $CO_2$ ) are different compounds because of their different elemental ratios.

Extensive Properties:
- Definition: These properties depend on the amount of matter present in a sample. The variable changes as the quantity changes.
- Example 1 (Mass): If one beaker weighs $1\,g$ , two beakers of the same type will weigh $2\,g$ , and three will weigh $3\,g$ .
- Example 2 (Volume): This is also an extensive property as it increases with the amount of material.
Intensive Properties:
- Definition: These properties do not depend on the amount of matter present. They are fixed variables regardless of whether you have a pinch or a large quantity.
- Example 1 (Density): The density of a metal is constant regardless of the size of the sample.
- Example 2 (Temperature): Water freezes at $0^\circ C$ and boils at $100^\circ C$ , regardless of whether you have $1\,liter$ or $10\,liters$ .
- Example 3 (Color): A sheet of white paper remains white even if you have $100$ sheets of the same paper.

SI Units (International System of Units): The preferred units used by scientists globally to ensure uniform communication and avoid errors.
- Mass: The SI unit represents the preferred unit as kilograms ( $kg$ ).
- Temperature: The SI unit is Kelvin ( $K$ ).
Temperature Conversion Formulas:
1. Converting Celsius to Kelvin: $K = ^\circ C + 273.15$ (Note: On exams, the constant may be rounded to $273$ depending on the provided formula.)
2. Converting Celsius to Fahrenheit: $^\circ F = (1.8 \times ^\circ C) + 32$
3. Converting Fahrenheit to Celsius: $^\circ C = \frac{^\circ F - 32}{1.8}$

Standard Form: $N \times 10^n$
- $N$ is the base, which must range from $1$ to $10$ .
- $n$ is the exponent, which can be positive or negative.
Conversion Rules:
- Decimal to the Left: Results in a positive exponent.
  - Example: $247.52 \rightarrow 2.4752 \times 10^2$
- Decimal to the Right: Results in a negative exponent.
  - Example: $0.0052 \rightarrow 5.2 \times 10^{-3}$
Mathematical Operations with Scientific Notation:
- Multiplication: Add the exponents.
  - Example: $(10^{-5}) \times (10^3) = 10^{(-5 + 3)} = 10^{-2}$
- Division: Subtract the exponents.
  - Example: $(10^{-5}) / (10^3) = 10^{(-5 - 3)} = 10^{-8}$
- Addition and Subtraction: Exponents must be unified (made uniform) before adding or subtracting. The base must remain within the range of $1$ to $10$ .
  - Example: $(4.31 \times 10^4) + (3.9 \times 10^3)$ . Convert the second term: $0.39 \times 10^4$ . Then add: $(4.31 + 0.39) \times 10^4 = 4.70 \times 10^4$ .

General Rule: All non-zero digits are significant.
Zero Rules:
- Leading Zeros: Zeros appearing before non-zero digits in a number less than one are NOT significant.
  - Example: $0.09$ has only one significant figure.
- Trailing Zeros with Decimals: Zeros at the end of a number after a decimal point ARE significant.
  - Example: $3.0$ has two significant figures.
- Captive Zeros: Zeros between non-zero digits ARE significant.
  - Example: In $0.003005$ , there are four significant figures ( $3$ , $0$ , $0$ , and $5$ ).
- Ambiguous Case: Large numbers with trailing zeros but no decimal (e.g., $1000$ ) are considered ambiguous. They should be written in scientific notation to clarify accuracy.
  - $1 \times 10^3$ (1 Sig Fig)
  - $1.0 \times 10^3$ (2 Sig Figs)
  - $1.00 \times 10^3$ (3 Sig Figs)
  - $1.000 \times 10^3$ (4 Sig Figs)

Addition and Subtraction:
- The result is limited by the number with the least number of decimal places.
- Step 1: Perform the calculation.
- Step 2: Round the result to match the least number of decimal places observed in the starting values.
- Example: $90.0409$ (4 decimal places) + $0.40$ (2 decimal places) = $90.4409$ . Final answer is $90.44$ ( $4$ significant figures).
Multiplication and Division:
- The result is limited by the number with the least number of total significant figures.
- Example: In a calculation like $2.666 \times 3.2$ , the answer will be restricted to two significant figures because $3.2$ only has two.