Matter, Measurement, and Problem Solving: Foundations of General Chemistry

Chapter 1: Matter, Measurement, & Problem Solving

What is Chemistry?

Chemistry is the scientific study of matter and the changes it undergoes. It is often referred to as the Central Science because it connects and explains many natural phenomena and other scientific disciplines.

• Matter: Anything that has mass and occupies space.

• Chemical Change: Transformation of substances into new substances with different properties.

• Physical Change: Alteration of the state or appearance of matter without changing its composition.

Scientific Problem Solving

Scientific problem solving is a logical process used to investigate and understand chemical phenomena.

1. State the Problem and Make Observations: Observations can be quantitative (numerical) or qualitative (descriptive).

2. Formulate a Hypothesis: Propose a possible explanation or solution.

3. Perform Experiments: Test the hypothesis and collect data.

4. Form a Conclusion: Use claim, evidence, and reasoning to draw conclusions.

• Theory: A well-tested explanation for observations; subject to refinement.

• Law: A statement describing consistent natural behavior (e.g., Law of Conservation of Mass).

States of Matter

Matter exists in distinct states, each with unique properties and particle behaviors.

• Solid: Definite shape and volume; particles vibrate in fixed positions.

• Liquid: Definite volume, no definite shape; particles move freely.

• Gas: No definite shape or volume; particles spread to fill container.

• Plasma: Hot, ionized gas with equal numbers of positive ions and electrons; distinct from neutral gases.

Physical and Chemical Properties and Changes

All matter exhibits physical and chemical properties, which determine how it can be classified and how it changes.

• Physical Properties: Characteristics observed without changing composition (e.g., color, density, melting point).

• Chemical Properties: Characteristics observed during chemical reactions (e.g., reactivity, oxidation).

Physical Changes

• Change in state or appearance without altering composition.

• Common changes: melting, boiling, condensation, sublimation, deposition, freezing.

Chemical Changes

• Atoms rearrange to form new substances with different compositions.

• Often accompanied by color change, heat change, or precipitate formation.

Elements, Mixtures, and Compounds

Substances in chemistry are classified as elements, compounds, or mixtures.

• Element: Pure substance that cannot be broken down by chemical means; listed on the periodic table.

• Compound: Substance formed by bonding elements in fixed ratios (e.g., $\mathrm{H_2O}$).

• Mixture: Combination of pure substances with variable composition; can be separated physically.

Types of Mixtures

• Homogeneous (Solution): Uniform composition throughout (e.g., salt water).

• Heterogeneous: Distinct regions with varying composition (e.g., chocolate chip cookie).

All pure substances are either elements or compounds.

Energy

Energy is the capacity to do work or cause change. It is fundamental to chemical processes.

• Potential Energy: Stored energy due to position (elastic, gravitational, chemical, electric, nuclear).

• Kinetic Energy: Energy of motion (thermal, electrical, radiant, sound, mechanical).

• Conservation of Energy: Energy cannot be created or destroyed, only transformed.

• Stability: Lower energy sites are more stable and favored.

Measurement

Measurement is essential for quantifying properties in chemistry. Units and prefixes help express values accurately.

Scientific Notation

• Used to express very large or small numbers as a number between 1 and 10 multiplied by a power of 10.

• Example: $42000 = 4.2 \times 10^4$

• Example: $0.00012 = 1.2 \times 10^{-4}$

SI Units and Prefixes

The International System of Units (SI) uses seven base units and various prefixes to scale measurements.

Quantity	Unit Name	Symbol
Mass	kilogram	kg
Length	meter	m
Time	second	s
Temperature	kelvin	K
Electric Current	ampere	A
Amount of Substance	mole	mol
Luminous Intensity	candela	cd

Prefix	Symbol	Factor
tera	T	$10^{12}$
giga	G	$10^{9}$
mega	M	$10^{6}$
kilo	k	$10^{3}$
hecto	h	$10^{2}$
deca	da	$10^{1}$
deci	d	$10^{-1}$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	u	$10^{-6}$
nano	n	$10^{-9}$
pico	p	$10^{-12}$

Unit Conversion

Units can be converted using conversion factors derived from equivalence statements.

• Factor-labeling method (dimensional analysis): $(\text{Unit a}) \times (\text{conversion factor}) = \text{Unit b}$

• Example: $9.00 \text{ inch} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} = 22.86 \text{ cm}$

Temperature Scales and Conversions

Three temperature scales are commonly used: Celsius, Fahrenheit, and Kelvin.

• Celsius to Kelvin: $T_{\text{K}} = T_{\text{C}} + 273.15$

• Kelvin to Celsius: $T_{\text{C}} = T_{\text{K}} - 273.15$

• Celsius to Fahrenheit: $T_{\text{F}} = 1.8 \times T_{\text{C}} + 32$

• Fahrenheit to Celsius: $T_{\text{C}} = \frac{T_{\text{F}} - 32}{1.8}$

Derived Units: Volume and Density

Derived units are formed from base units. Volume and density are important in chemistry.

• Volume: $1 \text{ L} = 1000 \text{ mL} = 1000 \text{ cm}^3 = 1 \text{ dm}^3$

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

• Mass: $\text{Mass} = \text{Density} \times \text{Volume}$

• Volume: $\text{Volume} = \frac{\text{mass}}{\text{density}}$

Uncertainty, Significant Figures, and Rounding Off

Measurements in chemistry are subject to uncertainty, which is reflected in significant figures.

• Significant Figures: All certain digits plus one estimated digit in a measurement.

• Exact Numbers: Have unlimited significant figures (e.g., counted objects, defined quantities).

• Scientific Notation: The exponent part is not counted as significant figures.

Rules for Calculations

• Multiplication/Division: Result has same number of significant figures as the input with the fewest significant figures.

• Addition/Subtraction: Result has same number of decimal places as the input with the fewest decimal places.

Rounding Off

• If the digit after the last significant figure is less than 5, leave the digit unchanged.

• If greater than 5, increase the last significant digit by one.

• If exactly 5, follow the "perfect 5" rule: if the preceding digit is even, leave it; if odd, increase it.

Example: Rounding 2.345 to three significant figures: 2.35 (since the digit after 4 is 5 and 4 is even).

Additional info: These foundational concepts are essential for understanding subsequent topics in General Chemistry, including atomic structure, chemical reactions, and quantitative analysis.