Chapter 1: Matter, Measurement, and Problem Solving – Study Notes

Chapter 1: Matter, Measurement, and Problem Solving

Structure Determines Properties

The physical and chemical properties of matter are determined by the structure and arrangement of its atoms and molecules. The state of matter—solid, liquid, or gas—affects how particles are arranged and interact, leading to different observable properties.

• Solids: Particles are closely packed in a fixed arrangement, resulting in definite shape and volume.

• Liquids: Particles are close but can move past each other, giving a definite volume but no fixed shape.

• Gases: Particles are far apart and move freely, resulting in neither definite shape nor volume.

The Classification of Matter by Components

Matter can be classified based on its composition into elements, compounds, and mixtures.

• Element: A pure substance consisting of only one type of atom (e.g., helium).

• Compound: A pure substance composed of two or more elements chemically combined (e.g., water).

• Mixture: A physical combination of two or more substances. Mixtures can be homogeneous (uniform composition, e.g., salt water) or heterogeneous (non-uniform composition, e.g., sand and water).

Physical and Chemical Changes

Changes in matter are classified as physical or chemical based on whether the composition of the substance changes.

• Physical Change: Alters the state or appearance without changing the composition (e.g., melting, boiling, dissolving).

• Chemical Change: Alters the composition, resulting in new substances (e.g., burning, rusting).

Physical and Chemical Properties

Properties of substances are categorized as physical or chemical.

• Physical Property: Can be observed without changing the substance’s composition (e.g., odor, color, melting point, boiling point, density).

• Chemical Property: Can only be observed by changing the substance’s composition via a chemical reaction (e.g., flammability, acidity, toxicity, corrosiveness).

Numbers and Chemistry

Chemistry is a quantitative science, relying heavily on numerical data and measurements. Key concepts include:

• Units of measurement

• Measured and calculated quantities

• Uncertainty in measurement

• Significant figures

• Dimensional analysis

The Units of Measurement

Standard units are essential for scientific communication. The two main systems are:

• Metric system: Used globally.

• English system: Used primarily in the United States.

• SI Units (Système International d’Unités): The standard system in science, based on the metric system.

The Standard Units

The SI base units for fundamental quantities are:

Quantity	Unit	Symbol
Length	Meter	m
Mass	Kilogram	kg
Time	Second	s
Temperature	Kelvin	K
Amount of substance	Mole	mol
Electric current	Ampere	A
Luminous intensity	Candela	cd

The Meter: A Measure of Length

The meter (m) is the SI unit of length, defined as the distance light travels in a vacuum in 1/299,792,458 seconds. It is slightly longer than a yard (1 m = 39.37 inches).

The Kilogram: A Measure of Mass

The kilogram (kg) is the SI unit of mass. One kilogram equals 2.205 pounds. The gram (g) is a common subunit (1 g = 1/1000 kg). Mass measures the amount of matter, while weight measures the gravitational pull on that matter.

The Second: A Measure of Time

The second (s) is the SI unit of time, defined by the duration of 9,192,631,770 periods of radiation from a cesium-133 atom.

The Kelvin: A Measure of Temperature

The kelvin (K) is the SI unit of temperature. Temperature measures the average kinetic energy of particles. The Kelvin scale starts at absolute zero (0 K), the lowest possible temperature (−273.15°C or −459°F), where molecular motion stops.

• Temperature Conversions:

• $^\circ C = \frac{(^\circ F - 32)}{1.8}$

• $K = ^\circ C + 273.15$

Note: The Kelvin scale has no negative values.

Prefix Multipliers

SI units use prefixes to indicate powers of ten. For example, kilo- (k) means 1,000, and milli- (m) means 0.001.

Prefix	Symbol	Multiplier
kilo	k	1,000 (103)
centi	c	0.01 (10-2)
milli	m	0.001 (10-3)
micro	μ	0.000001 (10-6)
nano	n	0.000000001 (10-9)

Derived Units: Volume and Density

Derived units are combinations of base units. Volume is measured in cubic meters ($m^3$), liters (L), or milliliters (mL). Density is mass per unit volume, typically in $g/cm^3$ or $kg/m^3$.

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

Density determines whether a substance will sink or float in another substance.

Substance	Density (g/cm3)
Charcoal (from oak)	0.57
Ethanol	0.789
Ice (at 0°C)	0.917
Water (at 4°C)	1.00
Aluminum	2.70
Iron	7.86
Gold	19.3

Intensive and Extensive Properties

• Intensive Property: Independent of the amount of substance (e.g., density).

• Extensive Property: Dependent on the amount of substance (e.g., mass).

The Reliability of a Measurement: Significant Figures

Significant figures reflect the precision of a measurement. All digits are certain except the last, which is estimated. The number of significant figures depends on the measuring instrument.

Counting Significant Figures

• All nonzero digits are significant.

• Interior zeroes (between nonzero digits) are significant.

• Leading zeroes (before the first nonzero digit) are not significant.

• Trailing zeroes (at the end of a number) are significant only if there is a decimal point.

Exact Numbers

Exact numbers have an unlimited number of significant figures. These include:

• Counting discrete objects (e.g., 3 apples)

• Defined quantities (e.g., 1 inch = 2.54 cm)

• Integral numbers in equations

Significant Figures in Calculations

• Multiplication/Division: The result has the same number of significant figures as the factor with the fewest significant figures.

• Addition/Subtraction: The result has the same number of decimal places as the quantity with the fewest decimal places.

Rules for Rounding

• Round down if the last digit dropped is four or less.

• Round up if the last digit dropped is five or more.

• In multistep calculations, round only the final answer.

Scientific Notation

Scientific notation expresses numbers as a product of a coefficient and a power of ten. For example:

• 0.000135 = $1.35 \times 10^{-4}$

Solving Chemical Problems: Dimensional Analysis

Dimensional analysis is a method for solving problems using conversion factors and unit equations. Always include units in calculations, and treat them algebraically.

• Unit Equation: A statement of two equivalent quantities (e.g., 2.54 cm = 1 in).

• Conversion Factor: A fraction derived from a unit equation, used to convert from one unit to another.

General form:

• Information given × conversion factor(s) = information sought

• $\text{Given unit} \times \frac{\text{desired unit}}{\text{given unit}} = \text{desired unit}$

Examples of Unit Conversions

• How many mL are in 1.63 L?

• $1.63\,L \times \frac{1000\,mL}{1\,L} = 1630\,mL$

• Convert 23.5 m to km, cm, nm:

• $23.5\,m \times \frac{1\,km}{1000\,m} = 0.0235\,km$

• $23.5\,m \times \frac{100\,cm}{1\,m} = 2350\,cm$

• $23.5\,m \times 1 \times 10^9\,nm/1\,m = 2.35 \times 10^{10}\,nm$

General Problem Solving Strategy

• Identify the starting point (given information).

• Identify the end point (what you must find).

• Devise a conceptual plan to connect the two.

• Sort, strategize, solve, and check your answer for reasonableness.