Chapter 1: Matter and Measurements – Study Notes

Chapter 1: Matter and Measurements

Introduction to Matter and Measurements

This chapter introduces the foundational concepts of matter and the importance of precise measurement in chemistry. Understanding the classification of matter, properties and changes, and the correct use of measurement units is essential for all subsequent topics in general chemistry.

• Matter is anything that has mass and occupies space.

• Measurement in chemistry involves both a numerical value and a unit, reflecting the quantity and the scale used.

Classification of Matter

• Pure Substances: Materials with a fixed composition and distinct properties (e.g., elements and compounds).

• Mixtures: Physical combinations of two or more substances; can be homogeneous (uniform composition) or heterogeneous (non-uniform composition).

• Example: Table salt (NaCl) is a pure substance; saltwater is a mixture.

Physical and Chemical Properties

• Physical Properties: Characteristics observed without changing the substance's identity (e.g., color, melting point, density).

• Chemical Properties: Characteristics that describe a substance's ability to undergo chemical changes (e.g., flammability, reactivity).

• Example: The boiling point of water is a physical property; iron's tendency to rust is a chemical property.

Physical and Chemical Changes

• Physical Change: Alters the form or appearance but not the composition (e.g., melting, freezing, dissolving).

• Chemical Change: Results in the formation of new substances (e.g., combustion, oxidation).

• Example: Ice melting is a physical change; burning wood is a chemical change.

Elements and the Periodic Table

• Students should learn the names and symbols of at least 50 common elements from the periodic table.

• Example: H (Hydrogen), O (Oxygen), Na (Sodium), Cl (Chlorine).

Measurement and Scientific Notation

Components of a Measurement

• Every measurement consists of a numerical value and a unit (e.g., 25.0 mL).

Scientific Notation

Scientific notation is used to express very large or very small numbers concisely. The number is written as a value between 1 and 9.999... multiplied by a power of ten.

• General Form: $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer.

• Example: 4,878,720 inches = $4.87872 \times 10^6$ inches.

• Example: 0.000000000000000000000327 g = $3.27 \times 10^{-22}$ g.

Metric Prefixes

Metric prefixes indicate powers of ten for SI units. Common prefixes are summarized below:

Prefix	Symbol	Multiplier	Example
mega	M	$10^6$	1 megameter (Mm) = $10^6$ m
kilo	k	$10^3$	1 kilogram (kg) = $10^3$ g
centi	c	$10^{-2}$	1 centimeter (cm) = $10^{-2}$ m
milli	m	$10^{-3}$	1 milligram (mg) = $10^{-3}$ g
micro	\mu	$10^{-6}$	1 microliter (\mu L) = $10^{-6}$ L
nano	n	$10^{-9}$	1 nanometer (nm) = $10^{-9}$ m

Significant Figures and Measurement Precision

Significant Figures (Digits)

• Significant figures include all certain digits plus one estimated (uncertain) digit.

• Zeros used only to position the decimal point are not significant.

• Example: 3.45 m has 3 significant figures; 0.1400 kg has 4 significant figures.

Certain and Uncertain Digits

• All measurements have a string of certain digits and one uncertain digit (the last digit).

• The more digits to the right, the more precise the measurement.

• Example: A ruler that measures to the nearest 0.01 cm is more precise than one that measures to the nearest 0.1 cm.

Reporting Measurements

• Report all digits known with certainty plus one estimated digit.

• On digital instruments, the last digit is considered uncertain.

Volume Measurements: Contained vs. Delivered

• Some glassware measures the volume contained (e.g., graduated cylinder), others the volume delivered (e.g., burette, syringe).

• Always note which type of measurement is being made.

Mathematical Operations with Significant Figures

Addition and Subtraction

• The result should have the same number of decimal places as the measurement with the least decimal places.

• Example: $4.87\ \text{mL} + 46.0\ \text{mL} = 50.9\ \text{mL}$ (rounded to one decimal place).

Multiplication and Division

• The result should have the same number of significant figures as the measurement with the fewest significant figures.

• Example: $3.4 \times 0.023\ \text{g} = 0.08\ \text{g}$ (rounded to two significant figures).

Exact vs. Inexact Numbers

• Exact Numbers: Values from counting or definitions (e.g., 12 eggs in a dozen) have infinite significant figures and do not limit the precision of calculations.

• Inexact Numbers: Measurements with uncertainty.

Rounding Rules

• If the digit to be dropped is less than 5, leave the preceding digit unchanged.

• If the digit to be dropped is 5 or greater, increase the preceding digit by one.

Unit Conversions and Dimensional Analysis

Dimensional Analysis

Dimensional analysis is a systematic approach to converting units using conversion factors. Units are treated algebraically and can be canceled or multiplied as needed.

• Conversion Factor: A ratio expressing how many of one unit equals another unit (e.g., $1\ \text{in} = 2.54\ \text{cm}$).

• General Formula: $\text{Given Unit} \times \frac{\text{Desired Unit}}{\text{Given Unit}} = \text{Desired Unit}$

• Only similar units can be added or subtracted; dissimilar units cannot be combined ("You cannot add apples and oranges").

Common Conversion Factors

Quantity	SI Unit	Metric Unit	Equivalent
Mass	kilogram (kg)	gram (g)	1 kg = 1000 g = 2.205 lb
Length	meter (m)	meter (m)	1 m = 3.280 ft
Volume	cubic meter (m3)	liter (L)	1 m3 = 1000 L = 264.2 gal
Temperature	kelvin (K)	celsius (°C)	see formulas below
Time	second (s)	second (s)	—

Steps for Unit Conversion

1. Assess the units and outline a strategy for conversion.

2. Determine the necessary conversion factors.

3. Set up the calculation so that units cancel appropriately.

4. Multiply and/or divide as indicated by the arrangement of units.

Density

Definition and Formula

• Density is the ratio of mass to volume, typically expressed in g/mL or g/cm3 for solids and liquids, and g/L for gases.

• Formula: $\text{Density} = \frac{\text{mass (g)}}{\text{volume (mL or cm}^3)}$

• Density is a physical property and can be used to identify substances.

• Density varies with temperature.

Example Problem

• A sample of table sugar with a mass of 2.500 g occupies a volume of 1.575 cm3. Density = $\frac{2.500\ \text{g}}{1.575\ \text{cm}^3} = 1.587\ \text{g/cm}^3$

Temperature and Heat

Temperature Scales

• Fahrenheit (°F): Relative scale; 0 °F is the freezing point of a salt-water mixture, 100 °F is near human body temperature.

• Celsius (°C): 0 °C is the freezing point of water, 100 °C is the boiling point.

• Kelvin (K): Absolute scale; 0 K is absolute zero, the lowest possible temperature.

Temperature Conversion Formulas

• Celsius to Fahrenheit: $^{\circ}\!F = (1.8 \times ^{\circ}\!C) + 32$

• Fahrenheit to Celsius: $^{\circ}\!C = \frac{^{\circ}\!F - 32}{1.8}$

• Celsius to Kelvin: $K = ^{\circ}\!C + 273$

• Kelvin to Celsius: $^{\circ}\!C = K - 273$

Heat and Specific Heat

• Heat is a form of energy, measured in joules (J) or calories (cal).

• 1 cal = 4.184 J

• Specific Heat is the amount of heat required to raise the temperature of 1 gram of a substance by 1 °C.

• Formula: $\text{Specific Heat} = \frac{\text{Heat (cal or J)}}{\text{mass (g)} \times \Delta T (^{\circ}\!C)}$

• Each substance has a unique specific heat value.

Example Problem

• How many calories are needed to raise 20.0 g of gold from 25 °C to 85 °C? (Specific heat of gold = 0.031 cal/g°C)

• Solution: $q = m \times c \times \Delta T = 20.0\ \text{g} \times 0.031\ \text{cal/g}^{\circ}\!C \times (85 - 25)^{\circ}\!C = 37.2\ \text{cal}$

Summary Table: Common SI and Metric Units

Quantity	SI Unit (Symbol)	Metric Unit (Symbol)	Equivalents
Mass	kilogram (kg)	gram (g)	1 kg = 1000 g = 2.205 lb
Length	meter (m)	meter (m)	1 m = 3.280 ft
Volume	cubic meter (m3)	liter (L)	1 m3 = 1000 L = 264.2 gal
Temperature	kelvin (K)	celsius (°C)	see formulas above
Time	second (s)	second (s)	—

Additional info: These notes expand on the provided slides and text, filling in definitions, formulas, and examples for clarity and completeness. Students are encouraged to practice with textbook and Mastering Chemistry problems for mastery.