Chemistry and Measurements: Units, Significant Figures, and Problem Solving

Chapter 2: Chemistry and Measurements

Units of Measurement

Chemists use the metric system and the International System of Units (SI) as standards for measurement. Understanding these units is essential for accurate scientific communication and calculations.

• Length: meter (m)

• Mass: kilogram (kg) in SI, gram (g) in metric

• Volume: liter (L) in metric, cubic meter (m3) in SI

• Temperature: degree Celsius (°C) in metric, Kelvin (K) in SI

• Time: second (s)

Significant Figures

Significant figures (SFs) are all the digits in a measurement known with certainty plus one estimated digit. Correct use of significant figures ensures the precision of calculations and reporting in chemistry.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

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

• Trailing zeros to the right of a decimal point are significant.

• Trailing zeros in a whole number with no decimal shown are not significant.

Rounding Significant Figures

When rounding numbers, retain the correct number of significant figures based on the calculation:

• For multiplication/division: The result should have the same number of SFs as the measurement with the fewest SFs.

• For addition/subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

Exact Numbers

Exact numbers are values that are counted or defined, not measured. They have an infinite number of significant figures and do not affect the precision of calculated results.

• Examples: 8 doughnuts, 2 baseballs, 5 capsules

• Defined equalities: 1 L = 1000 mL, 1 ft = 12 in., 1 kg = 1000 g

Metric Prefixes

Prefixes are used to indicate multiples or fractions of units in the metric system. Memorizing common prefixes is essential for unit conversions.

• Prefixes that increase the size of the unit: kilo (k), mega (M), giga (G), tera (T)

• Prefixes that decrease the size of the unit: deci (d), centi (c), milli (m), micro (μ), nano (n), pico (p)

Conversion Factors and Problem Solving

Conversion factors are ratios derived from equalities that relate different units. They are used to convert one unit to another in calculations.

• Example: 60 min = 1 h gives the conversion factors $\frac{60\ \text{min}}{1\ \text{h}}$ and $\frac{1\ \text{h}}{60\ \text{min}}$

• Example: 1 m = 100 cm gives the conversion factors $\frac{100\ \text{cm}}{1\ \text{m}}$ and $\frac{1\ \text{m}}{100\ \text{cm}}$

Common equalities are summarized in tables for reference during calculations.

Steps for Problem Solving Using Conversion Factors

1. State the given and needed quantities.

2. Write a plan to convert the given unit to the needed unit.

3. State the equalities and conversion factors needed to cancel units.

4. Set up the problem to cancel units and calculate the answer.

Example: Mass Conversion

To convert 178 lb to kilograms:

• Equality: 1 kg = 2.20 lb

• Conversion factor: $\frac{1\ \text{kg}}{2.20\ \text{lb}}$

• Calculation: $178\ \text{lb} \times \frac{1\ \text{kg}}{2.20\ \text{lb}} = 80.9\ \text{kg}$ (rounded to 3 SFs)

Density

Density is the ratio of the mass of a substance to its volume. It is a physical property used to identify substances and predict whether an object will float or sink in a fluid.

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

• Units: g/mL (solids and liquids), g/L (gases)

Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of water (1.00 g/mL at 4°C). It is a unitless quantity and is used in clinical and industrial applications.

• Formula: $\text{Specific gravity} = \frac{\text{density of sample}}{\text{density of water}}$

Chapter 3: Matter and Energy (Selected Tables)

States of Matter

Matter exists in three primary states: solid, liquid, and gas. Each state has distinct characteristics regarding shape, volume, particle arrangement, and movement.

Characteristic	Solid	Liquid	Gas
Shape	Definite	Takes shape of container	Takes shape of container
Volume	Definite	Definite	Fills container
Arrangement of Particles	Fixed, very close	Random, close	Random, far apart
Interaction Between Particles	Very strong	Strong	Essentially none
Movement of Particles	Very slow	Moderate	Very fast
Examples	Ice, salt, iron	Water, oil, vinegar	Water vapor, helium, air

Physical and Chemical Changes

Physical changes do not alter the chemical composition of a substance, while chemical changes result in the formation of new substances with different properties.

Examples of Physical Changes:

Water boils to form water vapor.

Sugar dissolves in water to form a solution.

Copper is drawn into thin wires.

Paper is cut into confetti.

Pepper is ground into flakes.

Examples of Chemical Changes:

Silver reacts in air to give a black coating.

Wood burns, producing heat, ashes, CO2, and water vapor.

Sugar forms caramel when heated.

Iron combines with oxygen to form rust.

Chapter 4: Atoms and Elements (Selected Tables)

Elements and Symbols

Each element is represented by a unique chemical symbol, usually one or two letters. The periodic table organizes elements by increasing atomic number and similar properties.

Element	Symbol	Source of Name
Uranium	U	The planet Uranus
Titanium	Ti	Titans (mythology)
Chlorine	Cl	Chloros: "greenish yellow" (Greek)
Iodine	I	Ioiedes: "violet" (Greek)
Magnesium	Mg	Magnesia, a mineral
Californium	Cf	California
Curium	Cm	Marie and Pierre Curie
Copernicium	Cn	Nicolaus Copernicus

Names and Symbols of Common Elements

Name	Symbol	Name	Symbol
Aluminum	Al	Gold	Au
Argon	Ar	Hydrogen	H
Calcium	Ca	Iron	Fe
Carbon	C	Lead	Pb
Chlorine	Cl	Magnesium	Mg
Copper	Cu	Nitrogen	N
Fluorine	F	Oxygen	O
Phosphorus	P	Potassium	K
Sodium	Na	Sulfur	S
Zinc	Zn	Silver	Ag

Periodic Table and Classification

The periodic table groups elements by similar properties and electronic structure. Major classifications include metals, nonmetals, and metalloids.

Metals, Metalloids, and Nonmetals

Property	Metal (Silver)	Metalloid (Antimony)	Nonmetal (Sulfur)
Appearance	Shiny	Blue-gray, shiny	Dull, yellow
Ductility	Extremely ductile	Brittle	Brittle
Malleability	Can be hammered into sheets	Shatters when hammered	Shatters when hammered
Conductivity	Good conductor of heat and electricity	Poor conductor	Poor conductor, good insulator
Uses	Coins, jewelry, tableware	Harden lead, color glass, plastics	Gunpowder, rubber, fungicides
Density (g/mL)	10.5	6.7	2.1
Melting Point (°C)	962	630	113

Subatomic Particles

Particle	Symbol	Charge	Mass (amu)	Location
Proton	p or p+	1+	1.007	Nucleus
Neutron	n or n0	0	1.008	Nucleus
Electron	e−	1−	0.000 55	Outside nucleus

Composition of Atoms

Element	Symbol	Atomic Number	Mass Number	Number of Protons	Number of Neutrons	Number of Electrons
Hydrogen	H	1	1	1	0	1
Nitrogen	N	7	14	7	7	7
Oxygen	O	8	16	8	8	8
Chlorine	Cl	17	37	17	20	17
Iron	Fe	26	58	26	32	26
Gold	Au	79	197	79	118	79

Additional info: The above tables and images provide essential reference data for understanding the structure of matter, measurement, and the periodic table, which are foundational for further study in chemistry.