Basic Chemistry

Chapter 1: The Chemical World

1. Matter, atoms, and molecules

Main idea: A substance’s properties depend on its particles, their arrangement, and their interactions.

Example: Water’s properties depend on its hydrogen and oxygen atoms and how they are bonded.

Remember: Chemicals are everywhere—including water and air. The word chemical does not automatically mean dangerous.

2. The scientific method

The scientific method uses observations, testable explanations, and experiments to build knowledge. It is flexible—not one rigid sequence.

Important: Falsifiable means testable against evidence, not “already false.”

3. Scientific laws versus theories

Both are tested against evidence. A theory does not become a law.

4. Conservation of mass and combustion

Law of conservation of mass: In an ordinary chemical reaction, total mass stays the same when all material is accounted for.

Combustion means burning.

When wood burns:

• It reacts with oxygen from the air.

• Atoms rearrange into new substances.

• Products include gases and material remaining as ash.

Complete comparison:
Mass of starting materials = mass of all products.

Your key correction: New substances can form without creating new atoms. Weighing only the ash leaves out gases that escaped.

5. Phlogiston: evidence changes explanations

Main lesson: When evidence contradicts an explanation, scientists revise or replace it.

Calx: The historical name used in this passage for a metal oxide.

6. Data and patterns

The water measurements show:

• Hydrogen mass + oxygen mass = water sample mass.

• Oxygen-to-hydrogen mass ratio is approximately 8:1.

Watch the difference: Water has two hydrogen atoms per oxygen atom, but approximately eight times as much oxygen mass as hydrogen mass.

Small differences in measurements can reflect uncertainty—not necessarily carelessness.

7. Reading graphs

Check these before interpreting a graph:

1. Axis labels: What is being measured?

2. Units: Years, grams, temperature, or something else?

3. Scale: What values are shown? Does the axis start at zero?

4. Trend and slope: Is the amount changing? How quickly?

Changing the axis scale changes the appearance—not the measurements.

8. Learning chemistry

• Curiosity: Ask why.

• Calculation: Use numbers and units to compare precisely.

• Commitment: Practice regularly, correct mistakes, and seek help.

Chapter 2

2.1 — Units give numbers meaning

A measurement includes a number and a unit.

10 meters and 10 feet are different lengths, despite having the same number.

The Mars Climate Orbiter example shows the consequence of mixing unit systems: pound-seconds and newton-seconds are not interchangeable.

Main takeaway: Check units before comparing or calculating.

2.2 — Scientific notation

Scientific notation expresses numbers as:

\[ a\times10^n \]

For positive numbers, the coefficient \(a\) is at least 1 but less than 10. The exponent \(n\) tells you the power of ten.

To convert into scientific notation:

1. Put the decimal after the first nonzero digit.

2. Count the places it moved.

3. Use that count for the exponent.

To convert back to ordinary notation:

• Positive exponent → move decimal right.

• Negative exponent → move decimal left.

Watch out:

• Count places moved, not just zeros.

• A negative exponent does not make the value negative.

• Both forms represent the same value.

2.3 — Measurements communicate precision

Significant figures are the meaningful digits reported in a measurement: the certain digits plus the final uncertain digit.

Examples:

• Marks every 1 mm → estimate to 0.1 mm.

• Marks every 0.1 g → estimate to 0.01 g.

In 24.6 mm, the 6 is estimated. Writing 24.60 mm would claim more precision than the illustrated ruler supports.

1.3 g and 1.30 g have the same numerical value, but different reported precision.

Counting significant figures

Instructor-specific rule: The book calls numbers such as 500 ambiguous. Your instructor expects one significant figure for that measured number as written.

Significant figures ≠ decimal places:
0.00620 has 3 significant figures, but 5 decimal places.

Exact numbers: check these first

Exact numbers have unlimited significant figures.

Your main practice target: Decide whether the number is exact or measured before counting digits.

• Exactly 20 pots → unlimited significant figures.

• Measured 20 g → one significant figure under your instructor’s convention.

2.4

Why do we round?
A calculator may display more digits than our measurements justify. Our reported answer should reflect the precision of those measurements.

Decimal places versus significant figures

• Decimal places: Count every digit after the decimal point.

• Significant figures: Count meaningful measurement digits using the rules from Section 2.3.

How to round

1. Identify the last digit you will keep.

2. Check the first digit you will drop.

3. If it is 0–4, leave the kept digit unchanged.

4. If it is 5–9, increase the kept digit by one.

Ignore digits farther to the right when deciding.

Example: 2.449 → two significant figures → 2.4.
Keep 2.4; the next digit is 4, so it stays unchanged.

Multiplication and division

\[ 4.2\times1.36=5.712\rightarrow\boxed{5.7} \]

4.2 has two significant figures, so report two significant figures.

Exact counts and defined conversion factors have unlimited significant figures, so they do not limit an answer’s precision.

Addition and subtraction

\[ 12.45+3.2=15.65\rightarrow\boxed{15.7} \]

3.2 has one decimal place, so report one decimal place.

Choose the quantity with the fewest decimal places, not the smallest numerical value.

The fuller rule is least precise place value. If a measurement is only precise to the tens place, the result of addition or subtraction must also end at the tens place.

Rounding whole numbers

\[ 687\rightarrow\boxed{690} \]

To keep two significant figures, keep 6 and 8, then use 7 to round the 8 upward. The final zero holds the ones place.

Write \(6.9\times10^2\) to make the two significant figures clear. Under your instructor’s convention, 690 without a decimal point has two significant figures.

Mixed operations

For:

\[ (6.25-2.1)\times3.42 \]

• Subtract: 4.15.

• Subtraction allows one decimal place. If reported now, it would be 4.2, or two significant figures.

• Keep 4.15 in the calculator.

• Multiply: 14.193.

• Report two significant figures: 14.

Keep extra calculator digits, but track how much precision each step allows.

Reading the question

Before calculating, locate:

• The task: Count, round, or calculate?

• The target: Significant figures or decimal places? How many?

• The format: Units, scientific notation, or no commas?

“No commas” means enter 1234, rather than 1,234.

2.5 — Basic Units of Measurement

A measurement needs a number and a unit.
Example: 25 g tells you the amount and what is being measured.

Measurement systems

• U.S. customary/English: Inches, feet, miles, pounds, gallons.

• Metric: Uses units and prefixes connected by powers of ten.

• SI: The internationally standardized system based on metric units.

Important SI base units: meter (m), kilogram (kg), second (s).

Mass versus weight

• Mass: Amount of matter.

• Weight: Gravitational force on that matter.

• Moving an object to a place with different gravity changes its weight, while its mass remains the same.

Metric prefixes

Capitalization matters: Mm = megameter; mm = millimeter.

Common relationships

\[ 1\text{ km}=1000\text{ m} \]\[ 1\text{ m}=100\text{ cm}=1000\text{ mm} \]\[ 1\text{ kg}=1000\text{ g},\qquad1\text{ g}=1000\text{ mg} \]\[ 1\text{ L}=1000\text{ mL},\qquad1\text{ mL}=1\text{ cm}^3 \]

Derived units combine units:

• Area: \(\text{m}^2\)

• Volume: \(\text{m}^3\)

• Speed: \(\text{m/s}\)

2.6 — Problem Solving and Unit Conversion

Dimensional analysis, also called the factor-label method, uses conversion fractions to change units.

A conversion factor is a ratio of equivalent quantities.

Example:

\[ 1\text{ m}=100\text{ cm} \]

This gives two possible factors:

\[ \frac{100\text{ cm}}{1\text{ m}} \qquad\text{or}\qquad \frac{1\text{ m}}{100\text{ cm}} \]

Choose the direction that cancels the starting unit.

\[ 3.25\text{ m}\times\frac{100\text{ cm}}{1\text{ m}} =325\text{ cm} \]

Meters cancel because they appear on top and bottom.

Arithmetic rule: Multiply by the fraction’s top number; divide by its bottom number.

\[ 640.0\text{ cm}\times\frac{1\text{ m}}{100\text{ cm}} =6.400\text{ m} \]

The conversion is exact, so the original measurement’s four significant figures are preserved.

Check the direction

For the same quantity:

• Smaller units → larger numerical value.

• Larger units → smaller numerical value.

2.7 — Multistep Conversions

When one factor cannot reach the desired unit, connect several factors.

Plan the units before calculating.

Example route: mg → g → kg

\[ 425\text{ mg} \times\frac{1\text{ g}}{1000\text{ mg}} \times\frac{1\text{ kg}}{1000\text{ g}} =\boxed{0.000425\text{ kg}} \]

Your instructor recommends: When converting between metric prefixes, go through an unprefixed reference unit, such as grams or meters.

Example: cm → m → km

Remember:

• Each factor must represent a valid relationship.

• Matching units cancel across the multiplied chain.

• Keep extra calculator digits until the final answer.

• Exact conversion factors do not limit significant figures.

2.8 — Converting Numerator and Denominator Units

“Per” means divided by.

\[ 18.0\text{ km/h}=\frac{18.0\text{ km}}{1\text{ h}} \]

To convert both units:

\[ 18.0\frac{\text{km}}{\text{h}} \times\frac{1000\text{ m}}{1\text{ km}} \times\frac{1\text{ h}}{3600\text{ s}} =\boxed{5.00\text{ m/s}} \]

• Kilometers cancel with kilometers.

• Hours cancel with hours.

• Meters remain on top; seconds remain on the bottom.

An unwanted denominator unit needs a matching unit on top.

Rates also connect different quantities

Example: To find time from miles and miles/hour:

\[ \text{distance in mi}\times \frac{1\text{ h}}{\text{miles traveled in one hour}} \]

Miles cancel, leaving hours. Multiply hours by 60 min/1 h to obtain minutes.

2.9 — Units Raised to a Power

Raise the entire conversion factor to the unit’s power—including the numbers.

Since \(1\text{ m}=100\text{ cm}\):

\[ 1\text{ m}^2=(100\text{ cm})^2 =\boxed{10{,}000\text{ cm}^2} \]\[ 1\text{ m}^3=(100\text{ cm})^3 =\boxed{1{,}000{,}000\text{ cm}^3} \]

Example setup for cubic inches to cubic centimeters:

\[ \text{given in}^3 \times \left(\frac{2.54\text{ cm}}{1\text{ in}}\right)^3 \]

Why cube the factor? Volume includes three lengths: length × width × height. All three lengths must convert.

cc means cm³.

2.10 — Density

Density is mass per unit of volume.

\[ \boxed{d=\frac{m}{V}} \]

Interpretation: A density of 2.0 g/mL means each milliliter of that substance has a mass of 2.0 g.

For equal volumes, the denser material has more mass. A larger sample of a uniform substance has more mass and volume, but the same density under the same conditions.

Three forms of the equation

Calculating density

27.2 g / 22.5 mL = 1.21 g/mL

Grams and milliliters do not cancel; together they form the density unit.

Density as a conversion factor

For a substance with density 2.0 g/mL:

• Volume → mass: multiply by \(\frac{2.0\text{ g}}{1\text{ mL}}\).

• Mass → volume: multiply by \(\frac{1\text{ mL}}{2.0\text{ g}}\).

Always match units first. If density uses grams but the mass is in kilograms, convert kilograms to grams.

Water displacement

For a fully submerged object:

\[ V_{\text{object}}=V_{\text{final water}}-V_{\text{initial water}} \]

Example: Water rises from 20.0 mL to 23.5 mL → object volume is 3.5 mL = 3.5 cm³.

Rectangular blocks

\[ \boxed{V=L\times W\times H} \]

Use matching length units. Then use the volume to calculate density or mass.

Other density facts

• Nonmixing liquids settle with denser liquids below less dense liquids.

• Density can change with temperature.

• Density can help identify a substance, but a matching density alone does not prove identity.

• 1 mL = 1 cm³, but 1 mL does not always have a mass of 1 g. That depends on the substance.

2.11 — Numerical Problem-Solving Strategy

Use Sort → Strategize → Solve → Check.

A solution map is your route from the given information to the answer.

Examples:

Chapter 3

3.1–3.2: Matter, atoms, and molecules

Matter is anything that has mass and occupies space. Air counts as matter even though you usually cannot see it.

• Atom: a basic building block of matter.

• Molecule: two or more atoms bonded together in a specific arrangement.

• Molecules can contain the same element, such as O₂, or different elements, such as H₂O.

Chemistry connects what we observe—melting, burning, rusting—to what happens to atoms and molecules.

3.3: States of matter

Gases are easily compressed because there is considerable space between their particles. Compression reduces that space; it does not shrink the particles.

Crushing versus compressing:

• Crushing: breaking something into smaller pieces, such as crushing a sugar cube.

• Compressing: squeezing something into a smaller volume, such as air in a sealed syringe.

Types of solids:

A powder can still be crystalline. Crushing salt does not automatically make it amorphous.

3.4: Classifying matter by composition

First ask: Is there one pure substance or a mixture of substances?

Elements and compounds are both pure substances.

Important distinctions:

• O₂ is an element: both atoms are oxygen.

• H₂O is a compound: hydrogen and oxygen are bonded in a fixed ratio.

• Salt water is a mixture: the amount of salt relative to water can vary.

• Pure sodium chloride is a compound. The textbook’s “table salt” example assumes pure NaCl.

• “Pure” describes composition, not whether something is natural, healthy, or safe.

Homogeneous means uniform within a sample. Two cups of salt water can have different salt concentrations while each is homogeneous.

3.5: Physical and chemical properties

A property describes a characteristic or ability of a substance.

Memory aid: Ask, “Must it become a different substance to demonstrate this property?”

• Measuring iron’s density: physical property.

• Iron’s ability to rust: chemical property.

3.6: Physical and chemical changes

State changes are physical changes. Ice, liquid water, and water vapor all contain H₂O molecules.

Adding another substance does not automatically mean a chemical change. Mixing sugar into water is a physical change.

Reversibility is not a reliable test. Breaking glass is difficult to reverse, but it is still a physical change.

Changes in color, temperature, or gas production can be clues to a reaction, but they do not prove one by themselves. Boiling produces bubbles without creating a new substance.

Property versus change:

• “Sugar can burn” describes a chemical property.

• “Sugar is burning” describes a chemical change.

Reactants → Products

• Reactants: starting substances.

• Products: substances formed.

• The arrow means “yields” or “produces.”

Separating mixtures

Physical separation takes advantage of differences in physical properties.

Volatile means easily vaporized.

Ordinary filtration does not remove dissolved salt from water.

Filtration and distillation do not split compounds into their elements. Distilling water produces water, not separate hydrogen and oxygen.

Connection to the cherry-soda video: Chemical reactions produced different compounds. Filtration and distillation then helped separate substances from the resulting mixtures.

3.7: Conservation of mass

Matter is neither created nor destroyed in an ordinary chemical reaction.

Total mass of reactants = Total mass of products

Example:

58g + 208g = 176g + 90g = 266g

You must account for all substances, including gases.

• Sealed flask: water vaporizes, but the total mass stays the same.

• Open flask: vapor can escape, so the mass remaining on the scale decreases. The escaped matter still exists.

3.8: Energy

What is energy?

Energy is the capacity to do work. Scientific work occurs when a force moves something through a distance—for example, pushing a shopping cart.

Forms of energy

As a cart rolls downhill, gravitational potential energy decreases and kinetic energy increases as it speeds up. Friction transfers some energy to the surroundings as thermal energy.

Thermal energy depends on the amount of matter as well as temperature. A hotter object does not always contain more total thermal energy than a larger, cooler object.

Conservation of energy

Energy cannot be created or destroyed. It can be transferred or transformed.

• Transferred: energy moves from hot coffee to your hand.

• Transformed: a flashlight converts chemical energy into electrical energy, then light and thermal energy.

When something stops moving, its energy has not disappeared. It may have transferred to the surroundings as thermal energy and sound.

A machine cannot continually supply energy without an energy source. Regenerative braking recovers some existing energy; it does not create energy.

Energy units

Joule (J) is the SI energy unit.

Capitalization matters: cal and Cal are different-sized units. Letter count does not tell you a unit’s size.

kilo means 1000, so a kilojoule is a larger unit than a joule.

Unit size versus numerical value

For the same amount of energy, larger units require a smaller number:

3000 J = 3 kJ

• Smaller unit: J.

• Smaller numerical value: 3, in the kJ expression.

• Energy amount: identical.

Think: 100 pennies = 1 dollar. Pennies are smaller, so you need more of them.

Among these units, smallest to largest:

J < cal < Cal < kWh

Therefore, kWh gives the smallest numerical value for the same energy.

Converting energy units

Arrange conversion fractions so the starting unit cancels and the desired unit remains.

Example: Convert 2.00 Cal to kJ.

2.00 Cal (1000 cal / 1 Cal) (4.184 J / 1 cal) * (1 kJ / 1000 J) = 8.368 kJ

Round only the final answer to three significant figures:

8.37 kJ

Example: Convert 0.450 kWh to J.

0.450 kWh * (3.60 * 10^6 J / 1 kWh) = [1.62 * 10^6 J]

Calculator and notation reminders

To enter (10^6), use 10 → xʸ → 6.

For the second example, enter:

0.450 × 3.60 × 10^6

Also remember:

8370 J = 8.37 kJ

Once you divide by 1000 to obtain kJ, don’t add another \(10^3\) to the kJ answer.

3.9: Energy in Chemical and Physical Changes

Physical and chemical changes can absorb or release energy.

• System: the substance or process being studied.

• Surroundings: everything outside the system that exchanges energy with it.

Exothermic versus endothermic

Memory aid: EXO = energy EXits; ENDO = energy ENters. Always consider energy relative to the system.

Reading energy diagrams

• Reactants higher → products lower: energy is released → exothermic.

• Reactants lower → products higher: energy is absorbed → endothermic.

Energy does not disappear when the system loses it—it transfers to the surroundings.

Reverse processes

Reversing a process reverses the energy transfer.

Important distinctions from our practice

Freezing is exothermic, even though ice is cold. Water must release heat to become ice.

Burning natural gas is exothermic, even though the reacting gases become hot. The classification describes the overall release of energy.

A cold pack’s process is endothermic because it absorbs heat from your body. Your body loses heat and feels colder.

Don’t classify a process only by whether something feels hot or cold. Ask where the energy goes.

3.10: Temperature

Temperature versus heat

Heat naturally transfers from warmer matter to cooler matter. For example, warm water transfers energy to an ice cube.

Temperature does not tell you the total thermal energy of a sample. The amount of matter also matters.

The three temperature scales

At standard atmospheric pressure.

• Absolute zero is the lowest temperature on the Kelvin scale. Particle motion is at its minimum; saying all motion stops is an oversimplification.

• Celsius and Kelvin have equal-sized intervals: a change of 1°C equals a change of 1 K.

• Write K, without a degree symbol.

• −40°C = −40°F: the numerical readings match.

Conversion formulas

For Fahrenheit ↔ Kelvin, use Celsius as the middle step.

These conversions require formulas because the scales have different zero points. They are not simply multiplication by a conversion fraction.

How to approach the book’s problems

1. Identify the starting scale and requested scale.

2. Choose the appropriate formula or two-step route.

3. Substitute the temperature, keeping its negative sign.

4. Calculate without rounding intermediate results.

5. Round the final answer and include the correct unit.

The conversion constants 273.15, 32, and 1.8 are exact. They do not limit the measurement’s precision.

For the whole-degree measurements in these Skillbuilders, report the final result to the nearest whole degree or kelvin, following the book’s examples.

Completed book Skillbuilders

3.7: Convert 358 K to Celsius.

[°C=358-273.15=84.85=85°C]

3.8: Convert 139°C to Fahrenheit.

[°F=1.8(139)+32=282.2=282°F]

3.9: Convert −321°F to Kelvin.

First convert to Celsius:

[°C={-321-32}/{1.8}=-196.111…]

Then convert to Kelvin:

[K=-196.111…+273.15 =77.0389…=77K]

Common mistakes to avoid

• Fahrenheit → Celsius: subtract 32 before dividing. Enter (F − 32) ÷ 1.8.

• Keep negative signs: −321 − 32 = −353.

• Round only the final result in a two-step conversion.

• Use the exact formula for schoolwork. “Double Celsius and add 30” is only an estimate.

• Example for your vehicle: 21°C = 69.8°F, approximately 70°F.

3.11: Temperature Changes and Heat Capacity

Specific heat capacity, or specific heat, is the energy required to raise the temperature of 1 gram of a substance by 1°C.

Its common units are:

J / (g * °C)

Water’s specific heat is 4.184 J / (g·°C): raising 1 g of water by 1°C requires 4.184 J.

High versus low specific heat

High specific heat means greater resistance to temperature change.

Be careful with “heats slowly”: that comparison assumes the same mass and rate of energy input. Heating speed also depends on how energy reaches the object.

Specific heat versus heat capacity

• Specific heat: energy needed per gram for a 1°C increase.

• Heat capacity: energy needed for the whole object to increase by 1°C.

A larger amount of the same substance needs more energy for the same temperature increase.

The book’s examples

Iron versus water: Water requires more energy to raise 1 g by 1°C because its specific heat is higher.

Coastal temperatures: Large bodies of water absorb or release considerable energy with relatively small temperature changes, helping moderate nearby temperatures.

Cooler and drinks: Warm drinks release energy as they cool, melting more ice. Prechilled drinks release less energy before reaching the cooler’s temperature.

Water jug versus rock: Equal masses starting at 38°C release different amounts of energy when cooling to the same lower temperature. Water releases more, because it has a higher specific heat.

Copper, iron, and aluminum plates: With equal masses, equal starting temperatures, and equal energy added, copper reaches the highest temperature because it has the lowest specific heat of those three.

Burning versus cooling: Burning charcoal releases chemical energy through a reaction. That differs from a warm rock releasing energy as it cools.

3.12 Notes: Energy and Heat Capacity Calculations

The main equation connects heat, mass, specific heat, and temperature change:

q = m C Delta T

Here, (C) means specific heat, not Celsius.

Calculate temperature change first

Delta T= Tf - Ti

Always subtract initial temperature from final temperature.

For the copper penny:

Delta T = 37.0 - (-5.0) = 42.0°C

Subtracting a negative becomes addition.

A temperature change of 1°C equals a change of 1 K. Do not add 273.15 to a temperature difference.

Choose the equation for what you need

Calculator reminder: Keep the entire denominator in parentheses:

q ÷ (m × C)

Positive and negative heat

Your key correction: The water absorbed heat, so its final temperature had to be higher than 25.0°C.

Use:

Tf = Ti + Delta T

If Delta T is negative, adding it automatically lowers the temperature.

Units and rounding

• Match the units to the specific heat. For J/(g·°C), use joules, grams, and Celsius temperature change.

• Convert kg to g or kJ to J when necessary.

• Use the specific-heat value supplied by your book or problem.

• Keep unrounded intermediate results; round at the end.

• For temperature subtraction, track decimal places.

• For multiplication and division, track significant figures.

• When adding Delta T to an initial temperature, use the addition rule for the final result.

Book problems we completed

Specific heat and temperature change

From:

Delta T = q / m C

For equal masses absorbing equal heat:

• Higher specific heat → smaller temperature change.

• Lower specific heat → larger temperature change.

• If A’s specific heat is twice B’s, B’s temperature change is twice A’s.

Important limit: q = m C Delta T calculates energy associated with a temperature change without a phase change. Melting or boiling requires a separate energy calculation.

Chapter 4

4.1: Experiencing Atoms at Tiburon

• Atoms are the building blocks of matter. They compose air, water, rocks, and our bodies.

• An atom is the smallest identifiable unit of an element.

• An element contains only one kind of atom and cannot be broken into simpler substances by ordinary chemical reactions.

• A molecule consists of two or more atoms chemically bonded together. Examples: O₂ and H₂O.

• Atoms are extremely small; even a tiny pebble contains an enormous number.

• The kinds of atoms present, their bonding, and their arrangement help determine a material’s properties.

Main takeaway: Chemistry connects observable matter with the atoms and molecules that compose it.

4.2 — Indivisible: The Atomic Theory

Main idea: All matter is made of atoms, even though matter may appear continuous.

Early ideas

• Greek philosophers Leucippus and Democritus proposed that matter consisted of tiny, indivisible particles.

• Atomos means “indivisible.”

Dalton’s atomic theory — 1808

1. Each element consists of tiny, indestructible particles called atoms.

2. All atoms of the same element have the same mass and properties, which distinguish them from other elements.

3. Atoms combine in simple, whole-number ratios to form compounds.

   • Example: H₂O has 2 hydrogen atoms for every 1 oxygen atom.

Modern updates to Dalton’s theory

• Atoms contain smaller particles: protons, neutrons, and electrons.

• Atoms of the same element can have different masses; these are isotopes.

• In ordinary chemical reactions, atoms are rearranged.

Evidence: Scientists can image and move individual atoms using a scanning tunneling microscope (STM).

Preview of atomic structure: An atom’s matter is unevenly distributed. Most of its mass is concentrated in a tiny nucleus, and most of its volume is empty space.

4.3 — The Nuclear Atom

Thomson’s discovery

• Discovered electrons: tiny, negatively charged particles within atoms.

• Proposed the plum-pudding model: electrons embedded in a sphere of positive charge.

• His discovery showed that atoms contain smaller particles.

Rutherford’s gold foil experiment

• Fired positively charged alpha particles at thin gold foil.

• Expected them to pass through with little deflection.

• These results disproved the plum-pudding model.

• Positive alpha particles were repelled by the positive nucleus.

Nuclear theory of the atom

1. Almost all the atom’s mass and all its positive charge are concentrated in the nucleus.

2. Electrons occupy the region outside the nucleus, which accounts for most of the atom’s volume.

3. A neutral atom has equal numbers of protons and electrons.

Key distinction to remember: The nucleus contains almost all the mass, but occupies very little volume.

4.4 — Properties of Protons, Neutrons, and Electrons

Atomic mass unit (amu)

• Unit used to measure atomic masses.

• Defined as 1/12 the mass of a carbon-12 atom.

• A proton is about 2,000 times heavier than an electron.

Electrical charge

• Opposite charges attract: positive and negative.

• Like charges repel: positive–positive or negative–negative.

• Protons and electrons have equal-sized but opposite charges.

• A neutral atom has equal numbers of protons and electrons.

• Neutrons contribute mass but no charge.

Useful calculations

• Approximate mass (amu) = protons + neutrons

• Net charge = protons − electrons

Example: 6 protons, 6 neutrons, and 6 electrons have approximately 12 amu and zero net charge.

Remember: Protons and neutrons provide almost all the mass; the balance of protons and electrons determines the charge.

4.5 — Elements: Defined by Their Numbers of Protons

• The number of protons identifies the element.

• Atomic number (Z) = number of protons.

• Changing the number of protons changes the element.

• The periodic table arranges elements by increasing atomic number.

Reading an element’s box

Remember: proton counts are whole numbers. The decimal atomic mass is NOT the proton count.

Chemical symbols

• Usually one or two letters.

• First letter is uppercase; second letter is lowercase: Na, not NA.

• Some come from older names, such as sodium (Na) and potassium (K).

Examples

For a neutral atom, the atomic number also equals its number of electrons.

4.6 — The Periodic Law and the Periodic Table

Periodic law: When elements are arranged by increasing atomic number, certain properties repeat. For example, lithium, sodium, and potassium have similar properties and line up in the same column.

• Mendeleev’s table (1869): He arranged elements mainly by increasing relative atomic mass and lined up elements with similar properties. He left gaps and used the pattern to predict undiscovered elements, including germanium.

• Modern periodic table: Elements are arranged by increasing atomic number, which equals the number of protons.

• The periodic law describes the repeating pattern. A scientific theory explains why it happens.

How to read the table

Metals, nonmetals, and metalloids

Four families to know

The color key changes with the chart. The same element can have several labels because each label answers a different question:

• Pb (lead) is a metal by type and a main-group element because it’s in 4A (14).

• At (astatine) is a halogen because it’s in 7A (17) and a metalloid according to your book’s Major Divisions chart.

• Checkpoint 4.5: A transition element and a metalloid is the pair that doesn’t overlap. The center transition block contains metals, and the metalloid boxes are outside it.

4.7 — Ions: Losing and Gaining Electrons

An ion forms when an atom gains or loses electrons. Its proton count stays the same, so it’s still the same element.

Reading ion symbols: The upper-right superscript shows the net charge. The lower-right subscript counts atoms. O²⁻ is one oxygen ion with a 2− charge; O₂ has two oxygen atoms. For a charge of 1+ or 1−, write just ⁺ or ⁻.

Calculating charge or counting electrons

• Protons = atomic number. Use the whole number in the element’s box.

• Charge = protons − electrons. Nickel with 26 electrons has a charge of 28 - 26 = +2, so it’s Ni²⁺.

• Given the charge? Start with the proton count. For a positive ion, subtract electrons; for a negative ion, add electrons. S²⁻ has 16 protons and 16 + 2 = 18 electrons.

• Different ions can have the same electron count. Na⁺ has 11 - 1 = 10 electrons, and Mg²⁺ has 12 - 2 = 10.

Predicting common charges from the periodic table

Valence electrons are the outermost electrons. For neutral main-group atoms, the A-group number usually gives the valence electron count. Helium is the exception: it’s in 8A but has 2. Many main-group atoms gain or lose electrons to match a nearby noble gas’s electron arrangement.

Transition metals can form cations with different charges, so their column alone generally won’t tell you which charge to use. If the problem gives you the electron count, calculate protons − electrons. If it asks what ion an element tends to form, use the group pattern.

4.8 — Isotopes: When the Number of Neutrons Varies

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. The extra neutrons change the mass. For example, carbon-12 and carbon-13 both have 6 protons, but carbon-13 has one more neutron.

Writing isotope symbols: Chlorine with 17 protons and 18 neutrons has a mass number of (17 + 18 = 35). Write it as Cl-35 In the second form, the upper left is the mass number and the lower left is the atomic number. From 4.7, remember that the upper right is where ion charge goes.

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Choose the calculation based on what’s missing:

Two things to keep straight: The mass number counts particles in one isotope’s nucleus; the atomic mass on the periodic table is a weighted average in amu. And C-12 and C-13 look identical in the book’s sphere model because it represents the whole atom without showing the tiny nucleus, where the extra neutron is.

4.9 — Atomic Mass: The Average Mass of an Element’s Atoms

Atomic mass is the weighted average of the masses of an element’s naturally occurring isotopes. It’s measured in amu and usually appears below the element symbol on the periodic table. Weighted means that more abundant isotopes contribute more to the average.

How to calculate average atomic mass

1. Convert each percent abundance to a decimal by dividing by 100. For example, 78.99% = 0.7899. The fractions should add up to 1 (or very close, if the percentages were rounded).

2. Multiply each isotope’s actual mass by its own decimal abundance.

3. Add the products. Keep extra digits until the end, then round and include amu.

Magnesium example from Skill Builder 4.9:
(23.99 * 0.7899) + (24.99 * 0.1000) + (25.98 * 0.1101) = 24.309099 = about 24.31 amu

How to check or predict your answer

• The average falls between the lightest and heaviest isotope masses.

• With two isotopes, equal abundances give the midpoint. If one is more abundant, the average is closer to its mass. That’s why gallium’s average is slightly below 70 amu: the lighter isotope is more common.

• You can work backward with two isotopes, too. In Checkpoint 4.11, 64.52 amu is closer to isotope B’s mass (64.9846 amu) than to isotope A’s mass (61.9887 amu), so B is more abundant.

Radioactive isotopes: An isotope is radioactive if its nucleus is unstable and emits radiation as it decays. The Hanford example illustrates why waste containing long-lived radioactive isotopes can remain a problem long after it’s produced.

Chapter 5

5.1 — Sugar and Salt

• A compound contains two or more different elements chemically combined.

• Compounds have different properties from the elements that form them.

• Table salt (NaCl): Sodium is a reactive metal, and chlorine is a poisonous gas. Combined, they form white crystalline sodium chloride.

• Sugar: Carbon, hydrogen, and oxygen combine to form a sweet, white crystalline solid.

• Elements combine in many ways to form the diverse compounds needed for life.

Main takeaway: Knowing which elements a compound contains doesn’t mean it has the same properties as those elements.

5.2 — Compounds Display Constant Composition

• Law of constant composition: Every sample of a particular pure compound contains the same elements in the same proportions.

• Joseph Proust first formally stated this law.

• Compounds have fixed proportions; mixtures have variable proportions.

• A larger sample contains more of each element, but the ratio stays the same.

Atom ratios and mass ratios are different

These differ because oxygen atoms are heavier than hydrogen atoms.

Calculating and comparing mass ratios

Mass ratio A:B = mass A ÷ mass B

For example, water containing 16 g oxygen and 2 g hydrogen has an oxygen-to-hydrogen mass ratio of 16 ÷ 2 = 8:1.

When comparing samples:

1. Divide the masses in the same element order for each sample.

2. Keep calculator digits until the end, then round appropriately.

3. Matching ratios support constant composition. Small differences can result from limited measurement precision.

Finding a missing mass

If mass A ÷ mass B = 3.0, there are 3 g A for every 1 g B.

With 9.0 g A:
Mass B = 9.0 ÷ 3.0 = 3.0 g

Remember: Fixed proportions do not mean equal amounts.

5.3 — Chemical Formulas: How to Represent Compounds

• A chemical formula identifies the elements in a compound and their relative numbers of atoms, not their masses.

• A subscript tells how many atoms of the element immediately before it are present. No subscript means 1.

• Changing subscripts changes the compound: CO and CO₂ are different compounds.

Writing formulas

• Normally write the metal first: Ag₂S, not SAg₂.

• With nonmetals, normally write the more metal-like element first—farther left, or farther down within the same group. Examples: CO₂ and SO₃.

• Use the atom counts given as subscripts; omit subscripts of 1.

Parentheses and polyatomic ions

A polyatomic ion is a group of bonded atoms with an overall charge that acts as one unit.

A subscript outside parentheses multiplies every atom inside, but does not affect atoms outside.

Example: Al₂(SO₄)₃

To find the total number of atoms, add the counts: 2 + 3 + 12 = 17 atoms.

Types of chemical formulas

• Find an empirical formula by dividing all subscripts by their greatest common factor.

• Molecular formulas are whole-number multiples of empirical formulas.

• Sometimes both formulas are identical, such as H₂O.

• Do not simplify a molecular formula when asked for actual atom counts.

Molecular models

• Ball-and-stick: Balls represent atoms; sticks represent bonds. Shows connections and three-dimensional shape.

• Space-filling: Overlapping spheres represent the space atoms occupy.

• Use the model’s color key to identify elements, then count each type of atom.

5.4 — A Molecular View of Elements and Compounds

Pure substances are elements or compounds, divided into four categories:

Diatomic elements to memorize

These seven elements normally occur as molecules containing two atoms:

H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂

A molecule does not have to be a compound: Cl₂ is a molecular element because it contains only chlorine.

Ionic compounds and formula units

• Metals tend to lose electrons, forming positive cations.

• Nonmetals tend to gain electrons, forming negative anions.

• Opposite charges attract, holding the ions in a repeating three-dimensional arrangement.

• Ionic compounds contain formula units rather than separate molecules.

• A formula unit gives the smallest whole-number ratio of ions that makes the compound neutral. NaCl = 1 Na⁺ for every 1 Cl⁻.

Recognizing particle pictures

• Separate atoms of one type → atomic element

• Separate bonded groups of one element → molecular element

• Separate molecules containing different elements → molecular compound, like checkpoint B

• A repeating array of positive and negative ions → ionic compound

How to classify: First identify whether there is one element or multiple elements. Then determine the type of basic unit. Categories can repeat—don’t rely on elimination.

5.5 — Writing Formulas for Ionic Compounds

• Ionic compounds contain positive ions (cations) and negative ions (anions).

• The compound must be charge-neutral: total positive charge + total negative charge = 0.

• Use the smallest whole-number ratio of ions that balances the charges.

• A monatomic ion is one charged atom. A polyatomic ion is a bonded group of atoms with an overall charge.

Steps for writing a formula

1. Write the cation first, followed by the anion, with their charges.

2. Use the charge numbers without their signs as subscripts for the opposite ion—the crisscross method.

3. Reduce the ion counts if possible and omit subscripts of 1.

4. Check that the total charge equals zero.

Reducing: Mg₂O₂ becomes MgO because the 2:2 ratio reduces to 1:1.

Formulas containing polyatomic ions

• Learn each polyatomic ion’s name, formula, and charge from Table 5.3.

• Treat the entire ion as one unit.

• Use parentheses when more than one copy of a polyatomic ion is needed.

• Never change the subscripts inside the polyatomic ion when balancing charges.

Remember: Superscripts show an ion’s charge; subscripts show how many atoms or groups are represented. The finished neutral compound’s formula does not include the individual ion charges.

5.6 — Nomenclature: Naming Compounds

• Nomenclature means a system for naming substances.

• Systematic names follow rules that help you go from a formula to a name—or from a name to a formula.

• Common names are familiar names, like nicknames. You learn them through familiarity.

Both names describe the same compound. The next sections teach different naming rules for ionic and molecular compounds.

5.7 — Naming Ionic Compounds

Ionic compounds contain positive ions (cations) and negative ions (anions). Name the cation first, followed by the anion.

1. Metals with a fixed charge

For a binary compound—one containing two different elements—use:

Metal name + nonmetal base name ending in -ide

• Do not use Roman numerals for metals with a fixed charge.

• Common fixed charges: Group 1 metals +1, Group 2 metals +2, Al³⁺, Zn²⁺, Ag⁺.

• Do not use prefixes such as di- or tri- when naming ionic compounds.

Common monatomic anion names

2. Metals with variable charges

Some metals form ions with different charges. Use:

Metal name(Roman numeral) + anion name

The Roman numeral indicates the charge of each metal ion, not the number of atoms.

To determine the metal’s charge:

1. Find the total negative charge from the anions.

2. The total positive charge must balance it.

3. If there is more than one metal ion, divide the total positive charge by the number of metal ions.

Example: FeCl₃

• Three Cl⁻ ions have a total charge of −3.

• One Fe ion must have a charge of +3.

• Name: iron(III) chloride.

Most metals with variable charges are transition metals. Tin and lead also have variable charges.

3. Compounds containing polyatomic ions

Keep the polyatomic ion’s name unchanged. Include a Roman numeral if the metal has a variable charge.

Example: Fe(OH)₂: Each hydroxide is OH⁻. Two hydroxides give −2, so iron must be +2.

4. Naming oxyanions

An oxyanion is a negatively charged ion containing oxygen.

Within the same oxyanion family:

• -ate: more oxygen than -ite

• -ite: fewer oxygen than -ate

• per-…-ate: more oxygen than -ate

• hypo-…-ite: fewer oxygen than -ite

Another example: NO₃⁻ is nitrate; NO₂⁻ is nitrite. These endings show relative oxygen amounts within a family; they do not indicate one universal oxygen count.

Everyday examples

Remember: Fixed charge → no Roman numeral. Variable charge → Roman numeral. Polyatomic ion → keep its name.

5.8 — Naming Molecular Compounds

Binary molecular compounds contain two different elements, generally nonmetals. Their names use prefixes to show the number of atoms.

Naming rules

1. Name the first element using its full name and a prefix for its atom count. Omit mono- on the first element.

2. Name the second element using a prefix and change its ending to -ide. Include mono- when there is one atom of the second element.

3. Sometimes drop the final vowel of a prefix before oxide: monoxide, tetroxide, and pentoxide.

Examples

Molecular versus ionic naming: NCl₃ is nitrogen trichloride because molecular compounds use prefixes. AlCl₃ is aluminum chloride because ionic compounds do not use these prefixes.