Chemistry · Chapter 1

Essential Ideas

Chemistry is the study of matter and the changes that matter goes through. This chapter hands you the tools that the rest of the book will run on. You will learn what matter is and how its particles are packed together. You will sort samples into solids, liquids and gases, and you will tell a physical change from a chemical one. Then you will start to measure. Every number in chemistry carries a unit, and that unit carries real meaning. You will meet the SI units, learn to report what your instruments actually tell you, and practice turning one unit into another. By the end of the chapter, your numbers will be worth trusting.

By the end of this chapter you can

Define matter and describe how particles are arranged in the three common states.
Sort any sample as an element, a compound or a mixture, and explain your choice.
Separate physical properties and changes from chemical properties and changes.
Name the seven SI base units and attach the common prefixes to any of them.
Count significant figures and round a calculated answer the correct way.
Convert between units by chaining conversion factors until the units cancel.
Calculate a density and convert among Fahrenheit, Celsius and kelvin.

Section 1Matter and its states

What counts as matter

Matter is anything that has mass and takes up space, which covers nearly everything around you. Your chair is matter, and so is the air in the room and the water in your glass. Light and sound are not matter, because they carry energy without holding any mass or volume.

All matter is built from atoms, and an atom is the smallest piece of an element that still behaves like that element. Atoms bond together into molecules, which are small groups of joined atoms. A single water molecule is two hydrogen atoms bonded to one oxygen atom, which chemists write as H₂O.

Solid, liquid and gas

The three states you meet most often are solid, liquid and gas, and what separates them is how the particles are packed and how freely they travel.

In a solid, the particles sit close together and stay in fixed positions. They still vibrate in place but cannot trade spots, so a solid holds both its own shape and its own volume.

In a liquid, the particles still touch each other, but they slide past their neighbors freely. A liquid keeps its volume while taking the shape of its container, so pouring 50 mL of water into a wide dish still leaves you with 50 mL.

In a gas, the particles fly apart in every direction and spread out to fill whatever holds them. Most of a gas sample is actually empty space, which is why you can squeeze a gas into a smaller can while a solid barely budges.

Matter heated to extreme temperatures can reach a fourth state called plasma, in which electrons are torn away from their atoms. Stars shine with plasma, and so does the gas inside a glowing neon sign.

Figure 1.1 The same particles in three states. In the solid they hold a tight pattern. In the liquid they touch but slide. In the gas they are far apart and fast, so the sample can be squeezed.

Heating or cooling moves a sample between these states. Ice melts into water, water boils into steam, and steam cools and condenses back into water again. Dry ice skips the liquid stage and turns straight into a gas, a change known as sublimation. Through every one of these changes the substance itself stays the same, and only the packing of the particles changes.

Pure substances and mixtures

A pure substance has exactly the same makeup all the way through the sample. An element is a pure substance built from only one kind of atom, such as copper or oxygen. A compound is a pure substance built from two or more elements bonded in a fixed ratio. Water always carries two hydrogen atoms for each oxygen atom, in every sample on Earth.

A mixture holds two or more substances that are not bonded together, so each one keeps its own identity. A homogeneous mixture looks completely uniform throughout, and salt water and clean air are both good examples. We also call a homogeneous mixture a solution. A heterogeneous mixture has visible parts you could pick out, like sand sitting in water or a bowl of trail mix.

Because nothing in a mixture is bonded, a mixture can always be separated by physical means. Boil a pot of salt water and the water escapes as steam, while all of the salt stays behind in the pot.

Worked example · a mixture by mass

A cook stirs 25.0 g of salt into 475 g of water. What percent of the finished solution is salt by mass?

Find the total mass

25.0 g + 475 g = 500. g of solution. Addition keeps the fewest decimal places, so this answer stops at the ones place.

Divide the part by the whole

(25.0 g ÷ 500. g) × 100 = 5.00 percent salt by mass.

Check it

Five percent of 500 g is 25 g, which matches the salt that was added, and the water makes up the other 95.0 percent.

Key points

Matter has both mass and volume, while energy has neither.
Solids keep their shape and volume, liquids keep only volume, and gases keep neither.
Elements and compounds are pure substances, while mixtures can be pulled apart physically.
A change of state rearranges the packing and never changes the substance itself.

Interactive Heat, cool and squeeze a sample and watch the particles change state. Open full ↑

Section 2Physical and chemical properties

Two kinds of property

A physical property is a trait you can measure without turning the sample into something new. Color, smell, hardness, melting point, boiling point and density are all physical properties. You can melt an ice cube to find its melting point and still have ordinary water at the end.

A chemical property describes the way a sample turns into a new substance, so you have to let the change happen before you can observe one. Iron rusting in damp air is a chemical property of iron, and so is the way paper burns or the way an antacid tablet fizzes in acid.

Does the amount matter?

Some properties depend on how much of the sample you happen to have. Mass, volume and length are extensive properties, so two liters of milk carry twice the mass of one liter.

Other properties stay exactly the same at any amount, and density, color, melting point and temperature are these intensive properties. Cut a copper bar in half and each piece still has a density of 8.96 g/cm³. Intensive properties help you identify an unknown sample, because they do not care how big the sample is.

Property	Kind	Why
Mass of a sugar cube	Extensive	Two cubes weigh twice as much
Volume of a gas sample	Extensive	More gas fills more space
Density of gold	Intensive	19.3 g/cm³ for a ring or a brick
Boiling point of ethanol	Intensive	78 °C for a drop or a drum
Flammable	Chemical	You learn it only by burning the sample

Physical change and chemical change

A physical change rearranges a sample without changing what the sample is made of. Melting, boiling, dissolving, cutting and bending are all physical changes, and the molecules are identical before and after.

A chemical change produces new substances, and we also call it a chemical reaction. Bonds break, atoms trade partners, and fresh bonds form in their place. Burning methane turns CH₄ and O₂ into CO₂ and H₂O, and those products carry their own new properties.

Figure 1.2 Melting ice is a physical change, since the same H₂O molecules come out the other side. Burning methane is a chemical change, since the atoms are rebuilt into different molecules.

A handful of clues can hint that a chemical change is under way. You might notice bubbles of a brand new gas, a shift in color, a solid forming inside a clear liquid, or heat and light pouring out. Treat all of these as hints rather than proof, because boiling water bubbles hard while remaining a purely physical change. The real test is whether a new substance is present at the end.

Matter is conserved

The law of conservation of matter says that matter is never created or destroyed during a chemical change. The atoms are only rearranged, and every single atom is still present at the end. That means the total mass of the products equals the total mass of the reactants, and this one rule lets you solve for a mass you never measured.

Worked example · a missing mass

Inside a sealed burner, 4.00 g of methane reacts with 16.0 g of oxygen, and the only products are carbon dioxide and water. If 11.0 g of carbon dioxide forms, what mass of water forms with it?

Add up what went in

4.00 g + 16.0 g = 20.0 g of reactants in total.

Set the products equal to that

Mass of water = 20.0 g − 11.0 g = 9.0 g of water.

Check it

Adding the products gives 11.0 g + 9.0 g = 20.0 g, so nothing has gone missing. Notice that the carbon dioxide outweighs the methane it came from, which makes sense because oxygen atoms joined the carbon.

Key points

Physical properties can be measured while the sample stays intact.
Chemical properties appear only when the sample becomes a new substance.
Extensive properties follow the amount, while intensive properties ignore it.
Bubbles, color shifts and released heat are clues to a reaction rather than proof.
The total mass stays the same before and after any chemical change.

Interactive Sort real changes into physical or chemical and see why. Open full ↑

Section 3Measurement and SI units

A number alone says nothing

Every measurement has two parts, a number and a unit, and neither part works alone. Asking a lab partner for five means nothing at all, because five grams, five liters and five kelvin are wildly different things. Write the unit down every single time.

Scientists in every country share one system of units, the SI units, and SI is short for the International System of Units. Seven base units hold the entire system up, and every other unit is built out of those seven.

Quantity	Base 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

Mass is the odd one out in that table, because the kilogram already carries a prefix inside its name. Grams are still what you will weigh samples in on most days in the lab.

Units built from other units

A derived unit is a combination of base units. Area is a length times a length, so area arrives in m², and volume is a length cubed, so its SI unit is m³. A cubic meter is enormous, roughly the size of a washing machine, so laboratories use the liter instead. One liter is exactly one cubic decimeter, and one milliliter is exactly one cubic centimeter.

Speed is measured in meters per second, written m/s, and density is mass over volume, often reported in g/cm³. Watch the pattern in those names, because the word "per" always signals division.

Mass and weight are two different quantities. Mass measures how much matter a sample contains, and it does not change when you travel. Weight is the pull of gravity on that mass, so a 1.00 kg block keeps its mass on the Moon while weighing about one sixth as much.

Prefixes do the heavy lifting

Real samples range from enormous to microscopic, so SI uses prefixes instead of long strings of zeros. Each prefix stands for a power of ten. Kilo means one thousand, so 1 km is 1000 m, and milli means one thousandth, so 1 mg is 0.001 g. Centi is one hundredth, micro is one millionth, and nano is one billionth.

Figure 1.3 The prefix ladder. Each rung is a power of ten away from the plain base unit in the middle. Moving up makes the unit bigger, so the number in front gets smaller.

A prefix can be glued onto whatever unit you like, so a nanosecond is a billionth of a second and a megajoule is a million joules. The rule behind the prefix never changes.

Worked example · prefixes in action

Part A. A flask holds 2.50 L of solution. How many cubic centimeters is that?

Use the two exact links

One liter is exactly 1000 mL, and one milliliter is exactly 1 cm³.

Scale up

2.50 L × 1000 = 2500 cm³, which we write as 2.50 × 10³ cm³ to hold on to three significant figures.

Part B. A single bacterium measures 1.5 µm in length. Report that length in meters.

Swap the prefix for its power of ten

Micro stands for 10⁻⁶, so 1.5 µm = 1.5 × 10⁻⁶ m, which is 0.0000015 m.

Check it

A meter is vastly bigger than a bacterium, so the number of meters should come out tiny, and it does.

Key points

A measurement is a number plus a unit, so never leave the unit off.
Seven SI base units cover length, mass, time, temperature, amount, current and light.
Derived units are built by multiplying and dividing the base units together.
1 L = 1 dm³ and 1 mL = 1 cm³, and both of those are exact.
A prefix is simply a power of ten attached to any unit you choose.

Interactive Build any measurement from the seven base units and their prefixes. Open full ↑

Section 4Uncertainty and significant figures

Every measurement carries doubt

No instrument is perfect, so a measurement is really a best value plus some uncertainty. The habit to build is straightforward. Read every digit you are certain of, then estimate one more digit past the finest mark on the scale. That final digit is the uncertain one, and you still write it down.

Picture a ruler with marks printed every centimeter. The edge of your sample sits past the 7 cm mark, about a third of the way toward 8, so you report 7.3 cm. The 7 is certain while the 3 is your estimate. A ruler marked every millimeter would let you report 7.34 cm instead.

A digital screen follows the same logic, so you trust the digits it displays while remembering that the last one still wobbles.

Accuracy is not precision

Accuracy describes how close a measurement lands to the true value, while precision describes how close repeated measurements land to each other. The two can easily come apart. A balance that always reads 2.00 g high is wonderfully precise and badly wrong. Readings scattered all around the true value can average out well while being anything but precise.

Figure 1.4 Four sets of shots at the same target. Tight groups are precise. Groups centered on the bullseye are accurate. You want both.

Counting significant figures

Significant figures are the digits in a measurement that carry real information about its size. Four rules cover nearly every case you will ever meet.

Every nonzero digit counts, so 48.2 carries three significant figures.
Zeros trapped between nonzero digits count, so 4.028 carries four.
Leading zeros never count, because they only park the decimal point, so 0.0056 carries two.
Trailing zeros count only when a decimal point is shown, so 1.200 carries four while 1200 stays unclear. Write 1.2 × 10³ whenever you mean two.

Counted objects and defined values are exact numbers, so they hold unlimited significant figures and never limit your answer. There are exactly 12 eggs in a dozen, and exactly 2.54 cm in an inch, because that is how the inch is defined.

Scientific notation ends the trailing zero problem for good. In 1.2 × 10³, only the digits in front of the power of ten count. Write 1.20 × 10³ for three figures and 1.200 × 10³ for four. No guessing.

Rounding a calculation

Your answer can never be more certain than the data behind it, and two rules keep you honest. For multiplication and division, keep as many significant figures as the measurement that carries the fewest. For addition and subtraction, keep as many decimal places as the measurement that carries the fewest.

Save the rounding for the very end, because rounding in the middle of a long chain lets small errors pile up.

Worked example · rounding both ways

Part A. A strip of foil measures 12.11 cm long and 0.0450 cm wide. Find its area.

Multiply, then count

12.11 cm × 0.0450 cm = 0.544950 cm². The length carries four significant figures, while the width carries three, since leading zeros never count.

Keep the smaller count

Rounding to three significant figures gives an area of 0.545 cm².

Part B. Add three measured masses together: 13.64 g, 0.7 g and 1.456 g.

Add, then find the weakest decimal place

13.64 + 0.7 + 1.456 = 15.796 g, and the 0.7 g is known only to the tenths place.

Round to the tenths place

The reported sum is 15.8 g. Notice that addition cares about decimal places, while multiplication cares about the count of digits.

Key points

Report every certain digit plus exactly one estimated digit.
Accuracy means close to the truth, while precision means close to each other.
Leading zeros are never significant, and captive zeros always are.
Trailing zeros count only when a decimal point is present in the number.
Multiply and divide by the digit count, then add and subtract by decimal place.

Interactive Read instruments, count significant figures and round a calculation. Open full ↑

Section 5Dimensional analysis

Multiply by one on purpose

Dimensional analysis is the habit of carrying units through a calculation and letting them steer the setup. Its main tool is a conversion factor, which is a fraction built out of an equality. Because 1 m = 100 cm, both of these fractions are equal to exactly one.

100 cm ÷ 1 m and 1 m ÷ 100 cm

Multiplying by one never changes how much you have, and it only changes the label on the amount. So pick whichever version puts the unit you want on top and the unit you want gone on the bottom, and that unwanted unit then cancels.

The units are also your error check. If the surviving unit is wrong, then your setup was wrong, and no amount of careful arithmetic will rescue it. Flip the factor over and try the chain again.

Chain as many steps as you need

You often will not know the single factor that takes you straight to the target, and that is perfectly fine. String several factors together instead and let each unwanted unit cancel in turn. Write the whole chain first, confirm that only the target unit survives, and save the arithmetic for last.

Figure 1.5 A chain of three conversion factors. Each unit that appears on top of one fraction and on the bottom of the next one cancels. Only inches are left standing.

Worked example · kilometers to inches

A hiking trail runs 5.00 km from end to end. How long is that trail in inches?

Plan the path

Travel from km to m, then from m to cm, then from cm to inches, using the exact link 1 in = 2.54 cm.

Write the chain

5.00 km × (1000 m per 1 km) × (100 cm per 1 m) × (1 in per 2.54 cm)

Cancel and compute

Kilometers, meters and centimeters all cancel away, leaving inches behind. The arithmetic runs 5.00 × 1000 × 100 ÷ 2.54 = 196,850 in.

Round and check

Only the 5.00 was measured, so the answer keeps three significant figures as 1.97 × 10⁵ in. An inch is a small unit, so a large count of them makes sense.

Rates are conversion factors too

Any ratio that ties two quantities together can serve as a conversion factor. A dose of 0.750 mg per kilogram of body mass is a factor, and so is a syrup labeled 25.0 mg per milliliter. Those two factors let you walk straight from a body mass to a volume you can pour.

Worked example · a two step dose

A drug is prescribed at 0.750 mg per kilogram of body mass. The patient has a mass of 68.0 kg, and the syrup on the shelf holds 25.0 mg per milliliter. How many milliliters should be poured?

Mass to dose

68.0 kg × (0.750 mg per 1 kg) = 51.0 mg of drug needed.

Dose to volume

51.0 mg × (1 mL per 25.0 mg) = 2.04 mL of syrup.

Check it

Run the chain backward, since 2.04 mL × 25.0 mg per mL = 51.0 mg, which is the dose we wanted. Every unit except milliliters cancelled somewhere along the way.

A squared unit needs its factor twice. To change cm² into m², multiply by (1 m per 100 cm) two times, which divides by 10,000 rather than by 100. The same trick handles cubic units three times over.

Key points

A conversion factor is a fraction whose value is exactly one.
Arrange it so the unwanted unit cancels, then confirm the unit that survives.
Chain factors together freely and leave the arithmetic until the end.
Rates such as milligrams per kilogram serve as conversion factors as well.
Exact factors never limit the significant figures in your final answer.

Interactive Chain conversion factors and watch the units cancel. Open full ↑

Section 6Density and temperature

Density packs mass into space

Density tells you how much mass is crammed into a given volume, and it is simply mass divided by volume.

d = m ÷ V

Solids and liquids are usually reported in g/cm³, which is identical to g/mL, while gases are so light that we report them in g/L. Liquid water is very close to 1.00 g/cm³. It peaks near 4 °C at 1.000 g/cm³ and drops to 0.997 g/cm³ by 25 °C.

Density is an intensive property, so a gold ring and a gold brick share the same density of 19.3 g/cm³. That steadiness makes density a strong clue to the identity of an unknown sample.

Whether something floats depends on its density rather than its mass, so a sample floats in a liquid whenever its density is lower than the liquid's. Ice has a density of 0.917 g/cm³, so ice cubes bob on water, while a steel bolt sinks because steel sits near 7.8 g/cm³. An enormous ship still floats because its shape traps air, which lowers the average density of the whole hull.

Figure 1.6 A density column. Liquids stack with the densest at the bottom. Each dropped object settles at the level where the liquid below it is denser than the object.

Worked example · naming a metal by density

A cube of metal measures 2.00 cm along every edge and has a mass of 71.7 g. Find its density and identify the metal.

Find the volume

V = 2.00 cm × 2.00 cm × 2.00 cm = 8.00 cm³.

Divide mass by volume

d = 71.7 g ÷ 8.00 cm³ = 8.9625, which rounds to 8.96 g/cm³ at three significant figures.

Match and check

Copper has a density of 8.96 g/cm³, so this cube is very likely copper. Multiplying back gives 8.96 × 8.00 = 71.7 g, which matches the measured mass.

Three temperature scales

Temperature tells you which direction heat will flow, because heat always moves from the hotter sample toward the cooler one on its own.

The Celsius scale sets 0 °C at the freezing point of water and 100 °C at its boiling point under 1 atm of pressure. That span is divided into 100 steps called degrees.

The Fahrenheit scale places those same two points at 32 °F and 212 °F. That gives 180 degrees across the identical span, so a Fahrenheit degree is smaller, and nine Fahrenheit degrees cover the same gap as five Celsius degrees.

The kelvin is the SI unit of temperature. Its steps are exactly the size of Celsius degrees, but the scale begins at absolute zero, the coldest temperature that can exist. Absolute zero is 0 K, which is −273.15 °C. Nothing can be colder, so kelvin never goes negative and it takes no degree sign at all. You say 298 kelvin rather than 298 degrees kelvin.

K = °C + 273.15 °F = (9/5 × °C) + 32 °C = 5/9 × (°F − 32)

Kelvin matters more than it first appears. Gas laws and energy equations only behave with kelvin, because a scale with negative numbers would let you double a temperature and get nonsense. Switch to kelvin early and you will dodge a long list of errors.

Worked example · across all three scales

Part A. A room sits at 25.00 °C. Report that temperature in kelvin and in degrees Fahrenheit.

Add for kelvin

25.00 + 273.15 = 298.15 K. Both values are known to the hundredths place, so the answer keeps that place.

Scale and shift for Fahrenheit

(9/5 × 25.00) + 32 = 45.00 + 32 = 77.00 °F. The 9/5 and the 32 are both exact by definition.

Part B. A thermometer reads a fever of 102.0 °F. Report that temperature in degrees Celsius.

Subtract first, then scale

102.0 − 32 = 70.0, and 5/9 × 70.0 = 38.888, which rounds to 38.9 °C.

Check it

Normal body temperature is 37.0 °C, so a fever sitting a little above that figure is exactly what we expect.

Key points

Density is mass over volume, and it never depends on the amount of sample.
A sample floats whenever it is less dense than the liquid holding it.
Water sits near 1.00 g/cm³, while ice is less dense at 0.917 g/cm³.
Kelvin steps match Celsius steps exactly, shifted along by 273.15.
Zero kelvin is absolute zero, which equals −273.15 °C.

Interactive Float, sink and measure density; convert between the three temperature scales. Open full ↑

The chapter in one breath

Matter has both mass and volume, and it reaches you as a solid, a liquid or a gas.
Pure substances are either elements or compounds, and everything else is a mixture.
Physical changes keep the substance intact, while chemical changes build brand new substances.
Matter is conserved, so the products of a reaction weigh exactly what the reactants weighed.
Seven SI base units plus a handful of prefixes can describe any measurement you will meet.
Significant figures record how certain a measurement is, and the rounding rules protect that record.
Dimensional analysis converts any unit into any other by multiplying through by one.
Density is mass divided by volume, and comparing densities tells you what will float.
Kelvin shares the step size of Celsius but begins at absolute zero, which is −273.15 °C.

ReferenceWords worth knowing

Here are the terms this chapter leans on. Each one shows up again later in the book.

Absolute zero: The coldest temperature possible, 0 K or −273.15 °C.
Accuracy: How close a measurement is to the true value.
Chemical change: A change that breaks and forms bonds, producing new substances. Also called a reaction.
Chemical property: A trait you can only observe by letting the sample turn into something new.
Compound: A pure substance built from two or more elements bonded in a fixed ratio.
Conversion factor: A fraction made from an equality, so its value is exactly one.
Density: Mass divided by volume, usually in g/cm³ for solids and liquids.
Derived unit: A unit made by multiplying or dividing base units, such as m/s.
Dimensional analysis: Carrying units through a calculation and using them to check the setup.
Element: A pure substance made of only one kind of atom.
Extensive property: A property that changes with the amount of sample, such as mass.
Heterogeneous mixture: A mixture with parts you can see and separate, like sand in water.
Homogeneous mixture: A mixture that looks uniform throughout. Also called a solution.
Intensive property: A property that stays the same at any amount, such as density.
Law of conservation of matter: The rule that matter is neither created nor destroyed in a chemical change.
Physical change: A change in form or state that leaves the substance itself alone.
Physical property: A trait you can measure while the sample stays the same substance.
Precision: How close repeated measurements are to each other.
Significant figures: The digits of a measurement that carry real information about its size.
Uncertainty: The amount of doubt that rides along with every measurement.

Check yourself

1. Is clean dry air an element, a compound or a mixture?

A homogeneous mixture. Air is mostly nitrogen and oxygen molecules that are not bonded to each other. The ratio can shift from place to place, so it is not a compound.

2. Which state keeps its own volume but takes the shape of its container?

A liquid. Its particles still touch, so the volume holds, but they slide freely, so the shape gives way. A solid keeps both and a gas keeps neither.

3. Chopping wood and burning wood. Which one is a chemical change, and how can you tell?

Burning. It makes new substances, including carbon dioxide gas, water vapor and ash. Chopping only makes smaller pieces of the very same wood.

4. How many significant figures are in 0.03080?

Four. The leading zeros only place the decimal point. The 3, the captive 0, the 8 and the trailing 0 all count, since a decimal point is shown.

5. Multiply 6.02 by 2.1 and report the answer properly.

13. The raw product is 6.02 × 2.1 = 12.642. The weaker value, 2.1, has two significant figures, so round to two: 13.

6. Add 24.681 g, 0.35 g and 1.4 g, then report the sum properly.

26.4 g. The raw sum is 24.681 + 0.35 + 1.4 = 26.431 g. The 1.4 g is known only to the tenths place, so the sum stops there.

7. Convert 3.50 kg into milligrams.

3.50 × 10⁶ mg. Chain two factors: 3.50 kg × (1000 g per kg) × (1000 mg per g) = 3,500,000 mg. Both factors are exact, so keep the three figures from 3.50.

8. A 250.0 mL sample of liquid has a mass of 227.5 g. What is its density?

0.9100 g/mL. Divide mass by volume: 227.5 g ÷ 250.0 mL = 0.91 g/mL exactly. Both values hold four significant figures, so write it as 0.9100 g/mL. Since this is below 1.00 g/mL, the liquid would float on water.

9. A gas cylinder reads 310. K. What is that in degrees Celsius?

37 °C. Subtract: 310. − 273.15 = 36.85. The 310. value is known only to the ones place, so round there and report 37 °C. That is near body temperature.

10. Aluminum has a density of 2.70 g/cm³. Find the mass of a cube 3.00 cm on each edge.

72.9 g. The volume is 3.00 × 3.00 × 3.00 = 27.0 cm³. Then mass = density × volume = 2.70 g/cm³ × 27.0 cm³ = 72.9 g.

11. Four shots land in a tight clump near the edge of the target. Are they accurate, precise, both or neither?

Precise but not accurate. The shots agree closely with each other, which is precision. They miss the true center, which means poor accuracy. A tool with a steady offset behaves this way.

12. In a sealed flask, 10.0 g of iron reacts fully with 4.30 g of oxygen to form rust. What mass of rust forms?

14.3 g. Matter is conserved, so the product mass equals the total reactant mass: 10.0 g + 4.30 g = 14.3 g. The flask is sealed, so no oxygen can escape and none can sneak in.

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