Guided example: solution

Step 1 · Find the stage

Guided example: solution

The prediction: if color warns birds off, the dull models draw more attacks. Line (4) agrees, so the conclusion keeps the hypothesis.

Guided example: solution

Line (2) explains why, but one week in one forest is not wide testing. It is still a hypothesis, not a theory.

Guided example: solution

Guided example: the route on the map

Practice 1: answer D

A took floating for weightless. Helium has mass; it is lighter than the air it pushes aside. B took a smell for a feeling: the smell is coffee molecules drifting through the air, and they have mass and fill space. C took invisible for empty: the jar's air has mass and fills the jar.

Practice 1: the route on the map

Practice 2: answer B

A throws out the data to save the hypothesis; a disagreeing result is what a test exists to catch. C: one measurement cannot make a law, and this one contradicts the claim. D: a theory explains why and has survived wide testing; this claim failed its first test.

Practice 2: the route on the map

Practice 3: answer D

A: no one watches atoms join; the statement is inferred from measurements, not seen. B: a hypothesis is still on trial; this one has passed two centuries of tests. C: "every compound" sounds like a law, but a law stops at what happens; this sentence goes on to say why.

Practice 3: the route on the map

Practice 4: answer A

B swaps law and theory: (2) gives no reason, and (3) explains. C: the pop was observed, but "probably because" adds an untested cause. D takes unseen particles for a guess; the particle picture has passed wide testing. E calls every explanation a theory; (1) explains one balloon and was never tested.

Practice 4: the route on the map

Guided example: solution

Step 1 · Count the kinds of particles

Every particle in the cylinder is the same Cl₂ molecule. One kind of particle: a pure substance.

Guided example: solution

A pure substance, so count elements, not atoms.

Guided example: solution

Guided example: solution

Guided example: the route on the map

Practice 1 · answer: D

A counted atoms, not kinds of atoms: four bonded P atoms are still one element. B: looking the same everywhere shows one phase, and one kind of particle already makes the sample pure. C: every pure substance has a fixed formula, elements included; this formula holds only P.

Practice 1: the route on the map

Worked example 1: solution

Step 1 · Count the kinds of particles

Every particle in the tank is the same CO₂ molecule. One kind of particle: a pure substance.

Worked example 1: solution

A pure substance, so count elements. The formula holds carbon and oxygen: two elements.

Worked example 1: solution

Worked example 1: solution

Worked example 1: the route on the map

Worked example 2: solution

A common first attempt

Stir in more salt: still clear, still salt water. The ratio changed with no chemical reaction. A compound's composition cannot change without one.

Worked example 2: solution

Water molecules and dissolved salt: two kinds. A mixture, and boiling, a physical change, separates them.

Worked example 2: solution

A mixture, so count phases. One phase, uniform throughout:

Worked example 2: solution

Worked example 2: the route on the map

Your turn: the route on the map

Practice 2 · answer: B

A: same properties throughout shows one phase, not one substance; the composition can still vary. C: uniform appearance does not show bonding; the acid and water separate by distillation, a physical change. D: several substances can share one phase; classification follows the phase count, not the substance count.

Practice 2: the route on the map

Worked example 3: kinds of particles

Step 1 · Count the kinds of particles

Worked example 3: kinds of particles

Step 1 · Count the kinds of particles

Each sample holds more than one kind of particle: three mixtures, in three physical states.

Worked example 3: phases and the class

Step 2 · Count the elements or the phases

Worked example 3: phases and the class

Step 3 · Name the class

Worked example 3: phases and the class

Step 3 · Name the class

Practice 3 · answer: C

Step 1: the same composition in every sample means one kind of particle, a pure substance. Step 2: heating turns it into carbon and water, new substances: a chemical change. A pure substance that a reaction breaks down holds more than one element: a compound.

A: a mixture varies in composition and separates by a physical change; charring is chemical. B: fixed composition marks any pure substance, and no reaction breaks an element down. D: counts the phases of the products, not of the sample.

Practice 3: the route on the map

Practice 4 · answer: B

Step 1: the same composition in every sample means one kind of particle, a pure substance. Step 2: turning into a yellow powder is a chemical change, but the powder outweighs the bead, so oxygen from the air joined the metal. Nothing broke off: one element.

C read every chemical change as a breakdown; this one combines the metal with oxygen. A: uniform shows one phase, and fixed composition rules out a mixture. D counted the bead and the powder after heating, not the phases of the sample.

Practice 4: the route on the map

Guided example: solution

Property or change?

"Boils at 78 °C" describes ethanol. It is a number on a label, not an event in a flask: a property.

Guided example: solution

Measuring the boiling point boils some ethanol. The vapor is still ethanol.

Guided example: solution

Guided example: solution

Guided example: the route on the map

Practice 1 · answer: D

A: boiling bubbles are the liquid's own vapor; nothing here boils, and CO₂ is neither vinegar nor baking soda. B: right verdict, false rule; melting ice is seen too, and it is physical. C: dissolving makes no gas; the foam is a new substance leaving the bowl.

Practice 1: the route on the map

Worked example 1: solution

Step 1 · Name the substance before and after

Melting: solid butter becomes liquid butter. Cool the pan and the same butter hardens back. Same substance, new form:

Worked example 1: solution

Browning: the butter becomes brown solids, smoke, and a sharp smell. Cooling leaves them brown. The butter is gone.

Worked example 1: solution

Worked example 1: solution

Worked example 1: the route on the map

Worked example 2: solution

Step 1 · Name the substance before and after

Worked example 2: solution

Worked example 2: solution

Both changes give off a gas. In (a) the gas is iodine, the same substance in a new state. In (b) oxygen bubbles out of a liquid that is not boiling.

Worked example 2: solution

Worked example 2: the route on the map

Practice 2 · answer: D

A: state is observed by looking; the liquid stays gasoline. B: floating compares two densities, and both liquids survive the comparison. C: evaporation trades liquid for vapor, still gasoline; chill the vapor and it condenses right back.

Practice 2: the route on the map

Practice 3 · answer: B

Practice 3 · answer: B

A: only oxygen on both sides, but O₃ is a different substance from O₂. C: a solid turning into gases looks like sublimation, yet two new formulas form. D: counts match, N: 2 = 2 · O: 4 = 4, as in every balanced equation; NO₂ still became N₂O₄.

Practice 3: the route on the map

Practice 4 · answer: A

B: "does not burn" still reports what a reaction test found, so it is a chemical property. C: (2) keeps the same formula, Cl₂, and only the state label changes; condensing is physical. It also drops (4). D: counts the condensation as a reaction because it is written as an equation.

Practice 4: the route on the map

Practice 5 · answer: C

A: melting-as-reaction slip; 2613 °C is extreme, but the liquid that forms is still CaO. B: density-as-reaction slip; density identifies lime, yet weighing and measuring a sample leaves it CaO. D: reads "a property of a chemical" as "a chemical property"; a data sheet lists both kinds, and a number with units never decides which.

Practice 5: the route on the map

Guided example: solution

Step 1 · Check the shape

The honey left the jar's shape and settled into the bowl's. It does not keep its own shape, so it is not a solid.

Guided example: solution

The honey covers the bottom of the bowl but does not fill it. It keeps its own volume: a liquid.

Guided example: solution

Honey's particles touch, which holds the 250 mL. They slide past one another, which gives up the shape. They just slide slowly.

Guided example: the route on the map

Practice 1 · answer: B

A matched only the touching: solid particles touch but stay locked in place. C matched only the motion: gas particles move freely, but far apart, not touching. D matched only the touching too: a solid's particles do not slide, so a solid keeps its own shape.

Practice 1: the route on the map

Practice 2 · answer: C

A resized the particles: particles keep their size in every state, and only the space between them grows. B made a new substance: the bubbles are water vapor, and H₂O sits on both sides of the arrow. D describes hot liquid water: touching particles would keep their own volume, and steam fills its container.

Practice 2: the route on the map

Practice 3 · answer: A

Two checks, one per sample. The helium fills its jug; the water keeps its 0.50 L.

B kept both volumes: 1.5 + 0.50 = 2.0, the helium treated as a liquid. C filled both jugs: 6.0 + 6.0 = 12.0, the water treated as a gas. D swapped the rules: 1.5 + 6.0 = 7.5, the gas kept its volume and the liquid spread.

Practice 3: the route on the map

Practice 4 · answer: C

Two moves: name each state with the two checks, then read the particle row.

Practice 4 · answer: C

Practice 4: the route on the map

Guided example: solution

Step 1 · Compute the range Step 2 · Compute the average

The range uses the trials alone. The average divides their sum by 3, an exact count.

Guided example: solution

Step 1 · Compute the range Step 2 · Compute the average

Range as a percent of the average; miss as a percent of the true value.

Guided example: solution

Step 1 · Compute the range Step 2 · Compute the average

Guided example: the route on the map

Practice 1 · answer: B

A swapped the definitions: W's 5.673-g average sits on the true mass, which is accuracy. C counted digits: decimals show a finer scale, not agreement. D judged by one trial: 5.67 g matches, but the other two readings miss.

Practice 1 · answer: B

Practice 1: the route on the map

Worked example 1: solution

Step 1 · Compute the range Step 2 · Compute the average

Worked example 1: solution

Step 1 · Compute the range Step 2 · Compute the average

A spread of 0.12% on a 50-g measurement: the trials agree. Precise.

Worked example 1: solution

Step 1 · Compute the range Step 2 · Compute the average

Worked example 1: solution

Step 1 · Compute the range Step 2 · Compute the average

Worked example 1: the route on the map

Worked example 2: solution

Step 1 · Compute the range Step 2 · Compute the average

Worked example 2: solution

Step 1 · Compute the range Step 2 · Compute the average

Not precise. Precision compares the trials with one another; the true value is not part of that comparison.

Worked example 2: solution

Step 1 · Compute the range Step 2 · Compute the average

Accurate. Nearness to the true value is accuracy's comparison, the one the first answer called precision.

Worked example 2: solution

Step 1 · Compute the range Step 2 · Compute the average

Worked example 2: the route on the map

Practice 2 · answer: D

C divided by the average, not the true value: 0.70 ÷ 12.04 × 100 = 5.8. B judged the set by one trial: (11.98 − 11.34) ÷ 11.34 × 100 = 5.6. A computed precision's number, the relative range: (12.09 − 11.98) ÷ 12.04 × 100 = 0.91.

Practice 2: the route on the map

Practice 3 · answer: A

C swapped the definitions: the 0.06-mL agreement is precision, and the 1.31-mL miss is inaccuracy. B judged the set by one trial: 26.28 − 25.00 = 1.28 mL compares a single reading with the true value, which is accuracy's comparison. D counted digits: significant figures report how finely the pipette is read, and every reading is still about 1.3 mL high.

Practice 3 · answer: A

Practice 3: the route on the map

Practice 4 · answer: D

A treated the 2% bar as 2 grams: 0.18 g is small only next to a large mass, and on a 5-g weight it is 3.6%. B swapped the definitions: relative range judges precision, percent error judges accuracy. C let one verdict answer both: high and low readings cancel in the average.

Practice 4: the route on the map

Practice 5 · answer: C

A treated the bar as 2 g or 2 mL: set 3's 2.9-g miss fails a 2-g bar but is only 1.2% of 250.0 g, and set 1's 0.064-g miss passes it but is 3.2%. B swapped the definitions on sets 1 and 2. D let one verdict answer both: set 2 scatters, yet its average lands within 0.2%.

Practice 5 · answer: C

Practice 5: the route on the map