Chemical properties and reactions

Evidence: The passage says "The density of water is 1.0 g/cm³. An object that is less dense than water floats in it." The Part 1 table gives each object's mass and volume.

Step by step:

1. Wood block: 30 \div 50 = 0.6 g/cm³ (less than 1.0 → floats).
2. Candle wax: 18 \div 20 = 0.9 g/cm³ (less than 1.0 → floats).
3. Rubber stopper: 33 \div 30 = 1.1 g/cm³ (more than 1.0 → sinks).
4. Glass marble: 15 \div 6 = 2.5 g/cm³ (more than 1.0 → sinks).

Only the wood block and the candle wax will float.

Tip: Floating depends on density (mass per volume), not on mass alone. The marble has the smallest mass but the greatest density, so it sinks.

Evidence: Trial 1 began at "250.0 g in total," and "when the bubbling stopped, the balance read 247.8 g."

Step by step:

1. By the law of conservation of mass, the products weigh the same as the reactants, so any mass missing from the balance must have left the flask.
2. The flask was open and the mixture "fizzed and bubbled," so carbon dioxide gas escaped into the room.
3. Missing mass: 250.0 - 247.8 = 2.2 g.

About 2.2 g of carbon dioxide escaped.

Tip: When an open container loses mass during a reaction that makes bubbles, the lost mass equals the gas that escaped. Subtract after from before.

Evidence: The graph shows the solubility of sugar at 60 °C as 287 g per 100 g of water. The passage says the graph shows "the greatest mass of sugar that can dissolve in 100 g of water at different temperatures."

Step by step:

1. Find 60 °C on the x-axis (water temperature).
2. Move straight up to the plotted line. The data point is just below the 300 g gridline.
3. Read across to the y-axis: about 287 g.
4. Do not confuse this with neighboring points: 238 g at 40 °C and 362 g at 80 °C.

About 287 g of sugar can dissolve at 60 °C.

Check: 287 g lies between the 40 °C value (238 g) and the 80 °C value (362 g), as expected because the curve rises steadily.

Tip: When reading a graph, say the axis labels aloud: x is temperature, y is grams dissolved. That prevents reading the wrong axis.

Evidence: The passage says "a pH below 7 is acidic" and that Ana's soil pH "was 4.8." The chart lists blueberries at "4.5 to 5.5" and potatoes at "5.0 to 6.0."

Step by step:

1. Classify: 4.8 < 7, so the soil is acidic, not basic or neutral.
2. Match a plant: 4.8 is inside the blueberry range (4.5 to 5.5). It is just below the potato range, which starts at 5.0, and far below tomatoes (6.0 to 6.8) and lilacs (7.0 to 8.0).

The answer is The soil is acidic, and it suits blueberries without any change.

Check: Blueberries are well known as acid-loving plants, which fits.

Tip: On the pH scale, low numbers are acidic, 7 is neutral and high numbers are basic. A lower number means more acidic, not less.

Evidence: In Trial 1 (open flask) the mass dropped from 250.0 g to 247.8 g. In Trial 2 (sealed with a balloon) "the balloon inflated" and the balance "still read 252.0 g." The passage states that "matter is neither created nor destroyed."

Step by step:

1. Both trials used the same reaction, which produces carbon dioxide gas.
2. In Trial 1 the gas escaped into the air, so the balance no longer measured it.
3. In Trial 2 the balloon trapped the gas (that is why it inflated), so everything stayed on the balance and the mass did not change.
4. Together, the trials show that mass is conserved; the open flask only seemed to lose mass.

The answer is The gas produced escaped from the open flask but was trapped by the balloon, so mass was conserved in both trials.

Tip: When two trials differ in only one condition (open vs. sealed), that condition explains the difference in results.

Evidence: The passage says the graph shows "how many grams of two salts can dissolve in 100 g of water at different temperatures." On the potassium nitrate curve, the point at 60 °C is at 110 g.

Step by step:

1. Find 60 °C on the horizontal (temperature) axis.
2. Move straight up to the potassium nitrate curve (not the nearly flat sodium chloride line).
3. Read across to the vertical axis: 110 g.
4. Because solubility is the greatest amount that can dissolve, 110 g is the maximum at 60 °C.

The answer is 110 g.

Tip: On a graph with two lines, say the name of the line out loud before you read it. Reading the wrong line is the most common error.

Evidence: On the graph at 40 °C, potassium nitrate's solubility is 64 g and sodium chloride's is 36 g per 100 g of water. The passage explains that a solution holding "less than the maximum is unsaturated."

Step by step:

1. Potassium nitrate: 50 g added, maximum 64 g. Since 50 < 64, all of it dissolves, and the solution is unsaturated (14 g more could still dissolve).
2. Sodium chloride: 50 g added, maximum 36 g. Only 36 g dissolves, so 50 - 36 = 14 g stays undissolved at the bottom, and the solution is saturated.
3. Note the trap: at 0 °C sodium chloride is more soluble than potassium nitrate, but by 40 °C the order has switched.

The answer is All of the potassium nitrate dissolves, but about 14 g of sodium chloride stays undissolved.

Tip: For "will it all dissolve?" questions, compare the amount added with the solubility at that exact temperature. More than the maximum means leftover solid.

Evidence: The diagram shows lemon juice at about pH 2 and black coffee at about pH 5. The passage says "each change of one pH unit means a tenfold change in acidity."

Step by step:

1. Difference in pH: 5 - 2 = 3 units.
2. Each unit is a factor of 10, so three units is 10 \times 10 \times 10 = 10^3 = 1{,}000
3. Lemon juice has the lower pH, so it is the more acidic one.

Lemon juice is about 1,000 times more acidic than black coffee.

Tip: On logarithmic scales (pH, earthquake magnitude, decibels), never just subtract the numbers. Turn the difference into a power of 10.

Evidence: The passage says the dish and steel wool started at "30.0 g," and after burning "the balance read 31.6 g." It also says "the iron combined with oxygen gas from the surrounding air" and "No pieces fell out of the dish."

Step by step:

1. The extra mass on the balance came from something added: oxygen from the air that became part of the iron oxide.
2. Subtract the starting mass from the final mass: 31.6\text{ g} - 30.0\text{ g} = 1.6\text{ g}

About 1.6 g of oxygen combined with the iron.

Check: Conservation of mass still holds: mass of iron + mass of oxygen (1.6 g) = mass of iron oxide. The balance just did not "see" the oxygen at the start because it was in the air, not in the dish.

Tip: When a product gains mass in an open container, look for a reactant that came from the air (usually oxygen). When it loses mass, look for a gas that escaped.

Evidence: The stem says that after the solid dissolves, "the pack feels very cold." A temperature drop in the pack means thermal energy is leaving its surroundings (your skin, the ankle) and going into the pack.

Step by step:

1. An exothermic process releases thermal energy to its surroundings, which feel warmer (like a hand warmer or a campfire).
2. An endothermic process absorbs thermal energy from its surroundings, which feel colder.
3. The cold pack takes in thermal energy from the ankle, so the ankle cools. The process is endothermic.
4. "Cold" does not flow out of the pack. Thermal energy always moves from warmer objects (the ankle) to cooler ones (the pack).

The answer is The process is endothermic: it absorbs thermal energy from the surroundings, such as the ankle.

Check: The swelling goes down because the ankle loses thermal energy to the pack, exactly what an endothermic process predicts.

Tip: Exo = exit (energy leaves, surroundings warm up). Endo = enter (energy goes in, surroundings cool down).

Evidence: In the expression 2\,\text{Ca(NO}_3\text{)}_2, the coefficient 2 means two formula units of calcium nitrate. The subscript 2 after the parentheses doubles everything inside them.

Step by step:

1. Inside the parentheses, \text{NO}_3 has 3 oxygen atoms.
2. The subscript 2 outside the parentheses means two \text{NO}_3 groups: 3 \times 2 = 6 oxygen atoms in one \text{Ca(NO}_3\text{)}_2.
3. The coefficient 2 in front means two of these units: 6 \times 2 = 12 oxygen atoms.

There are 12 oxygen atoms.

Check: Count the other atoms the same way: calcium 1 \times 2 = 2, nitrogen 1 \times 2 \times 2 = 4. Total atoms = 2 + 4 + 12 = 18.

Tip: A coefficient multiplies the whole formula. A subscript after parentheses multiplies everything inside the parentheses. A subscript after one symbol applies only to that element.

Evidence: The passage says "A liquid that is less dense floats on top of a liquid that is denser." The table gives each liquid's mass and volume.

Step by step:

1. Compute each density with D = \dfrac{m}{V}:
   • Honey: 28.4 \div 20.0 = 1.42 g/mL
   • Dish soap: 31.8 \div 30.0 = 1.06 g/mL
   • Water: 40.0 \div 40.0 = 1.00 g/mL
   • Vegetable oil: 23.0 \div 25.0 = 0.92 g/mL
2. Least dense on top, densest on the bottom: oil (0.92), water (1.00), dish soap (1.06), honey (1.42).

The order from top to bottom is vegetable oil, water, dish soap, honey.

Check: The water sample has the greatest mass (40.0 g), but it is not on the bottom, because density depends on mass and volume.

Tip: Layering, floating and sinking depend on density, not on how much of a substance there is. Always divide before you compare.

Evidence: In Trials 1–4 the tablets are all "Whole" while the water temperature rises from 10 °C to 55 °C, and the times drop from 72 s to 45 s to 28 s to 18 s. The passage says "A shorter time means a faster reaction."

Step by step:

1. Only one variable changes in Trials 1–4: the water temperature. Tablet form and water volume stay the same.
2. As the temperature goes up, the time goes down every time.
3. Shorter time = faster reaction, so warmer water makes the reaction faster.
4. The experiment measured time, not the amount of gas, so a claim about more gas is not supported.

The answer is The reaction is faster in warmer water.

Check: In warmer water, particles move faster and collide more often and with more energy, which is the scientific reason reactions speed up with temperature.

Tip: Before choosing a conclusion, identify which variable changed and what was measured. A conclusion must be about those two things only.

Evidence: The chart lists asparagus at "6.5 to 7.5" and Ana's soil at "4.8." The passage says garden lime "is a base, so mixing it into soil neutralizes some of the acid and raises the pH," while sulfur "lowers the pH."

Step by step:

1. Ana's soil (4.8) is below the asparagus range (6.5 to 7.5), so she needs to raise the pH.
2. Raising pH means making the soil less acidic, which a base does by neutralizing acid.
3. Garden lime is a base and raises the pH. Sulfur would lower it further, the wrong direction.

The answer is Mix garden lime into the soil to raise the pH.

Check: Moving from 4.8 toward 6.5–7.5 means moving toward neutral (7), which is what neutralization does.

Tip: To raise pH, add a base. To lower pH, add an acid (or something that forms an acid). Neutralization always moves pH toward 7.

Evidence: The passage says "The pH scale is logarithmic: each drop of one pH unit means the soil is 10 times more acidic." Ana's soil is pH 4.8.

Step by step:

1. Difference in pH: 6.8 - 4.8 = 2 units.
2. Each unit multiplies the acidity by 10, so two units multiply it by 10 \times 10 = 10^2 = 100
3. Ana's soil has the lower pH, so it is the more acidic one.

Ana's soil is 100 times more acidic.

Check: Step by step: pH 6.8 → 5.8 is 10 times more acidic; 5.8 → 4.8 is another 10 times; 10 \times 10 = 100. ✓

Tip: For pH comparisons, subtract the pH values and raise 10 to that power. A difference of 1 means 10 times, 2 means 100 times, 3 means 1,000 times.

Evidence: Part 2 says the cube has "a mass of 158 g," and the water level rose from "40.0 mL" to "60.0 mL." It also says "1 mL = 1 cm³," and the reference table lists iron at 7.87 g/cm³.

Step by step:

1. Volume by displacement: 60.0 - 40.0 = 20.0 mL = 20.0 cm³.
2. Density: D = \frac{m}{V} = \frac{158\text{ g}}{20.0\text{ cm}^3} = 7.9\text{ g/cm}^3
3. Compare with the table: aluminum 2.70, zinc 7.14, iron 7.87, lead 11.34. The value 7.9 is closest to iron (7.87).
4. Why this works: density is a physical property, so every sample of iron has the same density no matter its size.

The cube is most likely iron.

Tip: In displacement problems, the object's volume is the change in the water level, not the final reading. Using 60.0 mL gives 158 \div 60 \approx 2.6 g/cm³, which wrongly points to aluminum.

Evidence: A chemical change produces one or more new substances with new properties. Common signs are an unexpected gas, a new color, light or heat given off, or a new solid (precipitate) forming when liquids are mixed.

Step by step:

1. Bubbles in boiling water: the bubbles are water vapor, still water. This is a change of state (physical).
2. Two clear, colorless solutions forming a yellow solid when mixed: a solid that was not there before, with a new color, appears. This is a precipitate, strong evidence of a new substance (chemical).
3. Drink powder disappearing in water and turning it red: dissolving is a physical change; the powder's own color simply spreads through the water, and evaporating the water would give the powder back.
4. Ice cubes slowly shrinking in a freezer: the ice turns directly into water vapor (sublimation), a change of state (physical).

The answer is Two clear, colorless solutions are mixed, and a yellow solid forms.

Check: Only choice B produces a substance with properties (yellow, solid, does not dissolve) that none of the starting materials had.

Tip: Bubbles and color alone are not proof. Ask whether a new substance formed or whether the same substance just changed state or mixed.

Evidence: The table shows Trial 2 (25 °C, Whole, 45 s) and Trial 5 (25 °C, Crushed into powder, 20 s). Trials 3 and 6 also differ only in tablet form (40 °C).

Step by step:

1. To test one variable, the trials must differ in that variable only. Here the variable is tablet form.
2. Trials 2 and 5: same temperature (25 °C), different form. A fair test.
3. Trials 1 and 5: different form and different temperature (10 °C vs 25 °C). Two variables change, so the effect of crushing cannot be separated.
4. Trials 4 and 6: also differ in both temperature (55 °C vs 40 °C) and form.
5. Trials 2 and 3: both whole tablets; only the temperature changes. This tests temperature, not crushing.

The answer is Trials 2 and 5.

Check: Comparing them: 45 s for whole vs 20 s for crushed, so crushing more than doubled the rate. (Trials 3 and 6 give the same conclusion: 28 s vs 12 s.)

Tip: In an experimental design question, list what is different between the two trials. If more than one thing differs, it is not a fair test.

Evidence: The passage says "The hot plate delivered thermal energy at a steady rate the whole time." The graph shows segment D flat at 100 °C, and the passage gives 100 °C as water's boiling point.

Step by step:

1. Energy is still being added during D (the rate never changed), so no energy is added cannot be the reason.
2. Segment D is at the boiling point, so liquid water is turning into steam.
3. To change from liquid to gas, particles must be pulled far apart, overcoming the attractions that hold them together in the liquid. The added energy goes into this job instead of making the particles move faster.
4. Temperature measures the average speed (kinetic energy) of the particles. If the energy is not speeding them up, the temperature stays the same until all the liquid has boiled.

The answer is The energy is being used to overcome the attractions between water particles as the liquid turns into gas.

Check: The same thing happens in segment B at 0 °C, where energy separates particles from the solid ice structure.

Tip: Flat segment on a heating curve = energy changing the state, not the temperature. Energy is still flowing in.

Evidence: The passage says "the iron combined with oxygen gas from the surrounding air" and states the law of conservation of mass: "the total mass of the products equals the total mass of the reactants." The equation shows two reactants: iron and oxygen.

Step by step:

1. At the start, the balance measured the dish and the iron only. The oxygen was in the air, not on the balance.
2. During burning, oxygen from the air joined the iron to form iron oxide, which stayed in the dish.
3. So the final reading includes the mass of the oxygen that was never counted at the start. The mass was moved from the air into the dish, not created.
4. Mass of iron + mass of oxygen = mass of iron oxide, so the law is not broken.

The best response is The mass of the oxygen from the air was not on the balance at the start; the iron plus the oxygen equals the mass of the iron oxide.

Check: If the reaction were done in a sealed container with the air inside it, the balance reading would not change.

Tip: In open-container experiments, mass seems to appear when a gas from the air is a reactant and seems to disappear when a gas is a product. Count every reactant and product, including gases.

Evidence: The table gives honey: mass 28.4 g, volume 20.0 mL. The passage gives D = \dfrac{m}{V}.

Step by step:

1. Density of honey: D = 28.4 \div 20.0 = 1.42 g/mL.
2. Solve the formula for volume: V = \dfrac{m}{D}.
3. Substitute: V = \frac{355\text{ g}}{1.42\text{ g/mL}} = 250\text{ mL}

Each jar holds 250 mL of honey.

Check: 250 \times 1.42 = 355 g. ✓ Honey is denser than water, so 355 g of honey should take up less than 355 mL, and 250 mL does.

Tip: Three forms of one formula: D = m/V, m = D \times V, V = m/D. Use the units to check: g ÷ (g/mL) = mL.

Evidence: The graph shows that 100 g of water can dissolve 238 g of sugar at 40 °C and 287 g at 60 °C. The passage says a saturated solution leaves "any extra sugar" undissolved as solid, and an unsaturated solution "holds less than that amount."

Step by step:

1. At 40 °C: the maximum is 238 g. Since 250 > 238, only 238 g dissolves, and 250 - 238 = 12 g stays solid. The solution is saturated.
2. At 60 °C: the maximum rises to 287 g. Since 250 < 287, all 250 g dissolves. The solution is now unsaturated: 287 - 250 = 37 g more could still dissolve.

The answer is At 40 °C the solution is saturated with about 12 g of sugar left undissolved; at 60 °C all the sugar dissolves and the solution is unsaturated.

Check: Heating raises solubility (the curve goes up), so the leftover crystals at 40 °C should dissolve when the mixture is heated, which matches.

Tip: Compare the amount added with the solubility at each temperature. Added more than the maximum → saturated with leftover solid. Added less → unsaturated.

Evidence: The pH scale is logarithmic: each change of one pH unit is a tenfold change in acidity, and lower pH means more acidic. Pure water is pH 7.

Step by step:

1. Write 1,000 as a power of ten: 1{,}000 = 10 \times 10 \times 10 = 10^3.
2. Three factors of 10 means a change of 3 pH units.
3. More acidic means a lower pH, so subtract: 7 - 3 = 4.

The lake sample has a pH of 4.

Check: Count down: pH 6 is 10 times more acidic than 7, pH 5 is 100 times, pH 4 is 1,000 times. ✓

Tip: To go from "times more acidic" to a pH change, count the zeros: 10 → 1 unit, 100 → 2 units, 1,000 → 3 units. Then move down the scale for more acidic.

Evidence: The passage says the hot plate "delivered thermal energy at a steady rate the whole time." The graph shows segment B (melting) lasting from 1 min to 9 min, and segment D (boiling) lasting from 19 min to 73 min.

Step by step:

1. Because energy flows in at a steady rate, energy added is proportional to time.
2. Melting (B): 9 - 1 = 8 min.
3. Boiling (D): 73 - 19 = 54 min.
4. Ratio: 54 \div 8 \approx 6.8. So boiling all the water took nearly 7 times as much energy as melting all the ice.
5. Compare the other claims: the liquid water warmed for 19 - 9 = 10 min (segment C), longer than melting took (8 min), so melting did not take more energy than warming the liquid. The temperature stays constant during both B and D, so it did not rise the whole time. The steam (E) warmed 20 °C in 1 min, while the liquid (C) warmed 100 °C in 10 min (10 °C per minute); steam warms faster, not more slowly.

The best-supported conclusion is Turning the liquid water into steam took more than six times as much energy as melting the ice.

Check: This matches measured values for water: about 2,260 J per gram to boil it, but only about 334 J per gram to melt ice, a ratio of about 6.8.

Tip: On a heating curve made with a steady heat source, the length of a segment measures energy. Compare lengths (time), not heights.

Evidence: The passage says "the iron combined with oxygen gas from the surrounding air." In the original setup, that oxygen was not on the balance at the start, so the reading rose from "30.0 g" to "31.6 g."

Step by step:

1. To show conservation of mass, every reactant and every product must be weighed both before and after. This means making a closed system.
2. Sealing the steel wool inside a flask that contains plenty of air (with a stopper) and igniting it there, using wires through the stopper, puts the iron and the oxygen on the balance from the start. Nothing can enter or leave.
3. Using more steel wool would just make the mass increase larger; it would not stop oxygen from entering.
4. Weighing only the iron oxide afterward, without the dish, still does not account for the oxygen that came from the air, which was not on the balance at the start.
5. Using a fan to burn it faster brings in even more outside oxygen while the dish is open.

The answer is Burn the steel wool inside a sealed flask filled with air, and weigh the whole flask before and after.

Check: In a sealed flask, the oxygen that joins the iron is already part of the mass before the reaction, so the reading should stay the same, just as in a sealed balloon-and-flask vinegar experiment.

Tip: Show that mass is conserved almost always means close the system: seal the container so no gas can get in or out.