Density Transitional Reasoning Download PDF

Questions

1. 1.

   A student investigates how the volume of a substance changes during a phase transition while its mass is strictly conserved. The student places a solid block of pure ice with a mass of 180 g and a density of 0.90 g/cm³ into a sealed, graduated container. After the ice melts completely into liquid water with a density of 1.00 g/cm³ at constant mass, the student determines the resulting volume of the liquid. By how much did the volume of the substance change during this melting process?

   • A) It increased by 20 cm³.
   • B) It remained unchanged.
   • C) It decreased by 18 cm³.
   • D) It decreased by 20 cm³.
2. 2.

   A student investigates the mass-volume relationships of two homogeneous solid materials, P and Q, at room temperature. Laboratory measurements show that the mass of Material P increases by 42 g for every 14 cm³ increase in volume, while a uniform block of Material Q has a volume of 40 cm³ and a mass of 200 g. If the student prepares a 100 cm³ component made of Material P, what volume of Material Q is required to manufacture a component with the exact same mass?

   • A) 40 cm³
   • B) 60 cm³
   • C) 100 cm³
   • D) 167 cm³
3. 3.

   A materials engineer examines a solid composite part fabricated by fusing Metal A (density 3.0 g/cm³) and Metal B (density 7.0 g/cm³) without any internal voids or change in total volume. On laboratory instruments, the finished component is measured to have a total volume of 100 cm³ and a total mass of 540 g. Based on these measurements, what is the mass of Metal B contained in the component?

   • A) 120 g
   • B) 280 g
   • C) 420 g
   • D) 378 g
4. 4.

   A student investigates how the proportion of components affects the density of a liquid mixture without volume contraction. Liquid X has a density of $0.80\text{ g/cm}^3$ and Liquid Y has a density of $1.20\text{ g/cm}^3$. In Trial 1, the student prepares a mixture using equal volumes of Liquid X and Liquid Y, while in Trial 2, the student prepares a mixture using equal masses of Liquid X and Liquid Y. Which statement correctly identifies and explains the density obtained in each trial?

   • A) Trial 1 yields $1.00\text{ g/cm}^3$ because equal volumes result in an arithmetic average of densities, whereas Trial 2 yields $0.96\text{ g/cm}^3$ because the less dense liquid occupies a larger fraction of the total volume.
   • B) Trial 1 yields $0.96\text{ g/cm}^3$ because density depends inversely on volume, whereas Trial 2 yields $1.00\text{ g/cm}^3$ because equal masses result in an arithmetic average of densities.
   • C) Both Trial 1 and Trial 2 yield $1.00\text{ g/cm}^3$ because both mixtures contain identical 1:1 ratios of the two component liquids.
   • D) Trial 1 yields $1.00\text{ g/cm}^3$ because equal volumes balance the densities, whereas Trial 2 yields $1.04\text{ g/cm}^3$ because the denser liquid exerts a greater mass influence on the mixture.
5. 5.

   A student investigates the difference between the bulk density and the true solid density of a granular material. The student pours dry quartz sand with a mass of 160 g into an empty graduated cylinder, where the sand settles to an apparent bulk volume of 100 cm³. Next, the student slowly pours 50 cm³ of water into the cylinder, allowing the water to completely fill all pore spaces between the sand grains without trapping any air bubbles, which results in a final total volume reading of 114 cm³. Based on these measurements, what is the actual density of the solid quartz material forming the sand grains?

   • A) 1.40 g/cm³
   • B) 1.60 g/cm³
   • C) 2.50 g/cm³
   • D) 3.20 g/cm³
6. 6.

   A student conducts an experiment to determine the density of an irregularly shaped piece of paraffin wax that floats in water. On a digital balance, the dry wax sample has a mass of 48.0 g. To measure its volume, the student submerges a dense metal sinker into a graduated cylinder containing water, reading a volume of 160 cm³, and then completely submerges both the sinker and the attached wax sample together, reading a volume of 220 cm³. Based on these measurements, what is the density of the paraffin wax?

   • A) 0.80 g/cm³
   • B) 1.25 g/cm³
   • C) 0.40 g/cm³
   • D) 0.22 g/cm³
7. 7.

   An equal-arm balance is in equilibrium with an identical empty beaker resting on each pan. A student pours 240 cm³ of Liquid X, which has a density of 0.75 g/cm³, into the left-hand beaker. To return the balance to equilibrium, the student gradually pours Liquid Y, which has a density of 1.20 g/cm³, into the right-hand beaker. What volume of Liquid Y must be added to restore balance?

   • A) 180 cm³
   • B) 150 cm³
   • C) 240 cm³
   • D) 384 cm³
8. 8.

   A materials engineer examines two solid, uniform cubic blocks manufactured from the same titanium alloy. Cube 1 has an edge length of 2.0 cm and a mass of 36.0 g, while Cube 2 has an edge length of 4.0 cm. Since both cubes consist of the identical homogeneous material at the same temperature, what is the density of the alloy, and what is the mass of Cube 2?

   • A) Density: 4.5 g/cm³, Mass of Cube 2: 72.0 g
   • B) Density: 4.5 g/cm³, Mass of Cube 2: 288.0 g
   • C) Density: 4.5 g/cm³, Mass of Cube 2: 144.0 g
   • D) Density: 9.0 g/cm³, Mass of Cube 2: 576.0 g
9. 9.

   An aerospace engineer redesigns a solid drone component to minimize overall aircraft mass while keeping its exact physical dimensions unchanged. The original part is manufactured from a zinc alloy with a density of 6.8 g/cm³ and has a measured mass of 340 g. The engineer replaces this part with an identical-volume component fabricated from a carbon composite with a density of 1.8 g/cm³. By how many grams is the mass of the component reduced after this material substitution?

   • A) 90 g
   • B) 190 g
   • C) 250 g
   • D) 290 g
10. 10.

    Three mutually immiscible liquids—Liquid X (density 0.80 g/cm³), Liquid Y (density 1.00 g/cm³), and Liquid Z (density 1.25 g/cm³)—are poured into a tall transparent cylinder and allowed to settle into stable layers. A solid bead A with a mass of 45 g and a volume of 50 cm³, and a solid bead B with a mass of 66 g and a volume of 60 cm³, are then gently introduced into the cylinder. Assuming neither bead absorbs liquid or dissolves, where do bead A and bead B settle at equilibrium?

    • A) Bead A floats at the top surface of Liquid X, while bead B rests at the boundary between Liquid X and Liquid Y.
    • B) Bead A rests at the boundary between Liquid Y and Liquid Z, while bead B sinks to the bottom of the cylinder.
    • C) Bead A rests at the boundary between Liquid X and Liquid Y, while bead B rests at the boundary between Liquid Y and Liquid Z.
    • D) Both bead A and bead B sink through all liquids and rest at the bottom of the cylinder.
11. 11.

    A researcher investigates how temperature affects the density of vegetable oil. At 20°C, a 460 g sample of the oil occupies a volume of 500 cm³. When heated to 70°C, the oil expands to a volume of 520 cm³ with no loss of mass. A rigid polymer bead with a mass of 22.5 g and an invariable volume of 25.0 cm³ is tested in the oil at both temperatures. Which statement correctly describes the behavior of the bead at each temperature?

    • A) The bead sinks at 20°C because its mass is concentrated, but floats at 70°C because heating increases the upward buoyant capability of the oil.
    • B) The bead floats at both temperatures because the total mass of the oil sample remains much greater than the mass of the bead.
    • C) The bead sinks at both temperatures because the thermal expansion of the oil reduces its overall surface tension and support.
    • D) The bead floats at 20°C because its density (0.90 g/cm³) is less than that of the oil (0.92 g/cm³), but sinks at 70°C because thermal expansion lowers the oil's density to approximately 0.885 g/cm³.
12. 12.

    An airtight gas syringe contains a trapped sample of air with a volume of 150 cm³ and a density of 1.20 kg/m³ at room temperature. A student pushes the plunger inward without allowing any air to escape, compressing the sample to a final volume of 50 cm³ while the temperature remains constant. Based on the physical definition of density, what is the density of the compressed air, and what happens to the total mass of the trapped air?

    • A) The density remains 1.20 kg/m³, and the mass decreases by a factor of 3.
    • B) The density decreases to 0.40 kg/m³, and the mass remains unchanged.
    • C) The density increases to 3.60 kg/m³, and the mass remains unchanged.
    • D) The density increases to 3.60 kg/m³, and the mass increases by a factor of 3.
13. 13.

    A chemical technician prepares a uniform solution by thoroughly mixing two miscible liquids, Liquid A and Liquid B, without any change in total volume. Liquid A has a density of $0.70\text{ g/cm}^3$ and Liquid B has a density of $1.20\text{ g/cm}^3$. If the technician combines $140\text{ g}$ of Liquid A with $360\text{ g}$ of Liquid B, what is the density of the resulting mixture?

    • A) $0.95\text{ g/cm}^3$
    • B) $1.00\text{ g/cm}^3$
    • C) $1.06\text{ g/cm}^3$
    • D) $1.12\text{ g/cm}^3$
14. 14.

    A laboratory student uses a specific gravity bottle to find the density of an unknown liquid without using a graduated cylinder. The dry, empty bottle has a mass of 50.0 g, and its mass increases to 150.0 g when completely filled with pure water of density 1.00 g/cm³. After being emptied and thoroughly dried, the same bottle is completely filled with the unknown liquid, yielding a total mass of 132.0 g. What is the density of the unknown liquid?

    • A) 1.32 g/cm³
    • B) 0.82 g/cm³
    • C) 0.88 g/cm³
    • D) 1.22 g/cm³
15. 15.

    An overflow beaker filled to the brim with an oil of density 0.80 g/cm³ is placed on a digital scale, and the scale is tared to zero. A solid metal cylinder with a mass of 240 g and a volume of 60 cm³ is gently lowered into the beaker until it rests at the bottom, causing the displaced oil to spill entirely into an external dish. Based on the density of the liquid and the properties of the cylinder, what is the new reading displayed on the digital scale?

    • A) 240 g
    • B) 180 g
    • C) 192 g
    • D) 48 g
16. 16.

    A technician tests whether a decorative brass artifact is solid or contains an internal hollow space. The artifact has an external volume of 60 cm³ and a mass of 340 g. Given that the density of pure brass is 8.5 g/cm³, what can be concluded about the internal structure of the artifact?

    • A) It is hollow and has an internal cavity volume of 10 cm³.
    • B) It is hollow and has an internal cavity volume of 20 cm³.
    • C) It is hollow and has an internal cavity volume of 40 cm³.
    • D) It is completely solid and has no internal cavity.
17. 17.

    In an experiment to determine the density of an unknown liquid without transferring it between containers, a student measures the combined mass of a graduated cylinder and the liquid inside it. The scale records a total mass of 58 g when the cylinder contains 30 cm³ of the liquid, and 98 g when more liquid is added to reach a volume of 80 cm³. Based on this data, what are the density of the liquid and the mass of the empty cylinder?

    • A) Density is 1.25 g/cm³, and the mass of the empty cylinder is 20.5 g.
    • B) Density is 1.93 g/cm³, and the mass of the empty cylinder is 0 g.
    • C) Density is 0.80 g/cm³, and the mass of the empty cylinder is 34 g.
    • D) Density is 0.80 g/cm³, and the mass of the empty cylinder is 24 g.
18. 18.

    A uniform solid block with a density of 1.0 g/cm³ sinks to the bottom when placed in Liquid X (density 0.8 g/cm³) and floats when placed in Liquid Y (density 1.2 g/cm³). A student cuts this block into two unequal pieces, such that Piece 1 contains one-third of the original volume and Piece 2 contains two-thirds of the original volume. Which statement correctly predicts and explains the behavior of these two pieces when placed separately into the same liquids?

    • A) Both Piece 1 and Piece 2 will sink in Liquid X and float in Liquid Y because density is an intensive property that remains unchanged regardless of the size of the piece.
    • B) Piece 1 will float in Liquid X because its smaller mass reduces its density below that of Liquid X, while Piece 2 will sink.
    • C) Piece 2 will sink in Liquid Y because its larger mass and weight overcome the upward buoyant force of Liquid Y.
    • D) Both pieces will float in Liquid X because cutting a solid object decreases its density proportionally to the reduction in volume.
19. 19.

    A student investigates four liquid samples at constant temperature to determine whether any of them represent the same pure liquid: Sample P (mass 45 g, volume 50 cm³), Sample Q (mass 72 g, volume 80 cm³), Sample R (mass 90 g, volume 75 cm³), and Sample S (mass 120 g, volume 150 cm³). Density serves as a characteristic intensive property for identifying pure substances under identical conditions. Based on the student's measurements, which conclusion is scientifically valid?

    • A) Sample R has the lowest density among all four samples because it contains the smallest volume relative to its high mass.
    • B) Samples Q and S represent the same pure substance because both have larger masses and volumes than Sample P.
    • C) Samples P and R must consist of the same liquid because an increase in volume from 50 cm³ to 75 cm³ matches their mass ratio.
    • D) Samples P and Q could be the same pure substance because both have an identical density of 0.90 g/cm³.
20. 20.

    A student investigates the densities of two solid objects, K and L. Object K has a mass of 160 g and causes the water level in a graduated cylinder to rise from 100 cm³ to 140 cm³ when fully submerged. Object L is a rectangular block with a mass of 270 g and edge lengths of 3.0 cm, 3.0 cm, and 5.0 cm. Based on these measurements, which statement correctly compares the densities of the two objects?

    • A) Object K is denser than Object L because displacing less liquid always indicates a more compact solid structure.
    • B) Object K and Object L have equal densities because both objects yield a mass-to-volume ratio of 4.5 g/cm³.
    • C) Object L is denser than Object K because its calculated density is 6.0 g/cm³, whereas Object K has a density of 4.0 g/cm³.
    • D) Object L is denser than Object K solely because its mass of 270 g is greater than the 160 g mass of Object K.