Density Transitional Reasoning Practice

Questions

1. 1.

   An empty tank is filled by two taps, Tap K and Tap L, which supply miscible liquids of densities $1.2\text{ g/cm}^3$ and $1.8\text{ g/cm}^3$, respectively. Tap K is opened first, delivering liquid at a constant rate of $30\text{ cm}^3/\text{s}$ for 10 seconds. At that instant, without turning off Tap K, Tap L is opened at a constant rate of $20\text{ cm}^3/\text{s}$, and both taps continue to run together for an additional 10 seconds. Assuming no volume contraction occurs upon mixing, what is the density of the liquid mixture in the tank at the end of the 20-second period?

   • A) $1.50\text{ g/cm}^3$
   • B) $1.44\text{ g/cm}^3$
   • C) $1.35\text{ g/cm}^3$
   • D) $1.25\text{ g/cm}^3$
2. 2.

   A student prepares a homogeneous saline solution by dissolving 50 g of table salt into 160 cm³ of pure water with a density of 1.0 g/cm³. After the salt dissolves completely, the student observes that the total volume of the liquid in the graduated cylinder is 175 cm³. Based on these measurements, what is the density of the prepared saline solution?

   • A) 1.05 g/cm³
   • B) 1.20 g/cm³
   • C) 1.31 g/cm³
   • D) 0.91 g/cm³
3. 3.

   A student determines the density of an irregularly shaped piece of treated cork that floats in water. First, the student measures the mass of the dry cork on a digital balance as 36 g. Next, to measure its volume, the student fully submerges a steel sinker alone in a graduated cylinder of water, recording a level of 135 cm³, and then submerges both the sinker and cork tethered together, recording a level of 255 cm³. Assuming water has a density of 1.0 g/cm³, what is the density of the cork, and what volume of water does it displace when floating freely on its own?

   • A) 0.15 g/cm³ and 120 cm³
   • B) 0.30 g/cm³ and 120 cm³
   • C) 0.30 g/cm³ and 36 cm³
   • D) 0.27 g/cm³ and 84 cm³
4. 4.

   A student conducts an experiment to determine the density of air at room temperature and standard atmospheric pressure. First, the student evacuates a rigid glass flask fitted with a stopcock and measures its mass on a precision balance as 340.5 g. Next, ambient air is admitted into the flask at atmospheric pressure, increasing the measured total mass to 341.7 g. Finally, the flask is completely filled with pure water (density = 1.0 g/cm³), resulting in a total measured mass of 1340.5 g. Based on these experimental measurements, what is the density of the air?

   • A) 0.3417 g/cm³
   • B) 0.0120 g/cm³
   • C) 0.0009 g/cm³
   • D) 0.0012 g/cm³
5. 5.

   A laboratory technician pours three mutually immiscible liquids (A, B, and C) into a graduated cylinder. A sample of Liquid A has a mass of 240 g and a volume of 300 cm³, Liquid B has a mass of 260 g and a volume of 200 cm³, and Liquid C has a mass of 210 g and a volume of 210 cm³. After the liquids settle into distinct horizontal layers, the technician gently releases two small insoluble solid pellets: Pellet 1 (mass 18 g, volume 20 cm³) and Pellet 2 (mass 23 g, volume 20 cm³). Assuming none of the substances dissolve or react, which of the following correctly identifies the liquid layers from top to bottom and the equilibrium resting positions of the pellets?

   • A) Top to bottom: Liquid C, Liquid A, Liquid B; Pellet 1 rests at the surface of Liquid C, and Pellet 2 rests at the interface between Liquid A and Liquid B.
   • B) Top to bottom: Liquid A, Liquid B, Liquid C; Pellet 1 rests at the interface between Liquid A and Liquid B, and Pellet 2 rests at the bottom of the cylinder.
   • C) Top to bottom: Liquid A, Liquid C, Liquid B; Pellet 1 rests at the interface between Liquid A and Liquid C, and Pellet 2 rests at the interface between Liquid C and Liquid B.
   • D) Top to bottom: Liquid B, Liquid C, Liquid A; Pellet 1 rests at the interface between Liquid B and Liquid C, and Pellet 2 rests at the interface between Liquid C and Liquid A.
6. 6.

   An industrial chemist formulates a coolant by blending two miscible fluids, Fluid A and Fluid B, which experience no volume change upon mixing. In Trial 1, a rigid container with an internal volume of 300 cm³ is completely filled with Fluid A, yielding a measured liquid mass of 360 g. In Trial 2, the same container is completely filled with a mixture containing equal volumes of Fluid A and Fluid B, giving a total liquid mass of 315 g. If the chemist then completely fills the container with a mixture composed of 100 cm³ of Fluid A and 200 cm³ of Fluid B (Trial 3), what is the density of Fluid B and the total mass of the fluid mixture in Trial 3?

   • A) 1.05 g/cm³ and 330 g
   • B) 0.90 g/cm³ and 300 g
   • C) 0.75 g/cm³ and 270 g
   • D) 0.85 g/cm³ and 290 g
7. 7.

   An automated pharmaceutical packaging system fills airtight blister cavities, each with an internal volume of 2.5 cm³, with a uniform medicated gel. During a quality inspection, a sealed cavity is found to contain a trapped air bubble that occupies 20% of the cavity's volume, with the rest filled by the gel. If the net mass of the gel inside this defective cavity is measured to be 2.4 g and the mass of the air is negligible, what is the density of the gel and what is the expected mass of gel in a fully filled cavity?

   • A) 0.96 g/cm³ and 2.40 g
   • B) 1.20 g/cm³ and 3.00 g
   • C) 1.20 g/cm³ and 2.88 g
   • D) 1.50 g/cm³ and 3.75 g
8. 8.

   A student investigates how thermal processes and physical constraints alter the density of substances in three controlled setups. In Setup 1, a fixed mass of gas inside a cylinder fitted with a frictionless, movable piston is heated and expands. In Setup 2, a fixed mass of gas inside a sealed, rigid container of constant volume is cooled, while in Setup 3, a fixed mass of solid paraffin wax is completely melted into liquid wax, expanding in volume with no loss to evaporation. In which of these setups does the density of the substance decrease?

   • A) Setup 1 only
   • B) Setup 1 and Setup 2 only
   • C) Setup 2 and Setup 3 only
   • D) Setup 1 and Setup 3 only
9. 9.

   A quality control technician inspects three solid, homogeneous cylindrical components manufactured from the same pure metal alloy at constant temperature. Component 1 has a radius of $r$ and a height of $h$, Component 2 has a radius of $2r$ and a height of $h/2$, and Component 3 has a radius of $r/2$ and a height of $4h$. Which of the following correctly compares the densities ($d_1, d_2, d_3$) and the masses ($m_1, m_2, m_3$) of these three components?

   • A) $d_2 > d_1 = d_3$ and $m_2 > m_1 = m_3$
   • B) $d_1 = d_2 = d_3$ and $m_1 = m_2 = m_3$
   • C) $d_1 = d_2 = d_3$ and $m_2 > m_1 = m_3$
   • D) $d_3 > d_1 > d_2$ and $m_3 > m_1 > m_2$
10. 10.

    A student investigates the density of the glass used to manufacture small solid beads. The student pours 65 g of dry beads into a graduated cylinder, where they settle to an apparent bulk volume mark of 40 cm³ due to the empty air spaces between them. Next, the student gently adds 45 cm³ of water into the cylinder, ensuring that the water completely fills all the voids between the beads without trapping any air, bringing the final combined volume mark to 70 cm³. Based on these measurements, what is the density of the glass material?

    • A) 1.30 g/cm³
    • B) 1.63 g/cm³
    • C) 2.17 g/cm³
    • D) 2.60 g/cm³
11. 11.

    In a physics laboratory, a student pours two different pure liquids, X and Y, into identical cylindrical glass beakers until they reach the exact same liquid level. When placed on a digital balance, the mass of liquid X is found to be 240 g, while the mass of liquid Y is found to be 180 g. The student then places an identical solid cube of material Z into each beaker, observing that the cube floats partially submerged in liquid X but sinks to the bottom in liquid Y. Assuming constant temperature and no chemical interaction, which of the following correctly compares the densities $d_X$, $d_Y$, and $d_Z$?

    • A) $d_Z > d_X > d_Y$
    • B) $d_X > d_Z > d_Y$
    • C) $d_X > d_Y > d_Z$
    • D) $d_Y > d_Z > d_X$
12. 12.

    A dairy quality-control laboratory tests incoming shipments of milk to detect whether water has been added to dilute the product. At 20 °C, unadulterated milk has a known density of 1.035 g/cm³, whereas pure water has a density of 1.000 g/cm³. A technician takes a 200 cm³ sample from a delivery container, measures its total mass to be 204.2 g, and assumes no volume contraction occurs upon mixing. What volume of water is present in this 200 cm³ sample, and what percentage of the sample's total volume does it represent?

    • A) 40 cm³, representing 20% by volume
    • B) 60 cm³, representing 30% by volume
    • C) 70 cm³, representing 35% by volume
    • D) 80 cm³, representing 40% by volume
13. 13.

    A marine engineer designs a sensor buoy by assembling two homogeneous parts: a solid metal instrument casing with a volume of 200 cm³ and a density of 2.7 g/cm³, and an outer flotation collar made of synthetic foam with a density of 0.1 g/cm³. For the buoy to achieve the desired buoyancy in seawater, its overall average density must not exceed 0.75 g/cm³. What is the minimum volume of synthetic foam required for the flotation collar?

    • A) 600 cm³
    • B) 520 cm³
    • C) 450 cm³
    • D) 390 cm³
14. 14.

    A materials recycling facility uses flotation tanks to separate a mixture of three shredded polymers: Polymer X (0.92 g/cm³), Polymer Y (1.15 g/cm³), and Polymer Z (1.38 g/cm³). The mixture is first introduced into Tank 1 containing pure water with a density of 1.00 g/cm³, where the floating material is collected. The remaining sunken polymers are transferred to Tank 2 containing a salt solution so that one floats while the other sinks, completing the separation process. Which of the following correctly identifies the polymer collected from the surface of Tank 1 and an appropriate density for the solution in Tank 2?

    • A) Polymer Y is collected from Tank 1, and the solution in Tank 2 could have a density of 1.10 g/cm³.
    • B) Polymer X is collected from Tank 1, and the solution in Tank 2 could have a density of 1.25 g/cm³.
    • C) Polymer X is collected from Tank 1, and the solution in Tank 2 could have a density of 1.45 g/cm³.
    • D) Polymer Z is collected from Tank 1, and the solution in Tank 2 could have a density of 1.05 g/cm³.
15. 15.

    To investigate the thermal behavior of matter, a student places a fixed mass of pure water at 0 °C into a container equipped with a graduated volume indicator. The sample is then heated uniformly from 0 °C to 8 °C under constant atmospheric pressure. Based on the physical properties of water, which of the following correctly describes how its volume and density change during this heating process?

    • A) Its volume steadily increases throughout the entire heating interval, causing its density to decrease continuously from 0 °C to 8 °C.
    • B) Its volume decreases until the temperature reaches 4 °C and then increases, causing its density to peak at 4 °C before decreasing.
    • C) Its volume steadily decreases throughout the entire heating interval, causing its density to increase continuously from 0 °C to 8 °C.
    • D) Its volume increases until the temperature reaches 4 °C and then decreases, causing its density to reach a minimum at 4 °C before increasing.
16. 16.

    A chemist prepares two separate homogeneous mixtures at constant temperature using two miscible liquids, X and Y, with densities of 0.6 g/cm³ and 1.8 g/cm³, respectively. Mixture 1 is prepared by combining equal volumes of liquids X and Y, while Mixture 2 is prepared by combining equal masses of liquids X and Y. Assuming no volume contraction occurs upon mixing, what are the densities of Mixture 1 and Mixture 2?

    • A) Mixture 1: 1.2 g/cm³, Mixture 2: 1.2 g/cm³
    • B) Mixture 1: 1.2 g/cm³, Mixture 2: 0.9 g/cm³
    • C) Mixture 1: 0.9 g/cm³, Mixture 2: 1.2 g/cm³
    • D) Mixture 1: 1.5 g/cm³, Mixture 2: 1.0 g/cm³
17. 17.

    A rigid overflow can is completely filled to the brim with a liquid of density 0.8 g/cm³. A solid, homogeneous object with a mass of 150 g and a density of 2.5 g/cm³ is gently lowered into the container until it rests entirely at the bottom, causing the displaced liquid to pour into an external beaker. Assuming none of the spilled liquid remains on the outer walls of the can, what is the net increase in the total mass of the overflow can and its contents?

    • A) 48 g
    • B) 102 g
    • C) 90 g
    • D) 150 g
18. 18.

    A technician inspects a cast statue made entirely of pure copper, which has a known density of 9.0 g/cm³. The external volume of the statue is measured to be 150 cm³, but an electronic scale reveals its total mass is only 1080 g. Based on these measurements, which conclusion correctly determines the presence and volume of any internal hollow cavity within the statue?

    • A) The statue is completely solid because its total mass of 1080 g exceeds its external volume value of 150 cm³.
    • B) The statue contains a hollow cavity with a volume of 120 cm³ because that is the volume occupied by the missing copper.
    • C) The statue is completely solid because calculating an average density of 7.2 g/cm³ indicates that copper expands to fill the entire 150 cm³ space.
    • D) The statue contains a hollow cavity with a volume of 30 cm³ because the copper itself occupies only 120 cm³ of space.
19. 19.

    A student investigates the physical properties of an unknown pure liquid at constant temperature using an electronic balance and a graduated cylinder. When the cylinder contains 20 cm³ of the liquid, the balance reads a total mass of 46 g, and when the volume is increased to 50 cm³, the total mass becomes 70 g. Based on these experimental measurements, which of the following correctly identifies the density of the liquid and the mass of the empty graduated cylinder?

    • A) The density of the liquid is 0.8 g/cm³, and the mass of the empty graduated cylinder is 30 g.
    • B) The density of the liquid is 2.3 g/cm³, and the mass of the empty graduated cylinder is 0 g.
    • C) The density of the liquid is 1.4 g/cm³, and the mass of the empty graduated cylinder is 24 g.
    • D) The density of the liquid is 0.8 g/cm³, and the mass of the empty graduated cylinder is 16 g.
20. 20.

    A student determines the mass and volume of four solid, homogeneous blocks labeled K, L, M, and N under identical laboratory conditions. The measurements show that block K has a mass of 120 g and a volume of 40 cm³, block L has a mass of 90 g and a volume of 30 cm³, block M has a mass of 80 g and a volume of 20 cm³, and block N has a mass of 150 g and a volume of 60 cm³. Based on these experimental findings, which statement correctly evaluates the densities and possible material identities of the blocks?

    • A) Block N has the greatest density because it has the largest measured mass and volume.
    • B) Block M has a lower density than block K because its total mass is substantially smaller.
    • C) Blocks K, L, and N could be made of the same uniform material because each has a mass greater than its volume.
    • D) Blocks K and L could be made of the same material because they share an identical density of 3.0 g/cm³, while block M has the highest density overall.

Answers and step-by-step solutions appear after you finish the test.