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Density: Question 7

Syllabus 1.4

Structured Core 5 marks

A student wants to determine the density of an unknown liquid, liquid X, using a measuring cylinder and a digital balance.

(a) Describe how the student could use the measuring cylinder and the balance to find the mass and the volume of the liquid. [2]

(b) The empty measuring cylinder has a mass of 32.0 g32.0\text{ g}. After liquid X is poured in, the total mass is 109.0 g109.0\text{ g}, and the volume reading on the cylinder is 50.0 cm350.0\text{ cm}^3. Calculate the density of liquid X. [2]

(c) A sample of liquid X is poured gently into a beaker of water (density 1.00 g/cm31.00\text{ g/cm}^3), and the two liquids do not mix. State, with a reason, whether liquid X floats on top of the water or sinks below it. [1]

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Worked solution

Part (a): Describing the method

  1. Place the empty, dry measuring cylinder on the balance and record its mass.
  2. Pour a sample of liquid X into the cylinder and read the new volume from the scale on the side of the cylinder, with your eye level with the liquid surface.
  3. Place the cylinder (now containing the liquid) back on the balance and record the total mass.

The mass of the liquid alone is found by subtracting the mass of the empty cylinder from this total mass.

Part (b): Calculating the density of liquid X

Find the mass of the liquid:

m=109.0−32.0m = 109.0 - 32.0

m=77.0 gm = 77.0\text{ g}

Divide by the volume:

ρ=mV=77.0 g50.0 cm3\rho = \frac{m}{V} = \frac{77.0\text{ g}}{50.0\text{ cm}^3}

ρ=1.54 g/cm3\rho = \boxed{1.54\text{ g/cm}^3}

Part (c): Floating or sinking in water

Compare the density of liquid X with the density of water:

1.54 g/cm3>1.00 g/cm31.54\text{ g/cm}^3 > 1.00\text{ g/cm}^3

Since liquid X is denser than water, it sinks below the water rather than floating on top of it.

Final answers

  • (a) Weigh the empty cylinder, pour in the liquid, read its volume, then re-weigh; mass of liquid = total mass − mass of empty cylinder.
  • (b) Density of liquid X == 1.54 g/cm31.54\text{ g/cm}^3
  • (c) Liquid X sinks below the water.