8.1 Changes of state and the particle model — Practise

Work through these on your own. Keep the units with your numbers, and write the unit in your answer. A few questions ask for a short explanation, so read each one carefully before you start.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

A block of metal has a mass of 0.80 kg and a volume of 1.0 x 10^-3 m^3. Calculate its density.
A block of concrete has a density of 2700 kg/m^3 and a volume of 2.0 x 10^-3 m^3. Calculate its mass.
A liquid has a density of 900 kg/m^3. A sample of the liquid has a mass of 0.90 kg. Calculate the volume of the sample.
An irregular piece of metal has a mass of 84 g. It raises the water level in a measuring cylinder from 30 cm^3 to 62 cm^3. Calculate its density in g/cm^3.
Describe the arrangement and the motion of the particles in a solid, a liquid and a gas.
Explain why the mass of a substance is conserved when it melts. Give a reason in terms of the particles.
A rectangular block measures 2.0 cm by 5.0 cm by 10.0 cm. Its mass is 270 g. Calculate its density in g/cm^3.
An empty beaker has a mass of 85 g. When 200 cm^3 of a liquid is added, the total mass is 245 g. Calculate the density of the liquid in g/cm^3.
Describe how to measure the density of a liquid. Say which measurements you would take and how you would calculate the density.
A block of ice has a volume of 1.5 x 10^-3 m^3. The density of ice is 920 kg/m^3. Calculate its mass.
A metal cube has sides of length 4.0 cm. Its mass is 512 g. Calculate its density in g/cm^3.
A student has a regular metal block and an irregular stone. Say how the method to find the volume differs for the two objects, then explain why.

Answers and concise solutions

1. Density of the metal

Answer: $\rho = \dfrac{m}{V} = \dfrac{0.80}{1.0 \times 10^{-3}} = 800\,\text{kg/m}^3$ .

2. Mass of the concrete

Answer: $m = \rho V = 2700 \times 2.0 \times 10^{-3} = 5.4\,\text{kg}$ .

3. Volume of the liquid

Answer: $V = \dfrac{m}{\rho} = \dfrac{0.90}{900} = 1.0 \times 10^{-3}\,\text{m}^3$ .

4. Density of the metal

Answer: The volume is $62 - 30 = 32\,\text{cm}^3$ . Then $\rho = \dfrac{84}{32} = 2.625\,\text{g/cm}^3 = 2.6\,\text{g/cm}^3$ to 2 significant figures.

5. The three states of matter

In a solid the particles are close together in a regular pattern and vibrate about fixed positions.
In a liquid the particles are close together but not in a fixed pattern, so they can move around each other.
In a gas the particles are far apart and move quickly in random directions.

6. Why the mass is conserved

Melting is a physical change, not a chemical change, so no new substance is made.
The same particles are present before and after melting. None are created or destroyed, so the mass does not change.

7. Density of the block

Answer: Volume $= 2.0 \times 5.0 \times 10.0 = 100\,\text{cm}^3$ . Then $\rho = \dfrac{270}{100} = 2.7\,\text{g/cm}^3$ .

8. Density of the liquid

Answer: Mass of liquid $= 245 - 85 = 160\,\text{g}$ . Then $\rho = \dfrac{160}{200} = 0.80\,\text{g/cm}^3$ .

9. Measuring the density of a liquid

Measure the mass of an empty container, then measure the mass of the container with the liquid in it. The difference is the mass of the liquid.
Measure the volume of the liquid with a measuring cylinder.
Divide the mass of the liquid by its volume to find the density.

10. Mass of the ice

Answer: $m = \rho V = 920 \times 1.5 \times 10^{-3} = 1.38\,\text{kg} = 1.4\,\text{kg}$ to 2 significant figures.

11. Density of the cube

Answer: Volume $= 4.0^3 = 64\,\text{cm}^3$ . Then $\rho = \dfrac{512}{64} = 8.0\,\text{g/cm}^3$ .

12. Finding the volume of the two objects

For the regular block, measure its length, width and height with a ruler and multiply them to find the volume.
For the irregular stone there are no simple lengths to measure, so find the volume by displacement in water instead.