Density - Lecture notes 4-5 PDF

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Density Density describes how closely packed the particles are in a solid, liquid or gas.

Density is the amount of mass per unit volume. All matter contains particles. The difference between the different states of matter is how the particles are arranged:

in a solid – particles are tightly packed in a regular structure in a liquid – particles are tightly packed but free to move past each other in a gas – particles are spread out and move randomly Solid cube: side length 1 unit, 64 particles in tightly packed lattice. Liquid cube: 1 unit, contains approx 30 particles. Gas cube: side length 10 units contains 15 scattered particles. Changing the state of a material will change its density There is little difference between the density of a liquid and its corresponding solid (eg water and ice). This is because the particles are tightly packed in both states. The same number of particles in a gas would spread further apart compared to in the liquid or solid states. The same mass takes up a bigger volume - this means the gas is less dense.

Density also depends on the material. A piece of iron with the same dimensions as a piece of aluminium will be heavier because the atoms are more closely packed.

Scientists can find the density of a material by measuring the mass of a certain volume of the material, for example, one cubic centimetre.

Material Iron

7.8

Ice

0.98

Density in grams per cubic centimetre (g/cm³)

Water 1 Air

0.00129

Calculating density Density can be calculated using the equation:

This is when:

density (ρ) is measured in kilograms per metre cubed (kg/m3) mass (m) is measured in kilograms (kg) volume (V) is measured in metres cubed (m3) Example What is the density of a material of 0.45 cubic metres (m3) if it has a mass of 0.2 kg? Volume To calculate density, the volume of the material must be known. If the object is a regular shape, the volume can be found by using a ruler and then using the equation:

Volume = length × width × height

If the object has an irregular shape, the volume can be measured using a displacement can.

The displacement can is filled with water above a narrow spout and allowed to drain until the water is level with the spout.

Eureka can filled with water to just below overflow hole. Object lowered into can and displaces own volume of water. Water passes through overflow, down spout and collected in measuring cylinder. As the irregular object is lowered into the displacement can, the water level rises. Since the level was already up to the bottom of the spout, all the displaced water comes out of the spout and is collected in a measuring cylinder.

Thedisplaced water in the cylinder occupies the same amount of space that the object now does in the can, which means that their volumes are the same.

If the object fits directly into the measuring cylinder, fill the cylinder to a suitable level and take the reading. Carefully lower the object into the cylinder. The water level rises. Take the new reading.

The difference between readings is the volume of the object.

There are different ways to investigate density. In this required practical activity, it is important to:

record the mass accurately measure and observe the mass and the volume of the different objects use appropriate apparatus and methods to measure volume and mass and use that to investigate density Aim of the experiment To measure the density of liquids and solids.

Method Method 1: A regular shaped object

Use a ruler to measure the length (l), width (w) and height (h) of the object. Place the object on the top pan balance and measure its mass. Calculate the volume of the cube using (). Use the measurements to calculate the density of the object. Method 2: An irregular shaped object

Place the object on the top pan balance and measure its mass. Fill a measuring cylinder so that there is enough water to cover the object when it is placed inside the cylinder. Take the reading of the volume. Carefully lower the object into the cylinder. Take the new reading of the volume. Subtract the original reading to obtain the volume of the object. Use the measurements to calculate the density of the stone. Method 3: A liquid

Place the measuring cylinder on the top pan balance and measure its mass. Pour eg 30 cm3 of liquid (eg water) into the measuring cylinder and measure its new mass. Subtract the mass in step 1 from the mass in step 2. This is the mass of 30 cm3 of water. Use the measurements to calculate the density of the water. Results

Some example results could be:

Object Mass (g)

Volume (cm³) Density (g/cm³)

Steel block

468

60

Stone 356

68

Water 30

30

Analysis Using those results – the densities can be calculated using:

Density = mass ÷ volume

Mass of steel block = 468 g

Volume of steel block = 60 cm3

Density = mass ÷ volume = 468 ÷ 60 = 7.8 g/cm3

For a stone of mass 356 g, the volume of water in the measuring cylinder rose by 68 cm3.

Density = mass ÷ volume = 356 ÷ 68 = 5.2 g/cm3

Mass of 30 cm3 of water is found to be 30 g.

Density = mass ÷ volume = 30 ÷ 30 = 1 g/cm3

Evaluation Density can be measured for regular solids, irregular solids and liquids. Densities calculated from measurements are subject to experimental error. This could be because: the top pan balances used by different people may not be identically calibrated the resolution of the measuring cylinders may be different, causing different values for the volume to be recorded

Risk assessment Hazard Risk

Control measures

There are no significant risks associated with this procedure States of matter In everyday life, there are three states of matter – solids, liquids and gases. The differences between the three states are due to the arrangement and spacing of the particles and their motion.

Solids, liquids and gases Particles in a solid, tightly packed together in order. The particles in a solid:

are in a regular arrangement vibrate about a fixed position sit very closely together Particles in a liquid, packed together, very fluid. The particles in a liquid:

are randomly arranged move around each other sit close together Particles in a gas, random order, not together. The particles in a gas:

are randomly arranged move very quickly in all directions are far apart Changing state Adding or removing energy from a material can change the state. Heating a solid material will cause it to melt from a solid to a liquid. Continued heating will cause the liquid to boil or evaporate to form a gas. In some instances, when heating the solid material, it can go straight to being a gas without being a liquid - this process is called sublimation.

Cooling a gas will cause it to condense from a gas to a liquid and cooling it further will cause it to then freeze from a liquid to a solid.

Flow chart showing processes between solid, liquid and gas, using water, ice and steam from a kettle as an example. Labels show all the processes in how one can change to another. Water changing state Boiling is an active process. It occurs at a certain temperature, called the boiling point. People actively apply energy to a liquid to turn it into a gas using a heater such as a kettle.

Evaporation, on the other, hand is a passive process. The liquid will slowly absorb energy from the surrounding area so that some of its particles will gain enough energy to escape from the surface of the liquid and it can occur at any temperature.

Throughout all of these changes, the number of particles has not changed, just their spacing and arrangement. As a result, the total mass has not changed. It does not matter if a substance melts, freezes, boils, evaporates, condenses or sublimates. The mass does not change.

With changes of state, mass is conserved. It does not change. These changes in state are called physical changes because the process can be reversed (eg cooling instead of heating). This is different to the changes seen in a chemical reaction when the changes cannot be reversed so easily....