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School-college Physics Notes: Thermal energy 5.4 Density

Density & particle theory: 5.4 Three simple experiments to determine the density of a liquid - apparatus, method and calculation

Doc Brown's Physics exam study revision notes

5.4 Three simple experiments to determine the density of a liquid and calculations involved

To measure the density of liquid you need to weigh an accurately measured volume of the liquid.

(i) Measuring the density of a liquid using a measuring cylinder (2b) on diagram

If you are only using 10 ml of liquid, you should use a 10 ml measuring cylinder , a 50 ml measuring cylinder would not be accurate enough.

A clean empty measuring cylinder is weighed on the electronic balance (m1).

The liquid under investigation is poured to a convenient volume v eg 50 cm3 (in a 50 ml measuring cylinder for best accuracy)

Make sure the bottom of the liquid's meniscus rests exactly on the 50 cm3 mark.

The measuring cylinder and liquid are then reweighed (m2).

The difference between the weights gives you the mass m of the liquid (m = m2 - m1)

density of liquid ρ = m ÷ v

This is not a very accurate method, the measuring cylinder is not calibrated to a high standard.

(ii) Measuring the density of a liquid using a burette or pipette

(both more accurate than a measuring cylinder) (2a) and (2b) on diagram

Weigh a suitable container, eg a conical flask or beaker, on the electronic balance (m1).

Carefully measure into the container an accurately known volume v of the liquid under investigation.

You can use a burette (for any volume from 10 to 50 cm3) or a 25 ml (25 cm3) pipette.

In either case make sure the bottom of the liquid's meniscus rests exactly on the calibration mark for selected volume.

The container and liquid are reweighed (m2) and the difference in weight is the mass m of the liquid (m = m2 - m1)

density of liquid ρ = m ÷ v

This is a more accurate method than (i), a pipette or burette are calibrated to a higher standard than a measuring cylinder.

(iii) Measuring the relative density of a liquid using a density bottle

The liquid must not be too viscous (too sticky to run freely).

A density bottle is a glass chamber with a ground neck entrance. Into the neck goes a precisely fitting stopper with a capillary tube running down its central axis - see diagrams above. Its volume can be as little as 10-20 cm3 (10 ml).

Procedure

You need to do the experiment at a constant temperature because liquids expand/contract if heated/cooled i.e. density is temperature dependent.

Diagram (3a) The density bottle and stopper must be completely empty and dried in an oven before use - obviously must be allowed to cool down to room temperature at ~25oC.

The density bottle and stopper are then weighed on a mass balance, preferably to ± 0.01 g (m1)

Diagram (3b) The density bottle is then completely filled with pure water and the stopper pushed down to expel any excess water.

With a tissue of filter paper, any excess fluid on the top of the stopper should be carefully removed.

You should also make sure there is no spilt liquid on the outside of the bottle, if so, this should be carefully wiped off too.

In other words, all the exterior of the density bottle and stopper must be dry.

Also make sure you don't absorb any liquid from the capillary tube of the stopper.

Diagram (3c) The filled density bottle of water is then reweighed on the mass balance (m2).

Diagram (3d) The steps from 3a to 3c are then repeated and the final mass of the bottle/stopper filled is measured (m3).

Results (fiction!)

m1 = mass of empty bottle + stopper = 35.51 g

m2 = mass of empty bottle + stopper + water = 50.62 g

m3 = mass of empty bottle + stopper + liquid X = 48.42 g

Calculation

You can get the accurate density of pure water from a data table on the internet e.g.

 temperature 10oC 20oC 30oC density g/cm3 0.9997 0.9982 0.9957 density kg/m3 999.7 998.2 995.7

(Note: g/cm3 x 1000 = kg/m3)

However, as you can see, by assuming the density of water is 1.00 g/cm3 (1000 kg/m3), at 20oC you only introduce a 0.2% error.

(1.00 - 0.998)/1.00) x 100},

for a school/college laboratory, that's a pretty good accuracy for doing any real experiment.

Assuming constant temperature and therefore constant volume, the calculation is as follows.

m2 - m1 = mass of water = m4 = 50.62 - 35.51 = 15.11 g of water

m3 - m1 = mass of liquid X = m5 = 48.42 - 35.51 = 12.91 g of liquid X

Density of liquid ρwater = mwater ÷ vwater,   v = m ÷ ρ

Therefore volume of bottle = volume of water = mass of water ÷ density of water

= 15.11 ÷ 1.00 = 15.11 cm3

We can now calculate the density of liquid X.

Density of liquid X ρX = mX ÷ vX = mass of liquid X ÷ volume of liquid X

= 12.91 ÷ 15.11 = 0.854 g/cm3 (x 1000 = 854 kg/m3)

Source of errors

Not ensuring there is no excess liquid on the outside of the density bottle or on the top of the stopper.

Not ensuring the bottle is completely dry and empty before use.

Not ensuring all measurements are done at the same recorded temperature.

Again, this again is much more accurate than method (i) and probably more accurate than method (ii) - too, because you are calibrating the density bottle to a high standard of accuracy.

To calculate the density of liquid is no different from the calculations for a solid so I don't feel the need to add any more density calculations.

Keywords, phrases and learning objectives for density

Experiments to determine density of liquid apparatus method calculation density bottle burette measuring cylinder balance

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