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 cm^{3} (in a 50 ml measuring
cylinder for best accuracy)

Make sure the bottom of the liquid's
meniscus rests exactly on the 50 cm^{3} 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 cm^{3}) or a 25 ml (25 cm^{3}) 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 cm^{3} (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 ~25^{o}C.

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** |
10^{o}C |
**
20**^{o}C |
30^{o}C |

**density** g/cm^{3} |
0.9997 |
**
0.9982** |
0.9957 |

**density** kg/m^{3} |
999.7 |
**998.2** |
995.7 |

(Note: **g/cm**^{3} x 1000 = kg/m^{3})

However, as you can see, by assuming the
density of water is 1.00 g/cm^{3} (1000 kg/m^{3}), at **20**^{o}C
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
**ρ**_{water}**
= m**_{water}**
÷ v**_{water},
**v = m ÷ ****
ρ**

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

= 15.11
÷ 1.00 = **
15.11 cm**^{3}

We can now calculate the density
of liquid X.

Density of liquid
X **ρ**_{X}**
= m**_{X}** ÷ v**_{X}
= mass of liquid X ÷ volume of liquid X

= 12.91 ÷ 15.11 =
**
0.854 g/cm**^{3}
(x 1000 = **
854 kg/m**^{3})

**
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, t****his
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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