# Density

Density
Dr. MJ Patterson

Density is a property of all matter.  It is the ratio of an object's mass to its volume,

D = m/V.

Memorize this equation.  For the rest of your studies in chemistry, it will be assumed that you know and understand density.

The density of a material can provide a hint as to the identity of that material.  See the table below for the densities of some elements (This data is from WebElements www.shef.ac.uk/chemistry/web-elements).  If you can measure the density of an object made from an unknown metal, you can compare the density to this list (or a larger list) to determine the identity of that metal.

Density is simple to measure.  First, get a sample of the unknown.  Weigh it to find the mass.  Finding the volume depends on the state of the unknown.  If it is a liquid, pour it into a graduated cylinder.  If it is a solid, fill a graduated cylinder about half way with water.  Record the volume.  Drop in the solid sample. The water level should rise.  Record the new water level.  Subtract the two water levels, and the difference is equal to the volume of the solid.

 Element Symbol Density (g/cm3) chromium Cr 7.14 copper Cu 8.92 gold Au 19.30 iron Fe 7.874 lead Pb 11.34 mercury Hg 13.6 platinum Pt 21.09 silver Ag 10.49 tin Sn 7.31

Units! 1 mL = 1 cm3

The liter is not a standard volume unit in SI units, which use the cubic meter, or m3.  However, the liter is the common metric unit that everyone uses.  To convert between these units, just remember that 1 mL = 1 cm3.

Example 1:

When you were on the beach last weekend, you found an old corroded chunk of metal in the sand.  It caught your eye because it was round and flat like a coin.  You took it home and cleaned off all the corrosion.  What was left really looks like it might be an old Spanish coin.  You placed the metal on a balance and found that it has a mass of  52.76 g.  By water displacement, you found that it has a volume of 5.03 mL.  What is the identity of the metal in the coin?

Solution 1:

Calculate the density of the metal.

m = 52.76 g
V = 5.03 mL = 5.03 cm3

D = m/V = (52.76 g) / (5.03 cm3) = 10.5 g/cm3

(The answer should be rounded to 3 sig figs since 5.03 has only 3 sig figs.)

Comparing the density value to the chart, the best match is silver!  Not bad for a day at the beach!

Density as a Conversion Factor

We can write any of these densities as a conversion factor.  The density tells us how many grams are in exactly 1 cm3 or 1 mL of the substance.

As an example for silver:

1 cm3 = 1 mL = 10.49 g

Now we can use this conversion factor to calculate all sorts of things relating mass and volume.

Example 2:

A lab assistant had just weighed out 125 g of mercury when the container broke.  The nearest whole container was a 50 mL beaker.  Will it hold all of the mercury that spilled?

Solution 2:
The key here is to calculate the volume occupied by the 125 g of mercury.  The relationship between mass and volume is density.  From the chart above, we can write the conversion factor:

1 mL = 13.6 g

We can set up the conversion by putting the data to be converted, the 125 g, over 1, and then multiplying by the conversion factor as a fraction.  We want units of grams in the bottom of the conversion factor to cancel with the 125 g.

 (125 g Hg) (1 mL) = 9.19 mL (1) (13.6 g Hg)

Since the mercury only occupies a volume of 9.19 mL, it will easily fit inside a 50 mL beaker.

Example 3:

A balance in the lab has a maximum capacity of 325 g.  Will it be sufficient to weigh 200 mL of mercury?

Solution 3:
Once again we need the density of mercury to relate mass and volume.  From the given volume, we can calculate the mass and compare it to the capacity of the balance.

1 mL = 13.6 g

Start the conversion with the given 200 mL of Hg.  Use the density to convert to mass.  Make sure that mL goes in the bottom of the conversion factor to cancel with the 200 mL.

 (200 mL Hg) (13.6 g Hg) = 2720 g Hg = 2.72 kg Hg (1) (1 mL Hg)

The balance is not sufficient to weigh this sample of mercury.  Not even close!