__Introduction:__

The density is a fundamental physical characteristic of any sample of matter. It is considerably more important than other physical properties such as size or shape (incidental physical properties that may be of no help in identification) in that the numerical value of density for a pure substance at a particular temperature is a constant (never changes). The density may be readily and reproducibly determined in the laboratory if the mass and volume of a sample can be determined. Density (d = m / V) may be calculated by dividing the mass by the volume.

__Procedure:__

__Density of a Solid:__

- Masses are to be determined to the nearest 0.001 g on the top
loading
balance
__by difference__. First, weigh the bottle with the sample and then weigh the bottle alone. Record this data in your notebook. The difference in masses is the correct mass of the sample. - The volume of the solid is to be determined to the nearest 0.1
mL
__by the displacement of water__in a 25 mL graduated cylinder. Fill the graduated cylinder to approximately 15 mL and record the volume estimated to the nearest 0.1 mL. Tilt the cylinder (sharply for the heavy metal samples) and GENTLY slide the sample into the water, being careful that no water splashes out. Record the volume of the water plus sample. The volume of the sample is the difference between the two readings. This method may be used no matter what the shape of the sample. In the special case of regular geometric solids such as cubes or cylinders, volume could also be determined by measuring with a ruler and computing the volume. - Calculate the density of the solid. Divide the mass of the sample by its volume (d = m/V). Since the volume is the least precise (most uncertain) measured quantity used in this calculation, round off the density to the proper number of significant figures based on the volume. (Remember: the same number of significant figures as in the least precise measured quantity or, at most, one more.)
- Repeat Steps 1-3 two more times and compute the average
of three consistent density values. (If one value is obviously
different
from the other two, measure the density a fourth time and draw an X
through
the bad determination). The average value should be written to the
correct
number of significant figures.

The density of a liquid is often
approximated by measuring its
specific gravity. The specific gravity of a substance is the ratio of
the density of
that substance to the density of pure water. If equal volumes are
considered, the specific gravity becomes simply the ratio of two
masses. Numerically,__ the specific gravity is approximately equal to
the density__. Yet the specific
gravity has no units, while density is expressed as pounds per gallon,
grams
per milliliter, etc.

In this portion of the experiment,
instead of a graduated cylinder,
you
will be using a Gay-Lüssac specific gravity bottle, also
known as a
**pycnometer (pick-nah'-mih-ter):**

A pycnometer is a precision piece of
glassware that consists of two
portions: a bottle and a stopper. The bottom portion
is a small bottle with
a volume which may be accurately determined from the mass of water it
holds
at a particular temperature. The stopper is a capillary tube with
a
ground glass (frosted) bottom that fits snugly into the ground glass
(frosted)
neck of the bottle. For example, if the pycnometer holds 5.02 g
of
water, then its volume must be __about__ 5.02 mL because 1 g of
water
occupies about 1 mL (remember that the density of water is very nearly
1.00
g/mL at the temperature of the laboratory). Since the volume of the
container
may be accurately determined using the density of water, the entire
experiment
involves only the determination of the weights of the empty dry
pycnometer,
the pycnometer full of unknown liquid, and, finally, the pycnometer
full
of water, IN THAT ORDER.

- Obtain a dry pycnometer from the lab instructor
__DO____NOT____WASH THE____PYCNOMETER__. It must be dry for the accurate determination of its mass. It is important that the stoppers are not exchanged from bottle to bottle, since each stopper is ground to fit one bottle and no other. - Weigh the clean
__dry__bottle and stopper to the nearest 0.001 g on the top loading balance and record the mass. Be sure to record the number of the balance used. - Now obtain approximately 15 mL of the unknown liquid in your 25mL graduated cylinder (be sure to clean it and dry it thoroughly first)and record its identifying number. Use a disposable pipette to file the specific gravity bottle until the bottle is completely full. Insert the stopper so the ground glass (frosted) end is in the bottle. Note that the liquid should completely fill the capillary tube in the stopper. Dry the outside of the bottle with a tissue. Be sure to remove any liquid which collects at either the mouth of the bottle or the top of the stopper by lightly touching the areas with the tissue. DO NOT HOLD THE BOTTLE IN YOUR HAND FOR MORE THAN A FEW SECONDS. Why?
- In the case that the top does not fit tightly into the bottle, the capillary level may slowly drop to the level of the mouth of the bottle. If this should happen, allow the level of the liquid in the capillary to fall to the same point for both the unknown liquid and the water in the next step to insure that equal volumes are used.
- Weigh the bottle containing your unknown liquid to the nearest 0.001 g and record the mass. (Remember to 'Tare' the balance if you do not see 0.000g on the display).
- Pour the liquid down the sink and rinse the bottle several times with distilled water. Fill the bottle with distilled water and dry the outside as before. Weigh the bottle and water to the nearest 0.001 g and record the mass.
- Rinse the bottle several more times with distilled water and dry the outside.
- Determine the temperature of the distilled water by placing a thermometer into a beaker containing 50-100 mL of distilled water. Wait at least 10 minutes for the thermometer to equilibrate. Remember to read the temperature to a 0.1 °C. Also note that you must leave the thermometer in the water while you read its temperature. If you remove it from the water, the temperature will change since it is reading the air temperature. Calculate the volume of the pycnometer using the literature value for the density of water at the temperature of the lab.
- Calculate the specific gravity and density of the unknown liquid as shown on the following pages. Express the values to the proper number of significant figures.

** EXAMPLE CALCULATION - these numbers are only examples, your data will vary (DO NOT put this in your pre-lab):** A
clean, dry pycnometer weighs 27.420 g empty. When it is filled with an
unknown liquid,
it weighs 39.270 g. When it is filled with distilled water, it weighs
37.480
g. The temperature of the lab is 23.0 °C. From this
information, we can calculate the specific gravity and density of the
unknown liquid:

*EXAMPLE DATA*

Mass of pycnometer + unknown liquid: | 39.270 g |

Mass of pycnometer: | 27.420 g |

Therefore, the mass of unknown liquid: | 11.850 g |

Mass of pycnometer + water: | 37.480 g |

Mass of pycnometer: | 27.420 g |

Therefore the mass of water: | 10.060 g |

Specific Gravity = density of unknown / density of water

Specific Gravity = (mass of unknown / volume of unknown) / (mass of water / volume of water)

Since both liquids were weighed in the same pycnometer, the volumes are equal, and so cancel:

Specific Gravity = mass of unknown / mass of water

Specific Gravity = 11.850 g / 10.060 g = 1.178

Note that the Specific Gravity has no dimensions.

To determine the true density, we first
need to calculate the volume
of
the pycnometer. We have determined that the pycnometer holds
10.06 g
of water at 23.0 °C. We can then use a Handbook of Chemistry
and
Physics or this **Table of Water
Density
** to find that the density of water at this temperature 0.997538
g/mL.
Knowing this, we can rearrange the density
formula
to calculate the volume of the pycnometer:

volume of pycnometer = mass of water / density of water

V = 10.060 g / 0.997538 g/mL = 10.085 mL

Now that we know the volume of the pycnometer, and the mass of the unknown liquid, we can calculate the density of the unknown liquid:

d = m / V = 11.850 g / 10.085 mL = 1.1750 g/mL

(Updated 8/4/13 by C.R. Snelling)