__Introduction:__

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 may be calculated by dividing
the
mass by the volume:

After running this lab, you will
notice that it is very easy to measure the mass of an object to four,
five, or even six significant figures on modern electronic
balances. However, the volume is typically limited to two or
three significant figures by using a graduated cylinder. Because
of this, our overall measurement of the density is limited by our
ability to measure the density. In addition, the volume
measurement tends to be the most time consuming portion of the
measurement. To help overcome these problems, the concept of Specific Gravity was developed. Technically, the specific gravity of an object is its density divided by the density of water. That may seem like more work, but if you measure the volume of the unknown and the water in the same container, it is a constant and will cancel out. This means that the Specific Gravity (SG) is simply the mass of the object, divided by the mass of water:

__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 20 mL syringe similar to the one below:

- Obtain a clean, dry plastic syringe from your lab instructor.
- Weigh the clean
__dry__syringe 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 a 50 mL beaker (be sure to clean it and dry it thoroughly first). Be sure to record which unknown you are using.
- Use your syringe to suck up all of the unknown liquid. It
is possible that you will have some air bubbles in your syringe that
must be removed. Hold the syringe upright so any air bubble rise
to the top and GENTLY push them out.

- Once all of the air bubbles have been removed, dispense enough of your unknown liquid back into your beaker so that you have exactly 10 mL remaining. Use a paper towel to wipe off the syringe and weigh it to 0.001 g.
- Now dispense more unknown liquid back into your beaker until you have 8 mL remaining. Use a paper towel to wipe off the syringe and weigh it to 0.001 g.
- Dispense more unknown liquid back into your beaker
until you have 6 mL remaining. Use a paper towel to wipe off the
syringe and weigh it to 0.001 g.

- Dispense more unknown liquid back into your beaker until you have 4
mL remaining. Use a paper towel to wipe off the syringe and weigh it
to 0.001 g.

- Dispense more unknown liquid back into your beaker until you have 2
mL remaining. Use a paper towel to wipe off the syringe and weigh it
to 0.001 g.

- Dispense of the rest of your unknown, and then rinse the
syringe several times with distilled water.

- Use your syringe to suck up approximately 15 mL of distilled water. It
is possible that you will have some air bubbles in your syringe that
must be removed. Hold the syringe upright so any air bubble rise
to the top and GENTLY push them out.

- Once all of the air bubbles have been removed, dispense enough of the distilled water so that you have exactly 10 mL remaining. Use a paper towel to wipe off the syringe and weigh it to 0.001 g
- Dispense the rest of the distilled water, dry the syringe off and then return it to your instructor.

*EXAMPLE CALCULATION - these numbers are only examples, your data will vary:*

The
following table contains data similar to what you just collected:

Mass of empty syringe: |
10.165 g |

Mass of syringe + 10 mL of unknown liquid: |
20.127 g |

Mass of syringe + 8 mL of unknown liquid: |
18.094 g |

Mass of syringe + 6 mL of unknown liquid: |
16.023 g |

Mass of syringe + 4 mL of unknown liquid: |
14.092 g |

Mass of syringe + 2 mL of unknown liquid: |
12.162 g |

Mass of syringe + 10 mL of distilled water: |
20.165 g |

If you
plot this data in Excel as a scatter plot, with the volume of the
unknown liquid as the x-axis and the mass of the syringe as the y-axis,
you will obtain a plot similar to the one below:

First thing you want to notice is that all of the data points form an almost perfect straight line. The R^{2}
term is called the correlation coefficient and the closer it is to
1.0000 the better. If one or more of your points do not fit on
the line, or your correlation coefficient is less than 0.95, this means
there is a problem with one or more of your measurement and you will
have to go back and find out which one is off and repeat it.

The next thing you notice is the equation on the graph. As far as Excel is concerned this is simply the equation of the best straight line through your five measurements (the so-called linear regression). However, to us it represents both the density of the unknown liquid and the mass of the empty syringe! The first term of the equation, '0.9996x', is call the slope of the straight line. It is the change in mass, divided by the change in volume, which is the definition of density, so this is the density of your unknown liquid. The second term, '10.12', is called the y-intercept, and in our case represents the mass of the syringe when there is no liquid in it. This is neat because it lets us compare our measured mass versus the calculated mass for our syringe. Obviously, the closer they are to each other, the better the job you did making your measurements!

Now, what about that specific
gravity? Well, we have the mass of the syringe plus 10 mL of
unknown liquid, and the mass of the syringe plus 10 mL of distilled
water. If we subtract the mass of the empty syringe from both of
these measurements, we will be left with the mass of the 10 mL of
unknown liquid and the mass of 10 mL of distilled water. This is
exactly what we need to calculated the specific gravity (note, the SG
has no units):

Specific Gravity = mass of unknown / mass of water

Specific Gravity = 9.962 g / 10.000 g = 0.9962

(Updated 9/13/13 by C.R. Snelling)