The Density of Metals and Liquids
Roger Sandwick and Tom Moffett, Plattsburgh State University of New York, 2002
1. Density
Density is defined as the mass of a substance per unit volume. For a discussion of density see
your textbook.
In the first part of this experiment, you will determine the density of an unknown piece of metal
by dividing its mass by its volume. Since the mass is in the shape of a cylinder, its volume can
be calculated using the measured dimensions of length and diameter. In the second part of the
experiment, you will again calculate the density of the same piece of metal using a volume
obtained from immersion of the metal cylinder into a graduate cylinder filled with water.
Using two different methods will allow you to compare the accuracy of the methods. Scientists
are often called to compare the quality of measurements. You will identify the unknown piece of
metal by comparing its measured density with values in Table 1.
Table 1. Densities of some metals (g/cm3)
Aluminum
2.70
Copper
8.96
Lead
11.35
Iron
7.87
Magnesium
1.74
Zinc
7.13
In the second part of this experiment, you will determine the sugar concentration of a common
soda by comparison of its density with densities of known sugar solutions.
2. Intensive versus Extensive Properties
Certain properties can be used to identify a material. These properties, called intensive
properties, depend only on the characteristics of the material and not on the amount of material
that you have. Density is an example of such a property. Extensive properties depend on the
amount of material that you have. An example of such a property is volume. In your discussion,
try to comment on some other intensive and extensive properties.
Metal cylinders such as those that you will use in Parts 1 and 2 of this experiment, and solutions,
such as those you will use in Part 3, each have their own characteristic density. Since density is
an intensive property, we will use the measured densities to identify the material.
3. Top-Loading Balance
You will be using the top loading balance in this experiment. Your instructor will show you how
to use these devices. The balances are very simple to use. They have a power button that also
acts as a tare button. The tare facility allows you to automatically remove the weight of your
empty container from consideration. Because someone may have used the button before you
and your container may have a different weight then their container, you must be careful to
make sure the digital readout has zeroes showing before you weigh your material.
The second important thing to know about balances is that they need to be cleaned if you spill
chemicals on them. The balances are very expensive and require care.
4. Graphing
In this experiment you will prepare a graph of density vs. sugar concentration. Normally in an
experiment, one variable is changed in a controlled manner, and the value of the other variable is
measured. The variable that is controlled is called the independent variable and should be plotted
on the X-axis. The dependent variable is plotted on the Y-axis. When preparing a graph there
are a number of steps to keep in mind. A graph should take up as much space as possible on the
graph paper, this mans that you must choose an appropriate scale for your axis. Each axis needs
to be labeled (with appropriate units), and a clear title for the graph should be included. After
you plot your data points you need to fit them with a best fit smooth curve. The curve may be a
straight line, or some more complicated shape. The curve does not have to go through all the data
points, but instead is as close as possible to all the points.
5. Error and the Experimenter
Chemists deal with numbers and physical quantities. As examples, a chemist may need to know
how much heat is given off in a particular reaction, how distant two atoms are from each other in
some molecule, or want to measure the difference in volume of a gas before and after it is heated.
The uncertainty in the numbers with which the chemist deals is also important. Scientists should
always tell others how reliable a particular number is that they have measured. There are various
ways of signifying uncertainty or reliability.
At this point in your career as a scientist and a chemist, it may be difficult to grasp the physical
significance of the uncertainty in a particular measurement. Hopefully, after using some of the
various ways in which scientists communicate uncertainty and error, you will understand the
importance of this in your scientific work.
Percent error calculation:
% error = experimental value – accepted value
accepted value
x 100
Procedure
A. Density of Solids
Part 1. Obtain a piece of unknown metal from the side bench. Weigh it on the toploading balance to as many significant digits as possible and then measure its dimensions to the
nearest hundredth of a centimeter.
Calculate the density of the metal for each set of measurements (volume of a cylinder is πr2h).
Identify the metal using the data in Table 1. Calculate your percentage error.
Part 2. Determine the volume of the unknown piece of metal by carefully sliding it into
a graduated cylinder that is filled with a known volume of water (be sure there is enough water to
completely cover the metal piece). The difference in volumes before and after adding the metal
is the volume of the metal piece. Repeat this process with a different initial volume of water.
Make sure the metal piece is dry before each run.
Calculate the density of the metal for each run using the average weight from Part 1 and the
volumes determined in Part 2.
Determine the identity of the unknown piece of metal by comparing the average density obtained
from Part 2 with the densities of the metals in Table 1. After you choose the identity of the
metal, calculate the percentage error in the average of the density measurements in Part 2.
B. Density of Liquids
Determine the mass of an empty 10 mL graduate cylinder.
Add between 6 and 9 mL of 10 % alcohol solution to the graduate (record the volume to the
correct number of significant digits).
Determine the mass of the 10 mL graduate with the alcohol solution. The mass of the alcohol
solution can be found by subtracting the mass of the empty graduate.
Discard the solution down the drain, rinse the graduate, and repeat with the remaining solutions
and the unknown.
Calculate the densities for all solutions.
Use Excel to prepare a graph of density vs. % alcohol. Remember not to graph the unknown. Use
the density of the soda and your graph to determine the percent alcohol in the unknown.
LINEAR REGRESSION WITH EXCEL
1.
Boot up the computer. Click on Microsoft Excel. You'll see a spreadsheet with a large
number of cells that are identifiable by their column letter and their row number. The
upper top left cell is A1; the one just to the right of it is B1; the one just below A1 is A2,
etc.
2.
Enter your X data in column A and your corresponding Y data in column B (numbers
only).
3.
With the mouse, highlight this two column block of cells. Click on Chart Wizard (it's the
icon that looks like a blue, yellow and red bar graph -- top row of icons). An option will
come up asking you for what type of graph you'd like. Click on XY (scatter). For chart
subtype, click on the top picture. Click Next.
4.
Your graph should be shown. If it looks okay click Next again.
5.
This next page gives you the option of adding X and Y axis labels and a Chart Title. Type
the Chart Title under (what else") Chart Title, the X axis label under Value (X) axis, and
the Y axis label under Value (Y) axis. This page also gives you a way for dressing up
your graph the way you would like it. For example, I (Dr. Sandwick speaking) don't
particularly care for the gridlines that span horizontally across the graph. These can be
removed under gridlines. (Click off arrow) Click Next.
6.
You are now on the final page. If you want to go back to correct something (other than
data), do it now. Otherwise, click Finish and the figure will lay on the spreadsheet. Once
here, you can do a lot of things to get the chart the way you'd like it. For example, if you'd
like to remove the shading background, double click on it and then choose OK.
7.
To add the linear repression, click on Chart and then on Add Trendline. Click on the
picture labeled Linear (if it isn't already clicked). Click on Options and then on the box
for Display equation on chart. Also click on the box for Display R-squared value on
chart (this is the correlation of the line to the data, the closer the value is to one, the better
the agreement). Click on OK.
8.
To Print: Click on the graph so that boxes are shown on each corner and on the middle of
each side. Click File, Print, and OK. The graph should print.
Name: ____________________________________
Density of Metals and Liquids – Data Sheet
Section: ____
CHE 101
A. Density of Metals (part 1)
Density of Metals (part 2)
Unknown:
__________
________
________
Mass:
__________
Volume of solid
and water
Length:
__________
Volume of water
________
________
Radius:
__________
Volume of solid
________
________
Volume (Show Work):
Average volume of solid:
Density (Show Work):
Density (show work):
Identity of Solid: _______________
% error (show work)
% error (show work)
_____________
Name: ____________________________________
Density of Metals and Liquids – Data Sheet
Section: ____
CHE 101
B. Density of Liquids
Solution
_______
_______
_______
_______
_______
Mass of graduate
and liquid
_______
_______
_______
_______
_______
Mass of graduate
_______
_______
_______
_______
_______
Mass of liquid
_______
_______
_______
_______
_______
Volume
_______
_______
_______
_______
_______
_______
_______
_______
_______
_______
Density (show work)
Density:
% Alcohol in Unknown (from y = mx + b): _________________
Name: ____________________________________
Density of Metals and Liquids – Questions
Section: ____
CHE 101
Questions
1. In part B, which variable was the independent variable and which was the dependent
variable?
2. In part A, which method of determining volume is more accurate? Explain why.
3. Calculate the mass of soda inside a 2-L soda bottle, the density of soda is 1.07 g/mL.
4. A sample of lead has a mass of 820.0 g, how much water would the lead displace?
Name: ____________________________________
Density of Metals and Liquids – Pre Lab Questions
Section: ____
CHE 101
1.) What safety item must be worn at all times while in the lab?
a.) lab coat
b.) gloves
c.) safety glasses
d.) all of the above
2.) What are the normal units for density for each state of matter?
Solid
____________________________________
Liquid
____________________________________
Gas
____________________________________
3.) Determine the density of a 32.5 g metal sample that displaces 8.39 mL of water.
4.) A student measures the density of a solution to be 1.36 g/mL. Determine the percent error if
the accepted density was 1.25 g/mL.