Goal
· Be able to statistically analyze experimental data.
· Part 1: Use experimental data to determine the density of an unknown solid
· Part 2: Use experimental data to cali
ate a volumetric pipette
· Part 3: Use experimental to determine the density of a NaCl solution
· You will work in groups. Your instructor will provide you with experimental data to analyze.
· Open the Density and Treatment of Data experiment
.
· Complete the Pre-Lab on page 2 of the file and submit your work. You may answer the questions on a separate sheet of paper take an image of your work, save the file as a PDF and upload the file onto this assignment.
· Part 1: For each of three trials use the data provide to determine the density of the solid. Calculate the average density and standard deviation.
· Part 2: For each of three trials use the data provide to determine the volume of the pipette.
· Part 3: For each of three trials use the data provide to determine the density of the NaCl solution.
· Refer to the report Ru
ic as you prepare your report. Also, as this is the first typed report I provided a template. You may use the template to prepare your report.
· You may prepare your report in Word, Apple Pages, or Goggle Docs. However, save your final report as a PDF and upload onto this assignment.
· Complete the Post Lab Questions on page 8 and include your work in your final report. Type your answer to Post Lab Question 1 and 2 (a, b, and c). Post-Lab Question 3 can be completed on a separate sheet of paper. Paste an image of your work onto your report.
Table 1: Determination of the Density of a Metal
Trial 1 Trial 2 Trial 3
Mass of solid (g XXXXXXXXXX.1341
Volume of water and solid (mL XXXXXXXXXX
Volume of Water (mL XXXXXXXXXX
Table 2: Cali
ation of Pipette
Trial 1 Trial 2 Trial 3
Mass of flask + H2O (g)
XXXXXXXXXX
Mass of flask (g XXXXXXXXXX509
Mass of H2O (g)
Temperature of water (oC) 22.8
Density of water at Temp (kg/m XXXXXXXXXX
Table 3: Determination of the Density of a Liquid
Trial 1 Trial 2 Trial 3
Mass of flask + Unknown (g XXXXXXXXXX860
Mass of flask (g XXXXXXXXXX520
Density and Treatment of Data
Background
Density is a physical property of matter. What this means is that every pure substance has a charac-
teristic density at a given temperature. In other words, density can be used to identify a substance. One
is able to determine the density of a substance by determining its mass and volume. Since density is a
temperature dependent parameter, the resulting density is reported at the temperature at which it was
determined.
In this exercise you will accurately determine the volume delivered by a 10-mL volumetric pipet; that
is you will cali
ate a 10-mL volumetric pipette. Typically the volume delivered by a volumetric pipette
is etched on the the glass along with the temperature. However, in practice one should never assume that
the volume contained or even delivered by volumetric glassware is exactly that which is indicated by the
etching on the glass. Proper cali
ation avoids the introduction of systematic e
ors in your measurements.
Cali
ation is performed by first weighing the mass of water delivered by the pipet. The volume delivered
is obtained by comparing the mass of water to its density. Remember to measure the temperature of the
water so that you use the co
ect density in your analysis.
It is proper laboratory practice to report the accuracy and precision of ones experimental data. Accu-
acy refers to how close a given measurement comes to the true value (i.e. the Theoretical value). Precision,
on the other hand, is a measure of the reproducibility of a given measurement. That is, when an experi-
ment is repeated, precision tells us how close a measurement comes to another measurement. Precision is
determined by a statistical method named standard deviation In this experiment you will repeat several
measurements in order to generate data such that you are able to statistically analyze your results. Note
that reporting results without specifying the precision is meaninless since one does not provide information
pertaining to the reproducibility of the experiment. For example, suppose the density of a given metal was
determined to be 8.95 g/mL ±0.21 g/mL. The value, ±0.21 g/mL, tells us the precision of the density re-
ported. The precision in the latter case tells us that the density of the metal is between 9.16 g/mL and 8.74
g/mL. The lower the standard deviation the better the agreement is between subsequent measurements.
1
Pre-La
Name: Lab Section
1. The density of water at 21.0 oC is XXXXXXXXXXkg/m3. Using dimensional analysis express this density
in units of grams per milliliter. Be sure to show your work throughout.
density at 21.0 oC =
2. Using the data illustrated in the figure below. Determine the density of the metal cylinder. Be sure
to show all your work including proper units throughout. Report your response with the co
ect
number of significant figures.
10
20
30
40
50
60
70
80
50
60
mL
10
20
30
40
50
60
70
80
50
60
mL
meniscus
close-up view close-up view
metal
cylinder
33.625 g
top loading balance
metal cylinder
density of metal cylinder =
2
Experimental Procedure
1. Determining the density of a metal
(a) Obtain a metal slug and record the unknown number in your laboratory notebook.
(b) Use the analytical balance to determine the mass of the dry metal slug.
(c) Half-fill a 50-mL or 100-mL graduated cylinder with tap water and record its volume to the nearest
0.1 mL.
(d) To avoid splattering tie the metal slug with a nylon string and carefully drop it into the 50-mL (o
100-mL).
(e) Roll the metal slug around in the graduated cylinder to remove any air bu
les.
(f) Take the difference between the two water levels for the volume of the unknown solid.
(g) Repeat the procedure two more times using the same dry mass of the metal cylinder recorded before.
2. Cali
ation of Pipette
(a) Use the analytical balance to weigh a clean and dry 50-mL Erlenmeyer flask with a stopper. Weigh
the flask and stopper to ±0.001g. To avoid contamination handle the flask with a paper towel o
crucible tongs.
(b) Pipette 10-mL of deionized water into the weighed flask/stopper.
(c) Weigh the flask and its content to XXXXXXXXXXg.
(d) Using the addition method, repeat this procedure two more times. In addition method, subtract the
previous mass reading to obtain the mass of water for each trial.
(e) Determine the temperature of the water to 0.1◦C and look up the appropriate density (the density is
found in the CRC Handbook). Record the density and calculate the volume of water co
esponding
to one of aliquot of water delivered by the 10-mL pipet (the term aliquot refers to a sample taken fo
analysis). Question: Is the volume of the pipette really 10-mL?
3
3. Determination of the Density of a solution
(a) Obtain about 40-mL of an unknown solution. Record the unknown ID for the liquid.
(b) Use the analytical balance to weigh a clean 50-mL Erlenmeyer flask with a stopper. Handle the flask
with wrapped paper towel or crucible tong.
(c) Rinse the 10-mL pipet which you have cali
ated with about 2-mL of the unknown liquid to remove
any trace of residual water.
(d) Deliver 10-mL aliquot of the unknown solution into the weighed flask/stopper.
(e) Weigh the flask/stopper and solution.
(f) Do not empty the Erlenmeyer flask. Keep the unknown solution in the flask and transfer anothe
10-mL aliquot of unknown solution into the same flask/stopper and weigh again. To determine the
mass of the unknown solution that is added, subtract the previous mass reading. As you perform
calculations keep in mind units and significant figures.
Data Sheet
Determination of the Density of a Metal
Unknown ID: Trial 1 Trial 2 Trial 3
(a) Mass of metal (g)
(b) Volume of Water & metal (mL)
(c) Volume of water (mL)
(d) Volume of metal (mL)
(e) Density of metal (g/mL)
4
Cali
ation of Pipette
Unknown ID:
Trial 1 Trial 2 Trial 3
(a) Mass of flask & stopper plus water (g)
(b) Mass of flask & stopper (g)
(c) Mass of water (g)
(d) Measured Temperature of water (◦C)
(e) Density of water at measured Temp. ( gmL) (from CRC Handbook) =
(f) Calculated volume of water used (mL)
(g) Average volume of water used (mL) =
(h) Average volume of pipet = Average volume of water used (mL)=
Determining the Density of a Solution
Unknown ID:
Trial 1 Trial 2 Trial 3
(a) Mass of flask & stopper + solution (g)
(b) Mass of flask & stopper (g)
(c) Mass of solution per trial (g)
(d) Cali
ated Volume of pipet =
(c) Density of solution per trial (g/mL)
(e) Density of solution at measured Temperature ( gmL )=
5
Statistical Analysis of Experimental Data
All measurements are subject to random e
ors. Because of this, scientists are concerned with the
precision of their experimental data. Precision refers to how close measured values agree with one another.
Statistical analysis of experimental data provides insight on the degree of precision of the measured values.
In what follows you will learn how to apply statistics to the data you colected; this is why you were asked
to perform multiple trials. To begin let’s define a few terms. As you go through your calculations refer to
Table 4 to ensure that you are clear on the meaning of each term.
Table 4. Terms Pertaining to the Statistical Analysis of Experimental Data
Symbol Meaning
x Average value
|x| Absolute value (in this case of x). |x| refers to a value’s distance
from zero.
W This is the Range of the data set. It is defined as the absolute
difference between the largest value and the smallest value the
values in your data set are to the average value.
δ This refers to the difference between the average value and a
specific value from the data set. When calculating deviations it is
useful to calculate absolute deviations. |δ|
δ Average deviation
s This is the Standard Deviation and is used as a measure of
precision. It is a statistical calculation that tells you how close a
set of repetitive measurements are to each other.
The terms in Table 4 are expressed in the Equations below. Consider a set of N trials, x1, x2, x3, ...,
xN . The average value is calculated by applying Equation 1. Notice that the symbol used to define the
average is x. As such, the symbol used