Chemistry 117 Laboratory University of Massachusetts Boston
Name ______________________________________________________________________
Chemistry 117 Laboratory University of Massachusetts Boston
MASS AND DEN...
Name ______________________________________________________________________
Chemistry 117 Laboratory University of Massachusetts Boston
MASS AND DENSITY --------------------------------------------------------------------------------------------------------------------------------------------
In the Experiment “Length and Volume” you did some simple measurements and calculations involving the volume of a sphere. Today, we will measure the mass of the polystyrene spheres, using this measurement and the result from last week to calculate the density of the polystyrene spheres and perform some more sophisticated calculations to estimate the uncertainty in the density of the sphere. LEARNING GOALS 1. 2. 3. 4. 5.
Learn proper techniques for weighing using a triple beam and an analytical balance. Obtain a deeper understanding of the term “density” as a property of a substance. Appreciate how the precision of your tool affects the precision of your measurement. Appreciate how the precision of a derived term is limited by the precision of your measured terms. Learn the proper way to propagate error when multiplying or dividing two or more measured terms (such as mass and volume to obtain density).
Density Density is the mass of a substance divided by its volume. It is an inherent property of a substance. For instance, measuring the density of a metal can help you identify it. In chemistry applications, density is most often expressed in the units of g/mL or g/cm3 (1 mL = 1 cm3).
D=
m V
Precision and Error Propagation In this experiment we will measure the mass of a polystyrene ball using four different methods. Similar to last week’s experiment, the methods will highlight differences in terms of the precision in the measuring devices and the precision measurement strategies by using two different balances and by using both one and ten balls to make the measurements. You will combine your data with your classmates to obtain an average mass of a polystyrene ball along with a standard deviation for the measurements using each of the four methods. You will then use this data along with your most precise measurement of the volume of a polystyrene sphere from last week’s experiment to calculate its density. The uncertainty in the density is dependent upon both the uncertainty in the mass and the volume. Using the uncertainties in the factors (m and V) to estimate the uncertainties in the product (D) is referred to as “propagating the uncertainty”. Propagating the uncertainty is a much more refined method for estimating the uncertainty in a calculation then simply applying the rules of significant figures and should
Mass and Density
always be used when actual uncertainties are known in the measured quantities that are being mathematically manipulated. When two terms are multiplied together, the square of the relative uncertainty in their product (D) is equal to the sum of the squares of the uncertainties of the terms (m and V). In this case 2
2
⎛s ⎞ ⎛s ⎞ ⎛ sD ⎞ ⎜ ⎟ =⎜ m ⎟ +⎜ V ⎟ ⎝D⎠ ⎝ m⎠ ⎝V ⎠
2
Where D, m and V are the density, mass and volume, respectively. sm and sV are the uncertainties in the mass and volume (their standard deviations obtained from repeated measurements), and sD is the uncertainty in the density (the quantity that we are attempting to estimate using this formula). sD/D, sm/m and sV/V are the relative uncertainties in the density, mass and volume, respectively. You will be solving for sD. It follows that the relative uncertainty of the product term (in this case, the density) is limited by the term that has the greatest relative uncertainty. Let’s look at an example. mass of a polystyrene ball = 0.53572±0.00005 g volume of a polystyrene ball = 0.444±0.008 mL
sm/m = 0.00009 sV/V = 0.018
D = 0.53572/.444 = 1.21±0.02 g/mL Where did the 0.02 came from? 1
⎡⎛ s m ⎞ 2 ⎛ sV ⎞ 2 ⎤ 2 s D = D ⋅ ⎢⎜ ⎟ + ⎜ ⎟ ⎥ ⎢⎣⎝ m ⎠ ⎝ V ⎠ ⎥⎦ 0.02174 = (1.21) {(0.00009)2+(0.018)2}1/2} In this case, uncertainty in the density is limited by the uncertainty in the volume because the relative uncertainty in the volume is much larger than the relative uncertainty in the mass.
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Mass and Density
LABORATORY PROCEDURE Learn the technique for determining mass with a triple beam balance and an analytical balance from your instructor. We will be measuring the mass of the polystyrene balls using for strategies. The first two strategies involve weighing one polystyrene ball on each of the balances. Which balance is more precise? The other two strategies involve weighing ten polystyrene balls of each of the two balances. Each measurement and calculation should be recorded with the appropriate unit and the correct number of significant figures. Measuring Mass on the Triple Beam Balance. It is critical in this experiment to report the measurements with the correct precision (to the nearest 0.01 g for the triple beam balance). 1. Determine the mass of a clean small 50-mL beaker on a triple beam balance:
____________ __
2. Place one polystyrene sphere in the beaker. Determine the mass of the beaker + the sphere on the triple beam balance:
____________ _
a. Calculate the mass of one sphere on the triple beam balance: 3. Add 9 more spheres to the beaker (10 total). Determine the mass of the beaker + 10 spheres on the triple beam balance:
___ __ ________
_____ _______ _
b. Calculate the mass of 10 spheres on the triple beam balance:
____________ _
c. Calculate the average mass of a sphere by dividing the mass of 10 spheres by 10:
______________
Measuring Mass on an Analytical Balance. It is critical in this experiment to report the measurements with the correct precision (to the nearest 0.0001 g for the analytical balance).
4. Determine the mass of the beaker on an analytical balance:
______________
5. Place one polystyrene sphere in the beaker. Determine the mass of the beaker plus the polystyrene sphere on an analytical balance:
_____ ________
d. Calculate the mass of one sphere on an analytical balance:
_____________
6. Add 9 more spheres to the beaker (10 total). Determine the mass of the beaker plus 10 spheres on the analytical balance:
_____________ 3
Mass and Density
e. Calculate the mass of 10 spheres on an analytical balance:
_____________
f. Calculate the average mass of a sphere by dividing the mass of 10 spheres by 10:
_____________
Add your data and the data from four other lab groups to the table below and calculate an average and standard deviation for the mass of a sphere obtained from the four methods.
MASS of ONE SPHERE 1 ball method/ 10 balls method/ analytical triple beam (3c) (5d)
10 balls method/ analytical (6f)
Your Data From members of your lab, obtain five values for each of the four methods: Labmate #1: Labmate #2: Labmate #3: Labmate #4: Labmate #5: Calculate the mean and standard deviation of these calculations. Mean ± sD
7. Record the calculated volume of a polystyrene sphere from last week’s “ten balls” experiment
________±_______
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Mass and Density
Density Calculation Calculate the density using the average masses from the above table and last week’s data (#7) for the volume (D = m/V). Estimate the uncertainty in the density by propagating the uncertainties in the mass and volume, as outlined in the introduction. Your uncertainty should only have one significant digit and the last significant digit in the density should match the place of the standard deviation. METHOD
Lab Report Your lab report must consist of an abstract, answers to the five questions that follow and your data sheet (pg 3-5). Each question is worth 4 points. The abstract is worth 10 points. The data sheet is worth 30 points. The following is a grading rubric for the abstract. See syllabus for information on how to prepare a well-written abstract. Content 1 pts 1 pts 1 pts 1 pts 1 pts
All of the key pieces of data discussed. The data is interpreted correctly. The conclusions drawn from the data are correct. It is evident that the student understands the main points of the laboratory experiment. It is evident that the student was able to connect the learning goals of the experiment with data obtained in the experiment.
Quality of your writing 1 pts 1 pts 1 pts 1 pts 1 pts
It is written in complete sentence(s). The sentences are comprehendible to the reader. It summarizes the experiment and the result and puts the results in context of the learning goals. It is an appropriate length; 3-6 sentences. It is written in the passive voice with no pronouns or phrases such as “In this lab we”.
1. Which method gives the most precise measurement of the mass of the polystyrene ball? 2. Which method gives the most precise measurement of the density of the polystyrene ball? 3. For which sets of data is the difference in precision between the 1 ball and 10 ball weighing methods best reflected in the uncertainties of the densities? Explain. 4. The difference in the precision of the balances is best reflected using the data from the “1 ball” weighing method. Why do you think this is the case? 5. If you were given time to further develop this experiment, what aspect of the experiment (measuring the volume or measuring the mass) would you focus on if your goal was to more precisely measure the density of the polystyrene ball and Why?
