determining the density of a polystyrene spherealpha.chem.umb.edu/chemistry/ch117/117 labs/lab 1 -...

CHEMISTRY 117 University of Massachusetts Boston Laboratory Exercise #1

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Determining the Density of a Polystyrene Sphere

*There are two parts to this lab exercise. Please make sure to read and prepare for both parts before coming to lab.*

PART I: LENGTH AND VOLUME

I. LEARNING GOALS Almost everything that we do in Chemistry Lab this semester is going to involve measuring something. This first laboratory exercise has been designed around the following learning goals. • Provide practice in performing typical measurements. • Instill a deeper understanding of the concepts of precision and accuracy of measurement. • Learn to calculate the average and standard deviation of replicate measurements. • Begin to learn about significant figures. • Appreciate how the precision of a measuring tool determines the precision of the

measurement and thus the precision of the results.

II. INTRODUCTION Accuracy and Precision Precision refers to the degree of variability in the values obtained from repeated measurements. This variability can come from the inherent precision of the measuring device, as well as the technique of the experimenter making the measurements. Accuracy is a measure of how closely the mean (average) of the repeated measurements matches the true value of the “thing” being measured. One of the tried and true teaching strategies for addressing the concepts of precision and accuracy is the use of the dartboard analogy. If a dart player aims some darts at the bull’s eye, the following outcomes are possible.

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A not accurate or precise

B accurate, but not precise

C precise, but not accurate

D accurate

and precise


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For outcome A the darts are scattered over a wide area (low precision) and the average position of the darts is far above and to the right of the bullseye (low accuracy). For outcome B the darts are scattered over a wide area (low precision) and the average position of the darts is centered close to the bullseye (high accuracy). For outcome C the darts are focused in a tight area (high precision) and the average position of the darts is far above and to the left of the bull’s eye (low accuracy). For outcome D the darts are focused in a tight area (high precision) and the average position of the darts is centered close to the bull’s eye (high accuracy). Relating this analogy to the process of making a measurement in a chemistry lab, the bull’s eye represents the true value of the thing being measured and the average position of the darts represents the mean of the repeated measurements. This experiment will focus on evaluating the precision of three different methods for measuring the volume of a small sphere; that is, the variability in the data obtained from repeat measurements. To evaluate the accuracy of these methods one would have to know the true volume of the sphere (more on this later). The Precision of the Measurement Tool What is the diameter of the circle below? It’s larger than 0.5 units and less than 1 unit. It’s closer to 1 unit than 0.5 units. Could it be said that the diameter is 0.7 units, 0.8 units or maybe 0.9 units? How about 0.85 units? How precise is this measurement tool?

Below is the same measurement with a “better” ruler. It is clear that the circle is larger than 0.8 units and less than 0.9 units. It looks about half way between the two. It could be said that it is close to 0.85 units, but the last digit is really just an estimate.


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Below is the same circle enlarged and measured with a more precise ruler. It looks as if the circle is at least 0.86 units. It appears to be a little larger, maybe 0.861 units or 0.862 units. The measurement tool indicates that the eight and the six are correct, but the last digit is really an estimation. It is generally accepted (and should be commonly practiced in this laboratory) to estimate a single graduation to the nearest tenth (Thus if the graduation is to the hundredths place, the thousandths place should be estimated). This estimated digit determines the place of least significance when the measured value is reported.

The precision of the diameter measurement can have a great impact on calculations that are made later with them. In this quick experiment the diameter of a polystyrene sphere will be measured. Using this measurement the volume of the sphere can be calculated using the following equation:

Then the volume of the sphere will be measured by the method of water displacement using a graduated cylinder. It is important that the proper technique be used for reading volume with


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this instrument. After measuring the volume by this method, the results will be compared to those of five other groups. As the measurements are recorded and calculations are carried out, it is important to include the units and the correct number of significant digits.


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III. PROCEDURE A. Measurement of the volume with a ruler

Measure the diameter of a polystyrene sphere in centimeters using the metric ruler and write it in the data table below (1). Check with your TA whether you have reported this value with the proper significant figures. You may need three rulers, three hands, paper and a pencil to do this with the best possible precision.

B. Measurement of the volume using a graduated cylinder (one ball)

Fill a 25 mL graduated cylinder with about 12 mL of water. Measure the volume of water in milliliters by setting the graduated cylinder on the lab bench at eye level and carefully reading the bottom of the meniscus of the water level to the nearest 0.02 mL. Note it in the data table below (3). The increments of the graduated cylinder are every 0.2 mL, so the uncertainty in the measurement is ± 0.02 mL. Add one polystyrene sphere into the graduated cylinder (carefully! No Splashing!). Measure the total volume in milliliters by setting the graduated cylinder on the lab bench at eye level and carefully reading the bottom of the meniscus of the water level to the nearest 0.02 mL. Note it in the data table below (4).

C. Measurement of the volume using a graduated cylinder (ten balls)

Add nine more polystyrene spheres [10 total] (carefully! No Splashing!) to the graduated cylinder. Measure the total volume in milliliters by sitting the graduated cylinder on the lab bench at eye level and carefully reading the bottom of the meniscus of the water level to the nearest 0.02 mL. Note it in the data table below (6).


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DATASHEET (Pg 1 of 6) NAME:

Measurement of the volume with a ruler

1. Diameter of a polystyrene sphere using the metric ruler (in centimeters).

2. Calculate the volume of the polystyrene sphere in cm3 from the measured diameter (V = 4/3πr3, where r = d/2)

Measurement of the volume using a graduated cylinder (one ball)

3. Volume of water added to the graduated cylinder.

4. Volume of water plus one polystyrene ball.

5. Calculate volume of one polystyrene sphere: [Volume of sphere = total volume – volume of water]:

Measurement of the volume using a graduated cylinder (ten balls)

6. Volume of water plus ten polystyrene balls.

7. Calculate volume of ten polystyrene spheres: [Volume of ten spheres = total volume - volume of water]:

8. Calculate average volume of spheres: [Volume of one sphere = (1/10)volume of ten spheres]:

You now have three different measurements of the volume of a polystyrene sphere from #2, #5 and #8. From different members of your lab class, obtain five other values for each of the three methods. If you should find that your group completed the experiments quicker than the rest of your classmates, DON’T JUST SIT THERE WAITING FOR THEM TO FINISH. REPEAT THE EXPERIMENT and then you can use both sets of your data in Table 1. Table 1

#2 volume of sphere #5 volume of sphere #8 volume of sphere

from ruler from water displacement of one sphere

from water displacement of ten spheres

Your results:

Labmate #1

Labmate #2

Labmate #3

Labmate #4

Labmate #5


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DATASHEET (Pg 2 of 6)

Calculate the mean for the three measurements.

Table 2 Calculating the Means

From Ruler From Water displacement of one sphere

From Water displacement of ten spheres

Mean cm3 mL mL

The most commonly used measure of uncertainty is called the standard deviation. The standard deviation is a measure of the differences between the actual numbers and the mean.

Calculating the standard deviation using this equation is easiest if you break it down into steps. The following worksheets take you though each of the individual steps. The first step is to calculate the difference between each of the values (from Table 1) and the mean (from Table 2). Place these differences in Table 3: Table 3 Calculating the Deviation from the Mean

#2 #5 #8

from Ruler from water displacement of one sphere

From water displacement of ten spheres

Your number – mean:

Labmate #1 – mean:






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The second step is to square each of the differences calculated in the first step (Table 3): Table 4 Squaring the deviation from the mean

#2 #5 #8



(Your number – mean)2: cm6 mL2 mL2

(Labmate #1 – mean)2:





The third step is to add together each of values in the columns of Table 4: Table 5 Summing the squares of the deviations

from Ruler from water displacement of one sphere


Total of Squares: cm6 mL2 mL2

The final step is to divide the numbers in Table 5 by the number of data points minus 1 (or 5 in our case) and take the square root to get the standard deviations: Table 6 Calculating the standard deviations



Standard Deviation:

Often the results are reported as as the mean ± standard deviation. It is intended to represent a range of possible “values” based on the precision of the measurement. Table 7 Reporting the mean with the standard deviation



Overall Result ± ± ±


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PART II: MASS AND DENSITY

I. LEARNING GOALS • Learn proper techniques for weighing substances using a triple beam balance and an

analytical balance. • Instill a deeper understanding of the concepts of density. • Continue to learn about significant figures. • Appreciate how the precision of a measuring tool determines the precision of the

measurement and thus the precision of the results.

II. INTRODUCTION 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 (read “grams per milliliter) or g/cm3 (1 mL = 1 cm3).

III. 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 four 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.


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DATASHEET (Pg 4 of 6) NAME:

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:

2a. 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:

3a. Calculate the mass of 10 spheres on the triple beam balance:

3b. Calculate the average mass of a sphere by dividing the mass of 10 spheres by 10 (remember that 10 is an exact number in this case):

Measuring Mass on an Analytical Balance. It is critical in this experiment, as well as future experiments, 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:

5a. 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:

6a. Calculate the mass of 10 spheres on an analytical balance:

6b. Calculate the average mass of a sphere by dividing the mass of 10 spheres by 10 (remember that 10 is an exact number in this case):


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Add your data and the data from FIVE 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 Measurement method

1 ball method/ triple beam

(2a)

1 ball method/ analytical

(5a)

10 balls method/ triple beam (3b)

10 balls method/ analytical

(6b)

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 ± standard deviation of these calculations.

Mean ± sm

**Note: Excepting PART I, it is not necessary to calculate standard deviation long-hand. You are encouraged to seek out the owners manual of your calculator to determine how to calculate standard deviation quickly.**


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Density Calculation

Using the method that you deem most precise, record the mean and standard deviation of the volume of a polystyrene sphere from PART I above.

±

Calculate the density using the average masses from the above table and data from PART I for the volume (D = m/V). METHOD DENSITY 1 ball / triple beam (2a)

1 ball /analytical (5a)

10 balls /triple beam (3b)

10 balls /analytical (6b)

Measurement method

1 ball method/ triple beam

(2a)

1 ball method/ analytical

(5a)

10 balls method/ triple beam (3b)

10 balls method/ analytical

(6b)

Density


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IV. Lab Report The initial submission of your lab report will be worth up to 50 points. Use next page as a guide for a well-written lab report. The report will be graded during the lab writing workshop session. You will receive a 0, 30(√-), 40 (√), 50 (√+) based on how well you follow the guidelines.

1. TITLE 2. ABSTRACT 3. INTRODUCTION 4. MATERIALS AND METHODS 5. DATA and ANALYSIS 6. DISCUSSION 7. CONCLUSIONS There is no minimum page limit for a lab report, however if all sections are written appropriately and thoroughly, you will find that it will typically 2-4 pages in length. DISCUSSION POINTS As mentioned above, precision refers to the variation in data obtained from repeated measurements. Accuracy refers to the difference between the mean obtained from repeated measurements and the true value. Accuracy can only be evaluated if one has verified the accuracy of a measuring tool. This verification is usually accomplished by using a primary standard that has been accurately measured previously by some other validated method (in other words, the true value must be known). To receive full credit for your discussion sessions, the following questions should be answered.

• According to your class data (considering all five sets), which measurement method for volume of the spheres is the most precise? Least precise?

• According to your class data (considering all five sets), which measurement method for mass of the spheres is the most precise? Least precise?

• Are the most and least precise measurement methods the ones that you expected them to be? Explain.

• Explain why the precision is different when you measure ten balls to get an average volume and mass.

• If the true value for the density of a sphere is 1.05 g/mL , which method is most accurate?


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WHAT IS A LAB REPORT? A written lab report is a common scientific exercise that helps to convey why an experiment was performed, how an experiment was performed, what the results of the experiment were, and why those results are of significance. For this experiment, you are being tasked with writing a complete lab report. A complete lab report consists of:

• TITLE: A summation of the experiment in ten words or less. It should describe the main point of the laboratory work. For example: Effects of Atmospheric CO2 Concentrations on the Global Climate.

• ABSTRACT: A summary of what is contained within a lab report. This allows the author to highlight key information contained in the following sections and provides the reader with key points so they can determine if the lab report contains information they seek. The abstract should be the last thing that is written for the lab report, as it contains elements of all the other sections. An abstract should be roughly three to six sentences. This is more difficult than it sounds, so allow time for several revisions.

• INTRODUCTION: In a scientific research article this section of the paper is devoted to making the case for why the work is important and significant and for discussing the previous work reported in the literature that has led up to the work being reported in this paper. In a lab report the nature of the introduction section is a little bit different than in a research article. In a lab report you should focus the introduction on the learning goals of the experiment. Discuss how the experiment is designed to achieve these learning goals and how the experiment fits in with the broader curriculum of the corresponding lecture course.

• MATERIALS AND METHODS: This section should provide the details of how the

experiment was carried out. It should not be written as a recipe but more as a journal entry; a fairly detailed account of what was done in lab. A description of how the data was processed should also be part of the Methods section.

• DATA AND ANALYSIS: When appropriate you data should be displayed in tables and

figures. The figures and tables should have captions that describe what they are illustrating. You should also prepare sentences that introduce the tables and figures and describe what they show. To an extent these sentences and the captions will be and should be somewhat redundant.

• DISCUSSION: A description of what the data means. Points of discussion could

include: The discussion section will discuss the significance of the findings from the data analysis section. It is also in this section the questions that are being asked are addressed in the context of a well-written paragraph.


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(1) Was the goal of the experiment achieved? (2) If the results obtained are poor, what could have happened during the experiment to explain this?

• CONCLUSION:

The conclusion should be a separate paragraph that briefly reiterates what happened in the experiment, what the results are, and what those results mean.

In the upper right hand corner of your first page, be sure to include your name, your TA’s name, and the date the experiment was performed. It is imperative that scientists are able to communicate clearly in their writing. Thus, the lab report will be graded both on the content of the report and the quality of the writing.

determining the density of a polystyrene spherealpha.chem.umb.edu/chemistry/ch117/117 labs/lab 1 -...

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