Student_MeasurementsAccuracyPrecision 9_2023

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Measurements, Accuracy and Precision General Directions: All work should be completed and typed directly into this word document whenever possible. Alternatively, students may insert images of hand-written work/calculations. Save the file with your last name in the title (i.e. Student_Measurements_Lab.) Upload the completed document to Canvas in the correct assignment tab by the due date. Specific Directions: This lab has two Parts: Part A and Part B. Complete all data sections by typing in data after (1) reading the background and (2) watching the appropriate experiment videos carefully. After reporting necessary data in “Data Tables”, complete the “Calculations and Results Section” that follow. Then, write a ~1-2 paragraph “Discussion/Conclusion” for the entire lab (Part A+B). This should include a brief explanation of the general principles (in your own words) used in the experiment and how they relate to each other, the results of the experiments, and whether they were accurate according to your calculations. Preparing your Lab Notebook and Lab Report Prior to coming to lab, your notebook should include everything required by the video and document “Lab Notebook Guidelines”. This includes: the objectives of the experiment, necessary mathematical or chemical equations, a brief overview of lab procedures (1-2 written pages max) for all parts of the lab, and any tables that you will need for data analysis. Your summary should not be a copy of the lab procedures, but they should be detailed enough for you to follow in the lab. Write all observations directly into your lab notebook as you go. When you are finished, complete your calculations in your lab notebook, and if there is time complete the post lab questions. For your lab report, follow the directions in this document and follow the format that is provided on the lab grading rubric. ( These blank tables need to be in your notebook prior to attending lab. You will fill in the data directly into your notebook as you complete the lab. Failure to prepare your notebook will result in forfeiture of notebook points on your lab report. Remember to record units for your measurements. Data Table Part A. Station Readings Burets Graduated Cylinder Balances Rulers Data Collection Table for Part B Mass Empty Beaker Volume of Water Mass Beaker + Water Graduated Cylinder Buret Initial Vol.: Final Vol.: Vol of Water: Page 1 of 16

Measurements, Accuracy and Precision Data Table 2 Part B . Individual Observations Density of Water (g/mL) Graduated Cylinder Buret Result 1 (yours) Result 2 (Student A) Result 3 (Student B) Result 4 (Student C) Sum = Average (Mean) = Standard Deviation = % Error = % % OBJECTIVES 1. To record accurate and precise measurements using various laboratory instruments. 2. To determine and compare the accuracy and precision between a graduated cylinder and a buret by measuring the density of water. 3. To perform calculations with numbers with significant figures and to understand how they indicate how good a measurement is. BACKGROUND Part A: Measurements –, Significant Figures, Reading Equipment, and Calculations Significant figures: 1. Significant figures are nothing more than the number of digits we get from a measurement. The better a measurement is, the more significant figures you will have. Numbers that you don’t measure, such as conversion factors, have no significant figures. For example, if you measure a sample on a balance and the balance reads 2.543 g, then there are 4 significant figures. If you measure the same sample on a more sensitive balance, it may read 2.5438 g. The second measurement has 5 significant figures, and reflects a better measurement. Zeros at the beginning of small numbers (0.0000 53) are not significant. Likewise, zeros at the end of large numbers are not significant unless indicated with a decimal point or if they are included in scientific notation. 4.50 x 10 3 has 3 significant figures while 4,500,000 only has 2 significant figures. 2. The very last digit in a measurement is always the least certain. Two people reading the same length on a ruler may see 1.24 cm vs. 1.25 cm. All three numbers are significant figures, but the last number has a bit of uncertainty. Both values are correct because it is expected that the last number is the uncertain one. Page 2 of 16

Measurements, Accuracy and Precision 3. When making measurements be sure to record ALL the digits that the instrument allows for. Each one is considered significant. For example, a ruler that reads 1.36 cm has 3 significant figures. A beaker with 12.50 mL of liquid has 4 significant figures. Scientific equipment has markings that let you read its measurement to a certain number of significant figures. The last value in your reading will always be an estimate between the markings. This is why no two people will necessarily have the same exact number. DO NOT start rounding until you are doing calculations with these numbers. o Ruler example: Here we see a ruler with markings every number, but none in between. The measurement between 6 and 7 looks to be a little before the half ‐ way point. Acceptable answers for this measure of distance would be anywhere from 6.2 ‐ 6.4. o Volume example: When you read volumes in glassware, you read a point called the meniscus . When you add liquid to glassware, the interface between the air and the liquid being measured bends to form a shape like a “U”. This “U” shape is the meniscus. Always read the bottom of the meniscus so that it is at your eye level. The meniscus here is right around the 11.5 marking. Possible answers would be 11.49 ‐ 11.52. You read a thermometer in the same way. Calculations with Significant Figures For addition and subtraction, pick the number with the fewest decimal places. Use that same number of decimal places in your final answer. Example: 12.0 + 12.13 = 24.1 , 0.02 ‐ 0.0032=0.02 For multiplication and division, you need to determine which numbers are indeed significant. If a number starts with zeros, those are not significant. Any other zeros are. Count all digits in the numbers. In your final answer, use as many significant figures as the number with the fewest digits . If you end up with an answer with zeros at the end, it is best to write that in scientific notation if the answer is ambiguous. Example: 0.003520 x 125 = 0.44 = 0.440 143 /0.02010=7110 = 7.11 x 10 3 Page 3 of 16

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Measurements, Accuracy and Precision Part B: Accuracy & Precisions – Density Determination In this experiment, you will determine and compare the accuracy and precision of a graduated cylinder and a burette, by accurately weighing an exact volume of water delivered by each of these measuring devices. You will then calculate the density of water for each measurement (D=mass/V) and compare your results to those of your classmates, obtaining multiple results for each device. You will then determine the accuracy and precision for determining water density using each device. Accuracy and precision of measurements . Accuracy refers to the closeness of an experimental measurement (or the average of a set of measurements) to the “true”, “accepted”, or “correct” value. Its opposite, error , is the absolute difference between the experimental value (or the average of a set of measurements) and the “true”, “accepted”, or “correct” value. Error = |Experimental value – True value| Measurements that are accurate have low error, and measurements that are inaccurate have high error. Another way to express the accuracy of a measured value is to calculate is percent error: % Error = ¿ Experimental value − T rue value ∨ ¿ True value x 100 ¿ (1) In this part of the experiment, you will measure the accuracy of the two measurement devices by recording the mass of a given volume of water that each device delivers, and then calculating the density of water. The density of water at various temperatures has been measured very accurately by many experimenters, in many laboratories, and is therefore well known. Accepted values are shown in Table 1. At room temperature the density of pure water is near 1.00 g/mL, but the exact value depends on the temperature at which the measurement is made. In this experiment, we will express accuracy as % Error, so the measuring technique having the lowest % Error will be the most accurate. Table 1. Density of Water at Various Temperatures Temperature Density ºC g/mL 15.0 0.999099 16.0 0.998943 17.0 0.998774 18.0 0.998595 19.0 0.998405 20.0 0.998203 21.0 0.997992 22.0 0.997770 23.0 0.997538 24.0 0.997296 25.0 0.997044 Page 4 of 16

Measurements, Accuracy and Precision 26.0 0.996783 27.0 0.996512 Source: CRC Handbook of Chemistry and Physics, 50 th edition. Precision refers to the degree of agreement among several measurements of the same quantity, i.e. , the reproducibility of the measurements. Precision is not the same as accuracy , although non-scientists often misuse the two terms interchangeably. The method that your data would show as the most precise would be the one whose measurements are closest to each other, regardless of how near or far they are from the true value. The precision of repeated measurements of the same quantity can be assessed in many ways. One common way is the standard deviation (s) of the measurements: s = √ ∑ i = 1 n ( x i − ¯ x ) 2 n − 1 = √ ( x 1 −¯ x ) 2 +( x 2 −¯ x ) 2 +( x 3 −¯ x ) 2 + ... +( x n −¯ x ) 2 n − 1 (2) where n is the number of measurements i is the index number of each measurement. i = 1, 2, 3, …, n x i represents each of the “n” individual measurements (x 1 , x 2 , x 3 , …, x n ) ¯ x is the average of the measurements ( a.k.a. , the “mean” of the measurements) Σ is the summation operator (which indicates that you sum the terms that follow it) For example, the standard deviation of the following four measured values: 2 ft., 4 ft., 3 ft., and 1 ft. (for which the average is 2.5 ft.) would be calculated as: s = √ ( 2 − 2.5 ) 2 +( 4 − 2.5 ) 2 +( 3 − 2.5 ) 2 +( 1 − 2.5 ) 2 4 − 1 = 1.3 ft. Standard deviations always have the units of the quantity being measured (ft. in the above example.) As a “rule of thumb”, standard deviations usually should be rounded to two significant figures . The smaller the value of the standard deviation “s”, the smaller is the deviation of the individual data points around the mean, and the more precise are the measurements. To determine the precision of the volume-measuring devices, you will compare the density of water calculated using data from each of your devices, with the densities measured by four of your classmates. Techniques for Using Burets Accurately: 1. Water in the buret should drain freely, without leaving clinging drops on the inside. If that’s not the case for your buret use only the portion of the buret that drains freely. 2. Record your readings carefully. Burets are tricky to read, because they are calibrated from top to bottom. 3. Read burets to the nearest 0.01 mL. This requires interpolation between the smallest calib-ration marks on the buret, and there is some uncertainty in the digit in the second decimal place. DO NOT just add a zero after the first decimal place. This introduces a small error. 4. Some people find it helpful to read a buret while holding a piece of paper behind the buret to blank out objects or people across the room. Page 5 of 16

Measurements, Accuracy and Precision 5. Do NOT initially fill the buret to EXACTLY 0.00 mL. Just fill to within a couple of mL from the top, and read the value exactly. 6. Be sure the tip of the buret is free of air bubbles before you make the initial reading. You can do this most easily by opening and closing the stopcock rapidly several times to allow the liquid running through the tip to dislodge the bubbles. Do this even if you don’t see an air bubble, because one might be in the opaque Teflon stopcock where you can’t see it. 7. Wipe off any drop hanging from the buret tip immediately before measuring out the liquid. Also wipe off the outside of the tip itself so that no water is transferred from outside the buret. Technique for Using Graduated Cylinders Accurately: To obtain a specific volume in a graduated cylinder, use a medicine dropper to add the last few drops of water without going over the line. Use the dropper to remove some if you add too much. PROCEDURES Part A: Measurements: There are stations set up around the lab that you will visit. Read the equipment at each station and record your values in your notebook. You can start with any station. When you are finished, do the required calculations. Station 1: Reading burets Burets are long pieces of glass with calibrated markings on the side. They are marked backwards, where the 0.00 ‐ mL mark is at the top, and the 50.00 ‐ mL mark is near the bottom. These are used to measure the amount of liquid that is delivered by subtracting numbers. Read and record the volumes of the three burets in your laboratory notebook. Station 2: Graduated cylinders Graduated cylinders are used to measure more exact volumes of liquid. They are thin glass tubes with markings up the side, similar to a buret, except they start at 0.0 ‐ mL and go up. These will show a meniscus, so be careful when you are reading them. Read and record the volumes of the three graduated cylinders in your laboratory notebook. Page 6 of 16

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Measurements, Accuracy and Precision Station 3: Balances Balances are great for measuring the mass of objects. Use the balance to measure and record the mass (weigh) of one metal sample on three different balances . Station 4: Rulers Rulers are not used as often in chemistry as the other equipment you have seen in this experiment, however, depending on the discipline, rulers prove a valuable device for measuring distance. Measure and record the length of three strips of tape in your laboratory notebook. Calculate the average and the standard deviation for each instrument. PART B. Accuracy and Precision of Density Measurements Shared lab equipment will be out on the benches by the windows. Other equipment will be in your lab drawers. Be sure to make and record all measurements as accurately as you can, and to retain as many decimal places as possible or significant figures that the measuring device provides. Also, record values with proper units, and round final calculated values appropriately. Fill a large beaker with distilled water and place it on your workbench with a thermometer in it. Wait a few minutes for the thermometer to equilibrate, then measure and record the temperature of the water you will be using. Use this water for all of Part B. Prepare your buret with water in it. Your instructor will demonstrate and remind you of proper techniques. Graduated cylinder: 1. Measure the mass of a small beaker. 2. Measure between 11.5-13.5 mL of water using a graduated cylinder. Be sure to record the volume to the correct number of decimal places. Empty the water into the beaker. 3. Reweigh the beaker with the water in it. 4. Calculate the mass of the water and then the density. Watch significant figures. Buret: 1. Measure the mass of a small beaker. 2. Measure between 25.00-35.00 mL of water from the buret directly into the beaker. Be sure to record the volumes to the correct number of decimal places! 3. Reweigh the beaker with the water in it. 4. Calculate the mass of the water and then the density. Watch significant figures. Page 7 of 16

Measurements, Accuracy and Precision Page 8 of 16

Measurements, Accuracy and Precision Calculations: Calculate the density of water from your measurements using each device. If your density is significantly different from the known value, then repeat your measurements. Share your densities with at least three other people (more may yield better results.) Disregard any result that is in obvious disagreement with the others, unless it is yours (in which case repeat your measurement). For each measurement device, tabulate the following in your lab notebook. a) The density of water calculated by you and for at least three other students. b) The average density of water obtained for that volume-measuring device, i.e. , the average density for the graduated cylinder, and the average for the buret. c) The percent error of the density of water delivered for each measuring device. For each measuring device, use the average density calculated as the “Experimental value” in calculating the % Error. d) The standard deviation of the density of water for each measuring device. Based on percent error, determine which device (buret or graduated cylinder) the density of water was determined most accurately. Based on standard deviation, determine which device (buret or graduated cylinder) the density of water was determined most precisely. Page 9 of 16

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Measurements, Accuracy and Precision  Carefully read the entire document. Insert values, calculations, and explanations where necessary.  Upload the completed document to Canvas in the correct assignment tab by the due date . Note: The format of this lab report is a shorter “Worksheet”. No Title Page and Results Statement nor Discussion and Conclusion are needed. This Lab Report component contains 85 points. The remaining 15 points for this experiment are earned through completion of the Lab Quiz questions. Report Component Points Available Criteria & Maximum Point Deductions Points Earned Notebook Prep 10 –1 to –5 Not preparing notebook prior to experiment according to “Laboratory Notebook Guidelines” or the experimental procedure Lab Data Section/Data Tables 30 –1 to –15 Based on correct values obtained from experimental data. Be mindful of units, Sig Figs, and signs (potential negative quantities). Lab Calculations 30 –1 to –20 Based on correct calculations (final number, and some degree of work shown where necessary) Post-Lab Questions 15 –1 to –15 Based on Answer Key. Total points (out of 85): Page 10 of 16

Measurements, Accuracy and Precision Note: The format of this lab report is a shorter “Worksheet”. No Title Page and Results Statement nor Discussion and Conclusion are needed. For “Full Lab Reports” you will need these additional components. (For future experiments if you did need the components above, insert your title page and results statement here. Your Results statements should be a paragraph summary stating the goal of the experiment, and major pieces of data acquired. Include which device was most accurate and why. Include which device was most precise and why ) Page 11 of 16

Measurements, Accuracy and Precision 30 Points Total. Lab Data Section: Report Sheet Complete the following report sheet using your lab data from your notebook. Points are earned for complete tables and correct values. (8 Points). Complete the report sheet table. I nclude units with your measurements in the “Readings” and “Average” columns. Station Readings Average Standard Deviation 1. Burets 2. Graduated Cylinders 3. Balances 4. Rulers Temperature of Water: [Insert Value Here] Density of Water at this temperature from Table 1: [Insert Value Here] (6 points). Density of Water Individual Results: Volume of Water (mL) Mass of Water (g) Density of Water (g/mL) Grad. Cylinder Buret (8 points). Density of Water Based on Several Students’ Data: Student Name Grad. Cylinder Buret 1. 2. 3. 4. Page 12 of 16

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Measurements, Accuracy and Precision Sum Average (mean) Standard Deviation Percent Error (8 points). Assess the lab equipment (cylinder vs. buret ): Which instrument most accurately determined the density of water: [Insert answer here] Which instrument most precisely determined the density of water: [Insert answer here] Page 13 of 16

Measurements, Accuracy and Precision 30 Points Total. Lab Calculation Section General Directions for inserting calculations: A. Label and complete these calculations in your lab notebook, then take a photo and insert images below. Or B. Type the calculations that you are solving. Remember to include proper units!  For this choice, use the “Insert  Equation” function in MS Word. Show examples of the following calculations from the laboratory procedure below. Part A: Calculations 9 Points Total. Show average volume calculations for the buret and graduate cylinder, and average masses from the balances: (Buret Avg)= [Remove this statement and enter calculation here] (Grad Avg)= [Remove this statement and enter calculation here] (Balance Avg)= [Remove this statement and enter calculation here] 12 Points Total. Show standard deviations from your buret reading (“BuretStdv”), your graduate cylinder reading (“GradStdv”): (Buret Stdv)= [Remove this statement and enter calculation here] (Grad Stdv)= [Remove this statement and enter calculation here] Part B: Calculations 9 Points Total. Show average density calculations (“DensityAvg”) and standard deviation calculations (“DensityStdv”) below: (DensityAvg)= [Remove this statement and enter calculation here] (DensityStdv)= [Remove this statement and enter calculation here] Page 14 of 16

Measurements, Accuracy and Precision Discussion/Conclusion Statement (20 points): Note: The format of this lab report is a shorter “Worksheet”. No Title Page and Results Statement nor Discussion and Conclusion are needed. For “Full Lab Reports” you will need these additional components. [For future experiments if you did need the components above,. Insert Discussion/Conclusion paragraphs here. Discussion and conclusion statements should be stand-alone paragraphs that anyone could read and quickly understand what you determined, how precise and/or accurate your results were, sources of error, potential improvements to the experiment and applications of the experiment to a broader topic. Some discussion of the topics and how they relate is expected] Discussion/conclusion statements should be stand-alone paragraphs that anyone could read and quickly understand what you determined, how precise and/or accurate your results were, sources of error, potential improvements to the experiment and applications of the experiment to a broader topic. For example, do not simply state that the objective of the experiment was met but rather state what the actual result was. Avoid repeating the procedures from the experiment but be clear when you discuss sources of error and improvements: “It was difficult to get the volume correct” vs “Due to lack of experience it was difficult to use the pipet bulb and the volumetric pipets which may have resulted in significant errors in the volume.” Do not include personal statements about the experiment –I did not understand the procedures…. Note: The format of this lab report is a shorter “Worksheet”. No Title Page and Results Statement nor Discussion and Conclusion are needed. For “Full Lab Reports” you will need to include these additional components. Think about the following topics below. An excellent discussion and conclusion paragraph would address the following. : - (X points) Part A: Discuss which device was the most precise, which was the least precise (reference the standard deviation). How do you know? Are the results surprising/expected, why or why not, and potential sources of error - (X points) Part B: which device was most accurate, and which was most precise (reference the standard deviation and % error appropriately). How do you know? Are the results surprising/expected, why or why not, sources of error - (X points). Find a real-world example related to any topic covered in this experiment, discuss it briefly and include a citation. Page 15 of 16

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Measurements, Accuracy and Precision (15 points) Post Lab Questions: Measurements, Accuracy, and Precision Accuracy is determined by comparing the true or actual value to an individual experimental value or the average of many experimental values. *** If the true value is not given, the average of all the experimental values is assumed to be true value and accuracy is determined by comparing the average to the individual experimental values . Precision is determined by comparing how close all the experimental values are to each other. The following data was collected by students in your laboratory section. Decide which value to you will use to complete the experimental calculations. The amount of error in your final experimental result depends on your decision. Each student (A, B and C) used a different balance and weighed the beaker four times. The balances they used in the laboratory read to a hundredth of a gram (XXX.XX g) . The results shown below were recorded by each individual. Student A Student B Student C Masses (g) Acquired 128.50 127.9 128.56 128.46 128.0 128.53 128.60 127.9 128.54 128.53 128 128.50 1. 3 points. What additional information about the observers, instruments, and the conditions under which the data were collected would you like to have known to make a better judgement of the data reliability? Provide two potential pieces of information and briefly (60 words or less) explain your answer. [Insert answer here] 2. 6 points. Which student’s set of data is the most precise? Show necessary equations and calculations, and briefly (60 words or less) justify your explanation. [Insert answer here] 3. 6 points. What set student measurements are the least accurate**? Is there any evidence for or against the accuracy of the data? Briefly (60 words or less, using complete sentences) suggest how this student could improve their experimental techniques. [Insert answer here] Page 16 of 16