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

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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