CHEM 7L Manual - Experiment 1 Fall 21 PDF

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Experiment 1 lab manual with descriptive procedures and necessary calculations and background information...

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EXPERIMENT 1: PRECISION AND ACCURACY A. INTRODUCTION The goals of this experiment are to: (1) identify glassware that dispenses a specific volume most accurately, (2) demonstrate the effect of number of trials on assessment of measurement precision, and (3) how to upload data to the Canvas website. Part I. Accuracy In scientific research, accuracy indicates how closely an experimental value approaches the true value. Accuracy is often reported as a percent error relative to the true value, expressed as a positive percentage: % 𝑒𝑟𝑟𝑜𝑟  󰇻

󰇛 󰇜󰇛 󰇜

󰇻  100%

 

EQUATION 1-1

The ability to determine accuracy requires knowledge of the true value, one that is sometimes found by other measurements, or perhaps by theoretical calculation. Sometimes the true value is unknown and the % error cannot be determined. For example, in Expt. 2, you will determine the concentration of an unknown solution. Because you do not know the actual concentration of the solution, the % error cannot be reported. Part 2. Precision Precision should not be confused with accuracy! Precision refers to the reproducibility of a measurement. If you were to repeat the same measurement multiple times, the results would not be identical because there are natural statistical variations for each trial. Precision indicates how close the results are to one another regardless of whether the measurements are accurate or not. Precision can be quantified with statistical analysis. If a measurement is subject to random rather than systematic influences, then the measured values will be distributed on a Gaussian curve centered on the average value of the measurements. These statistical variations are quantified by the population standard deviation, also referred to as the root mean square deviation, (Equation 1-2), 𝝈, for N trials. This curve is centered at the true population mean; the spread of measurements for the entire population, where the number of trials is very large, is described by 𝜎. Population Standard Deviation

 ∑ 󰇛 󰇜

𝜎



EQUATION 1-2

However, if the number of trials is a subset of the larger population, one reports a sample standard deviation, s, (Equation 1-3), where the denominator is 𝑛  1 and the average is the arithmetic mean of this small subset of trials. In CHEM 7L, given the small number of trials in all experiments, error should be reported as the sample standard deviation unless noted otherwise. Sample Standard Deviation

 ∑ 󰇛  󰇜

𝑠



EQUATION 1-3

n is the number of trials (n is a subset of N) 𝑥 is the measured value for the ith trial 𝑥 is the average (or mean) of a limited sample of n trials 𝜇 is the average (or mean) of the population The number of trials, n , may refer to a single person performing multiple trials, or multiple people performing the same, single trial. An example calculation of sample standard deviation is: four students take an identical quiz, and receive scores of 88, 76, 92, and 81. The average and sample standard deviation for 𝑛  4 is 84  7. As n becomes very large (to approach N), the value of 𝑥 should approach the true, population mean, 𝜇.

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Fall 2021, Expt. 1, Page 1

A reproducible, and therefore precise, experiment will have a small standard deviation compared to the average value. The ratio of the standard deviation to the average value of all n trials is quantified by the percent relative standard deviation (%𝑹𝑺𝑫) in Equation 1-4. 

%𝑅𝑆𝐷   100% 

EQUATION 1-4

Part 3. How to report the average and sample standard deviation The average and corresponding sample standard deviation must be reported properly. When only a few measurements are made, the sample standard deviation cannot be known with better precision than one, or possibly two, significant figures. The reason will be discussed in lecture. In all 7L experiments, the average and sample standard deviation should be reported following the three steps: 1. Be realistic. Calculate the sample standard deviation; do not round values in this calculation. When you report the sample standard deviation, state one or two sig. figs. depending on the leading value:  Report two sig. figs. if the leading value is a “1” or “2”, e.g. a calculated value of 0.01341893 will be reported as 0.013; a calculated value of 2.181933 will be reported as 2.2; a calculated value of 0.241 will be reported as 0.24.  Report one sig. fig. if the leading value is “3” to “9”, e.g. 0.3444 becomes 0.3; 4.1 becomes 4; 0.0581 becomes 0.06. 2. Be consistent. Report the average to the same decimal place as the standard deviation (s should have one or two sig. figs described above). It would not make sense if average and standard deviation were reported to different levels of precision. Examples of average and standard deviation reported correctly: 25.363 ± 0.013 (thousandths place); 24.4 ± 2.2 (tenths place); 24.36 ± 0.24 (hundredths place); 24.4 ± 0.3 (tenths place); 24 ± 4 (ones place); 20 ± 10 (tens place) 3. Check the result. The calculated average and standard deviation should not be more precise than the instrument. If you make a set of measurements such that the standard deviation is more precise than the instrument, you should report the precision of the instrument. For example, if after steps 1 and 2, the temperature is calculated as 25.36 ± 0.04, but you used a thermometer with precision to the tenths place (e.g. 0.1°C), the average and standard deviation should be reported as 25.4 ± 0.1. If there are multiples steps in the analysis, the average and standard deviation should follow the sig. fig. rules of addition, multiplication, etc.

B. EXPERIMENTAL PROCEDURE Summary of procedure. You will dispense nominally ten mL of water using three different pieces of glassware: beaker, graduated cylinder, and volumetric pipet (Figure 1-1). This process will be repeated three times for each piece of glassware. The targeted volume will be compared with the actual volume based on the mass of dispensed water and the known density of water. Density (ρ) is defined as mass/volume and depends on temperature. The volumes determined by your measurements of mass allow you to identify the most accurate and precise piece(s) of glassware. The target (theoretical) dispensed volume is 10.000 mL based on the precisions of the instrument and known density. To gain additional information about the effect of number of trials (n), you will compare your sample standard deviation for three trials (𝑛  3) for the graduate cylinder to the trials of the entire class for the same type of glassware (𝑛  3  24 for 24 students taking three measurements from each student).

Figure 1-1. Three types of glassware used to measure 10 mL of water – beaker (left), graduated cylinder (middle), and volumetric pipet (right). Photos are not to scale.

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Fall 2021, Expt. 1, Page 2

Before coming to laboratory, prepare three tables in your laboratory notebook to organize your data. Table 1-1 is an example of the format: Table 1-1. Example of data table for the first piece of glassware, a 50-mL beaker. Temperature of water (in ºC) Density of water at indicated temperature above (in g/mL) Mass of empty Mass of vial+cap vial+cap, (g) with H2O, (g) Mass of H2O, (g)

volume of H2O from mass and density, (mL)

Beaker, trial 1 Beaker, trial 2 Beaker, trial 3

Step-by-Step Procedure 1. Obtain 100 mL of deionized water in a beaker. Record the temperature of the laboratory and the water in the beaker. The temperature of the water should be within 1 ºC of the temperature of the lab. Record the temperature of the water in your beaker to the nearest 0.5 ºC. While you are waiting for the temperature of the water to equilibrate, proceed with the steps 2, 3, and 4 below, progress to step 5 once the temperature criteria have been met. 2. Obtain three glass vials with caps. Clean with DI water, and dry with a paper towel or Kimwipe to remove residual water. Label each vial and cap such that the same cap is paired with the same vial. 3. Weigh the three empty glass vials with its corresponding cap and record each mass to the nearest 0.0001 g in your notebook. 4. Obtain and clean the glassware you will compare for volumetric delivery: a 50-mL beaker, a 10-mL graduated cylinder, and a 10-mL volumetric pipet. 5. Use a beaker to measure the volume. b. Fill your 50-mL beaker to a volume of 10 mL using the room temperature water from Step 1. c. Pour the water from the beaker into one of the pre-weighed glass vials. Secure the cap on the vial. Repeat two more times such that you have delivered 10 mL of water from the beaker into each of the three pre-weighed vials. d. Weigh each capped vial with water, and record the three masses in a table in your notebook. 6. Use a graduated cylinder to measure the volume. a. Empty the vials from Step 5, and remove any water drops using a paper towel or Kimwipe. b. Fill your 10-mL graduated cylinder to a volume of 10 mL using the room temperature water from Step 1. Be sure to read from the bottom of the meniscus while you are at eye level with the meniscus. c. Pour the water from the cylinder into one of the re-weighed, empty glass vials. Cap this vial. Repeat two more times such that you have delivered 10 mL of water from the graduated cylinder into each of the three pre-weighed vials. d. Weigh each capped vial with water, and record the three masses in a table in your notebook. 7. Use a pipet to measure the volume. a. Empty the vials from Step 6, and remove any water drops using a paper towel or Kimwipe. b. Practice using your pipet and plastic bulb with water (do not use the water that you set aside to equilibrate to room temperature; instead, you may use cold water from the sink). c. Pipet 10 mL of the room-temperature water from Step 1 into one of the pre-weighed glass vials from Step 3 and cap the vial. Repeat two more times such that you have delivered 10 mL of water from the volumetric pipet into each of the three pre-weighed vials. d. Weigh each capped vial with water, and record the three masses in the table in your notebook. Copyright 2021 by Brian Leigh UCSD Not for distribution

Fall 2021, Expt. 1, Page 3

C. CALCULATIONS Use the table of densities (Table 1-2) to determine the volumes of water transferred to the vial for each trial. You should have a total of nine volumes from the three trials each of the beaker (Step 5), graduated cylinder (Step 6), and pipet (Step 7). Using your own data, calculate the averages and sample standard deviations for each piece of glassware for your three trials; show the work for this calculation in your notebook (i.e. write down each step). Determine your % error for each piece of glassware. Determine which piece of glassware gave the most accurate result. Post your three measurements for the graduated cylinder on the board at the front of the classroom. Calculate the average and sample standard deviation for the graduated cylinder for the entire class; you can use a spreadsheet to perform this calculation. The Excel function STDEV (or STDEV.S, depending on your version of Excel) reports the sample standard deviation. Compare your %RSD for your set of three beaker trials with the %RSD for the entire class.

Table 1-2. DENSITY OF WATER AS A FUNCTION OF TEMPERATURE T (C)

Density (g/cm3)

T (C)

Density (g/cm3)

T (C)

Density (g/cm3)

5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5

0.99999 0.99998 0.99997 0.99995 0.99993 0.99990 0.99988 0.99984 0.99981 0.99977 0.99973 0.99968 0.99963 0.99958 0.99953 0.99947 0.99941 0.99934 0.99927 0.99920 0.99913 0.99905 0.99897 0.99889 0.99880 0.99872 0.99862 0.99853 0.99843 0.99834

20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5

0.99823 0.99813 0.99802 0.99791 0.99780 0.99769 0.99757 0.99745 0.99733 0.99720 0.99708 0.99695 0.99681 0.99668 0.99654 0.99641 0.99626 0.99612 0.99598 0.99583 0.99568 0.99553 0.99537 0.99522 0.99506 0.99490 0.99473 0.99457 0.99440 0.99423

35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5

0.99406 0.99389 0.99372 0.99354 0.99336 0.99318 0.99300 0.99281 0.99263 0.99244 0.99225 0.99206 0.99186 0.99167 0.99147 0.99127 0.99107 0.99086 0.99066 0.99045 0.99024 0.99003 0.98982 0.98961 0.98939 0.98917 0.98896 0.98874 0.98851 0.9831

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D. UPLOADING YOUR DATA Chem 7L requires you to input your raw data and calculated results directly into TritonEd. It is crucial that your uploaded information is formatted properly to receive full credit. Read the following directions carefully and input the data on the next page. Instructions on how to upload data. Do not mix text and numbers in a single input field. This means you should not use units when inputting a number. Correct Incorrect 532 532 nm 12.4 12.4 mL 34.2 34.2% Do not use commas when inputting a number Correct 2532

Incorrect 2,532

Most of the data you input will be numbers. Each section will have a separate field to input text as needed. Text fields will say “Input Text Here” Each input cell should contain a single number. Do not input multiple numbers separated by a dash. After each number input there will be an area for you to input text to explain any issues. Correct Incorrect 25 25 was the most u Do not use parenthesis to denote negative numbers Correct -2532

Incorrect (2532)

Use Excel notation to denote ×10x notation, where the letter E replaces the ×10 and the exponent is not superscripted – note there are no spaces in front of or behind the “E” Correct Incorrect 2.532E2 2.532x10^2 2.532E2 2.532 x 10^2 -2.532E2 (2.532)x10^2 -2.532E-2 -2.532x10^(2) 4.5E-2 4.5E(2) 6.02E23 6.02 E 23 Sometimes your answer may have a standard deviation associated with it, be sure to put that standard deviation in its own input field. Correct Incorrect 2.53 ± 0.04 2.53 ± 0.04 ±

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Data to input: 1)

500.2 g/mL

2)

pH 7.43

3)

-254.34%

4)

2.45 ×105 °C

5)

-6.15 ×10^2 moles

6)

4.87×10-10 km

7)

(34)

8)

12,345

9)

65.74 ± 0.14

10)

(Input TEXT in this field) the units from #5

Input the data from the Experiment 1 Template

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Fall 2021, Expt. 1, Page 6...