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Experiment 1
To Measure or Not? Err on the side of
measuring.
What do thermometers and graduated cylinders have in common? Graduate degrees
1.1 Measurements & Error
If someone asked you, “How confident are you in that answer?”, it might make you second-guess your work. How- ever, when we take measurements in lab, we are often limited by lab equipment and errors. So, when someone asks that question in chemistry and it’s broad applications, they are actually asking, “How confident are you in that answer, when do you become uncertain in that answer, and how can we apply this knowledge?”
Today, we will learn how to make measurements using common lab equipment, how to estimate digits, and under- stand how uncertainty in a measurement propagates through calculations. Furthermore, we will begin to learn how to interpret results in lab, with consideration for the confidence and uncertainty in our measurements.
Introduction
Accuracy Vs. Precision
To begin to understand error, we must first distinguish accuracy versus precision. Precision quantifies how similar data points are, while accuracy refers to how close the data points are to the true value. Referring to the dartboards in Fig. 1.1 where the bullseye is considered the true value, if an experiment is replicated 5 times and the results are
- Similar to each other but not close to the true value, then the data set is precise but not accurate. (Fig. 1.1a)
CHEM 1215 Experiment 1 Fall 2023
- Close to the true value, but not similar to each other, then the data set is accurate but not precise. (Fig. 1.1b)
- Neither close together, nor close to true value, then the data set is neither accurate nor precise. (Fig. 1.1c)
- Close to the true value and similar to each other, then the data set is both accurate and precise. (Fig. 1.1d) This is what we aim to achieve.
Figure 1.1: The accuracy and precision of a data set is depicted, where the bulls-eye represent the true value. Each of the following represent (a) precise, (b) accurate, (c) neither precise nor accurate, and (d) accurate and precise data.
Significant Figures
“I am unconscious of intentional error, I am nevertheless too sensible of my defects not to think it probable that I may have committed many errors.”
Although Washington is a significant figure in American history, he is not the significant figure we will be discussing. However, his acknowledgement that we add error into things we do is particularly relevant.
Significant figures (sig figs, SFs) are a tool to understand the accuracy, precision, and errors associated with measurements. For example, if a person says that an electric toothbrush is about $100, you do not know if it is closer to $90, $99.05, $100.00, $108, or $142. From here, it is worth asking two questions: (1) “Is this estimate accurate?” and (2) “Is this estimate precise?” Because different brands of electric toothbrushes have different prices, this answer is not likely to be precise. Since we pay for things to the cent, an estimate of $100 is also not likely to be accurate. Significant figures enable us to know what digits are known accu- rately and can prevent us from asserting more information than we can reasonably know.
CHEM 1215 Experiment 1 Fall 2023
Estimated Digits (Our friend, “ED”)
When a measurement is made in lab, we record all of the numbers that we can accurately determine and then we add an estimated digit (“ED”).
As an example, examine the graduated cylinder in Fig. 1.2 a. Notice that the liquid inside seems to be “climbing” the wall of the cylinder. This is due to the capillary action resulting from interactions between the liquid (in this case, water) and the glass of the cylinder, as well as the surface tension of the liquid. The crescent shape it creates is called a meniscus. For all measurements of aqueous solutions, we will measure at the bottom of the meniscus at eye level. (If you do not make readings at eye level, you induce parallax errors into your measurements.) In the graduated cylinder shown, each delineation (e.g. line marking) is 0.1 mL. In Fig. 1.2 a, the bottom of the meniscus is above the 2.5 mL mark and below 2.6 mL. This means we accurately know the volume to the tenths place (i.e. 2.5 mL) and then, we will estimate the hundredths place (i.e. 2.51 mL). The final digit is significant, but also uncertain (e.g. If you said it is 2.52 mL, that is also correct!). This measurement will have 3 significant figures with some uncertainty associated with the hundredths place since it is the estimated digit.
This process process of estimating a digit beyond the accuracy of the delineations applies to most mea- surements in lab: volumetric glassware (1.2 a,c), mass balances, thermometers (1.2 b), rulers, and even instrumentation. It is worth noting that some glassware have interesting delineations, where the accuracy of the segments and the estimated digit can become conflated. For example, if delineations of a graduated cylinder are by 5 mL and the meniscus of an aqueous sample is between 25 and 30 mL, the ones place becomes the estimated digit (See Figure (1.2 b as an example.).
Check your understanding: Determine the the temperature with the correct number of significant figures depicted in Fig. 1.2 b.
8.5˝C, 2 SFs
Determine the volume of the buret with correct number of significant figures in Fig. 1.2 c. Note: this glassware reads from top (0.00 mL) to bottom (5.00 mL), so be sure to read the meniscus accord- ingly.
2.34 mL, 3 SFs
Fall 2023 Experiment 1 CHEM 1215
1
2
3
4
5 mL
Eye level
2.51 mL
Meniscus
(a) (c)
4
3
2
1
0
5 2.34 mL
(b)
2 8.5 mL
4
6
8
10
0
oC
oC
Figure 1.2: Depictions on how to properly read menisci of aqueous solutions in various lab ware. (a) A graduated cylinder containing an aqueous solution with a volume of 2.51 mL, where the hundredths place is the estimated digit. (b) A thermometer with delineations of 0.2˝C and a temperature of 8.5˝, where the tenths place is both limited by the delineations and is the estimated digit. (c) A buret containing an aqueous solution with volume is 2.34 mL, where the hundredths place is the estimated digit.
Significant Figures & Calculations
Since each measurement in lab will contain its own significant figures, calculations from different mea- surements with different uncertainties affect the final answer. One very important thing to note is that the significant figures SHOULD ONLY be evaluated in the final answer.
- When numbers are added or subtracted, the final answer is limited by the least precise digit (aka the least precise estimated digit). EXAMPLE: A solution is made by adding 1.302 grams of potassium chloride and 0.2084 grams of calcium chloride to 20. grams of water. Determine the mass of the solution.
;290,(<=++0<>(/?(1@+9<-0(3/..-+2A(8/B(@=<8(B9..(78*>()->(?/+(
@+9<-0(3/..-+2A(8/B(@=<8(B9..(78>()->(?/+(
1.302 grams 0.2084 grams
Since the ones place is the least precise estimated digit, the answer will be reported to the ones place as 22 grams.
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Fall 2023 Experiment 1 CHEM 1215
Procedure
Part A: Making Volume Measurements
- For three sealed glassware samples, including a 10 mL graduated cylinder, 100 mL graduated cylinder, and buret, record the unknown letter and volume reading for these three sealed glassware. Hint: It would be wise to have your TA check your volume readings and be sure to report these in Table 1.2.
Part B: Density
Density ρ quantifies how much material can be packed into a given space. Generally, density is calculated as the mass m divided by the volume V, shown in Eqn. 1.1. In chemistry, we often use the density units of grams (g) per milliliter (mL) or cubic centimeter (cm^3 ). Because 1 mL = 1 cm^3 , these volume units are interchangable.
ρ “ m V
The higher a density, the more mass that is packed within a volume. The lower a density, the less mass that is packed within a volume. Density values for some common materials are shown in Table 1.1. It can be seen that gold is the most dense element listed in this table, while isopropanol is the least dense.
Density by Volume Measurements
- Obtain an unknown metal sample of your choice.
- Measure the mass of the unknown metal.
- Determine the volume of the unknown metal using a ruler (and calculations).
- Determine the volume of the unknown metal through volume displacement of water.
(a) Add water to a graduated cylinder (enough to immerse your metal sample). Record the initial volume of the water. (b) Add the metal sample to the graduated cylinder at an angle (so the bottom of the graduated cylinder does not shatter upon impact). (c) Record this final volume of the water and the metal. (d) Calculate the volume displaced by the unknown metal.
Applied Density
- Shake the plastic 2 liter bottle containing two liquids and two plastics from Table 1.1. Note: One of the liquids is 3.5 M NaCl water.
- Set the bottle on the cabinet and observe it for about 1-2 minutes. Repeat as needed.
CHEM 1215 Experiment 1 Fall 2023
Table 1.1: Density of some common materials at 20˝C. Material Physical Descriptor Density g/cm^3 Isopropanol clear liquid 0. Milk white opaque liquid 1. Olive oil green liquid 0. Seawater clear liquid 1. Water clear liquid 0. 3.5 M NaCl water clear to opaque liquid 1. Aluminum light gray solid 2. Brass yellow-gold solid 8. Copper red-brown solid 8. Gold golden solid 19. Iron silver solid 7. Lead dark grey solid 11. Magnesium dark silver solid 1. Steel dark gray solid 7. Zinc silver solid 7. High Density Polyethylene (HDPE) plastic 0. Polypropylene (PP) plastic 0. Polystyrene (PS) plastic 1. Low density polyethylene (LDPE) plastic 0. Polyethylene terephthalate (PETE) plastic 1. Polycarbonate plastic 1.
- Record your observations. Hint: It would be beneficial to draw depictions of the bottle in your lab report at various time points.
Part C: Molar Mass
Grams to Moles
Grams are a unit of measurement that does not directly relate to atoms. For example, 1 gram of helium will have many more atoms present than 1 gram of francium because helium is a much, much smaller atom than francium. Therefore chemists use a different unit—moles! One mole has 6.022 x 10^23 parti- cles (similar to how a carton has 12 eggs). This number is Avagadro’s number, NA, and directly relates atoms/molecules/particles to moles! Since the mole is a count of particles (e.g. atoms, molecules, etc.), a mole of one element can have a different mass than a mole of a different material (accounting for dif- ferences in protons and neutrons!). But each of these moles will have the exact same number of particles.
CHEM 1215 Report: Experiment 1 Fall 2023
1.2 Report: Measurements & Error
Student
Name: uID:
Section: TA:
Note: You will be graded on significant figures in this lab report.
Part A: Making Volume Measurements
- Report your unknown letters and volume measurements for the sealed glassware in Table 1.2.
Table 1.2: Volume measurements of sealed glassware containing water.
Graduated Cylinder Graduated Cylinder Buret 10 mL 100 mL 50 mL Unknown Letter Volume (mL)
Part B: Density
Density by Volume Measurements
- Report the mass of the metal. g
- Determine the volume of the metal from geometric measurements. cm^3 Show your work for your calculations.
- Calculate the density of the unknown metal based on the previous volume. g/cm^3 Show your work for your calculations.
Fall 2023 Report: Experiment 1 CHEM 1215
Density by Volume Displacement
- Calculate the volume displaced by the unknown metal. mL Show your work for your calculations.
- Calculate the density of the metal based on the previous volume. g/mL Show your work for your calculations.
Further Analysis of Density
- Which density do you have more confidence in? Briefly explain in 1-2 sentences. Hint: It is worthwhile to frame this in the context of the lab content.
Fall 2023 Report: Experiment 1 CHEM 1215
Beyond the Lab Bench
- In 2-3 sentences, hypothesize how density might used in a real world application (such as micro plastic contamination, biological fluid samples, material synthesis and separation, or an area of your interest).
