Lecture 2 - Significant Figures and Dimensional Analysis

Wednesday, January 10, 2024

2:55 PM

"A scientist’s aim in a discussion with his colleagues is not to persuade, but to clarify." - Leo Szilard Welcome back to CHEM 111 If you have not gotten your course textbook yet, I uploaded the first chapter to Canvas under Week 1. This will be deleted next week. Homework this week: Complete Syllabus Quiz and Reading Quiz 1. (past due) If I don't get the syllabus quiz you got an email after class asking about your intent to take the course. No reply by 12:00 PM Friday and you will be dropped from both lecture and lab. I will accept the first reading quiz until Friday (only time I will accept one of these late) Reading Quiz 2 and Surveys (by end of day Friday) Aktiv Chemistry HW 1 (Chapter 1) (by end of day Sunday) My office hours will start in the CIC next Friday from 11AM - 1PM. If you have questions you are free to go to the CIC to get help anytime they are open. Additionally, you can make in-person or Zoom appointments with me via the ﷟HYPERLINK "calendly.com/bricejurban/office-hours"link in the syllabus page on Canvas. Email is also great! You can stop by office at any time this Friday if you only have a few questions or want to say hi, otherwise just make an appointment :) Today's schedule: Precision and Accuracy
Precision and Accuracy Rules for the number of Significant Figures to report Dimensional Analysis - A way to simplify calculations that involve quantities with units Unit Conversions with one step Unit Conversions with two or multiple steps Unit Conversions with compound units e.g. density, pressure, speed Please have your scientific calculator out so you can follow-along. I will have several problems for you to work out during class that you will turn in at the end. This will count as your participation credit for this week. Accuracy vs Precision Untitled picture.emf Accurate and Precise Accurate but not Precise Precise but not Accurate Not Accurate Not Precise The only type of experiment that can be carried out with complete accuracy (with zero error) is the counting of objects. 12 eggs in a egg carton
12 eggs in a egg carton 120 students in our class The United States of America consists of 50 states, 1 federal district, 5 unincorporated territories, 9 minor outlying islands, and 326 Indian reservations Quantities that are measured on the other hand always have some inherent uncertainty. Accuracy is defined as how close our result is to the actual value. On the dart board, the concentric rings represent degrees of certainty. The inner ring, or bullseye, is the most accurate. The farther the darts are from the bullseye, the less accurate the throw was. If we measure the density of a pure sample of gold (19.32 g∙﷐cm﷮−3﷯) and it only measures to be 18.58 g∙﷐cm﷮−3﷯ then our accuracy is low. Possible reasons for inaccuracies: Improper calibration Incorrect technique Adulterated sample The percentage error of a sample is a measure of the accuracy of the measurements during an experiment. 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟= ﷐𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒 −𝑡𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒﷮𝑡𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒﷯×100 Actual, True, Accepted, or Standard value are synonyms The ﷟HYPERLINK "https://hbcp-chemnetbase-com.libproxy.boisestate.edu/contents/ContentsSearch.xhtml?dswid=-539"CRC Handbook of Chemistry and Physics (BSU login is broken at the moment) is one of the de facto reference books for standard or "true" values. side note: We almost never work with absolute truths in Chemistry. As scientists perform better and more refined experiments their measurements may change with time. That is why there 114 editions of this book now. side note 2: My favorite reference manual is that put out by the ﷟HYPERLINK "https://pdg.lbl.gov/"Particle Data Group. It contains information on astrophysics and particle physics with up-to-date references.
side note 2: My favorite reference manual is that put out by the ﷟HYPERLINK "https://pdg.lbl.gov/"Particle Data Group. It contains information on astrophysics and particle physics with up-to-date references. Precision is a measure of how close repeated measurements agree with one another and how sensitive the measuring instrument was used On the dart board, how clustered the darts are represents how much each throw agreed with one another. A talented archer has high precision. Note that the bullseye, is not the highest value in the game of darts but rather the triple 20 1024px-Dartboard_heatmap.svg.png undefined If we measure the density of gold once again with a more precise balance that can read to 0.0001 grams, now the precision might be 18.583 g∙﷐cm﷮−3﷯ instead of 18.58 g∙﷐cm﷮−3﷯. The additional decimal place in our density is indicative that the precision was higher. For measurements that require a human eye, instead of a digital printout, you are always allowed one more guess, than the markings that are given. You will learn about this in lab in a few weeks, but here is an example of the difference in precision between pieces of glassware used to measure volume. Note the cost difference . . . Fisher Scientific Glassware Untitled picture.png Untitled picture.png Untitled picture.png
Glassware Calibrated To deliver (TD) a certain volume Untitled picture.png 100 mL Griffin Beaker Untitled picture.png 100 mL Class B Graduated Cylinder Untitled picture.png Class A Buret Increments 10 mL 1 mL 0.1 mL Cost $6.75 $53.75 $381 Fisher Scientific Glassware Calibrated to contain (TC) a certain volume Untitled picture.png Class A Volumetric Flask Untitled picture.png
Class A Volumetric Pipet Tolerance 100 mL ±0.01 100 mL ±0.08 Cost $90 $89 Never use an Erlenmeyer flask for measuring a volume. They are for Titrations, recrystallization, and preparing cultures 20-1890477-FB501250-STD-00.jpg-650.jpg Fisherbrand Reusable Glass Wide-Mouth Erlenmeyer Flasks 250mL; Graduated Erlenmeyer Flask Cost $11 Significant Figures The higher the precision of an instrument (e.g. a beaker vs a buret) the more decimal points out we can record. This is significant and we should indicate that in our scientific notebook and when we publish our results.
We can only be as precise as our least precise measurement in chemistry. Example 1: If we measure the mass of a post-1983 US penny with a kitchen balance it might record 2.5 g. If we use a jewelry or analytical balance, it will be more precise and might measure as 2.500 g. We should record every digit that the scale gives us. Even though in math class, we would truncate the trailing zeros, in chemistry we keep them when the instrument calls for it. Untitled picture.png Untitled picture.png 2.500 g
2 sig figs 4 sig figs When we record a number we can tally up how many of the figures are significant. This is what we mean by significant figures. In example 1, the first measurement of the penny has 2 significant figures and in the second there are 4 significant figures. If you record the 2nd measurement as 2.5 g that would be incorrect. Here are the rules you must know, frontwards and backwards. All nonzero digits in a number are significant (1-9) Zeroes between nonzero digits are significant Leading zeroes are never significant even after a decimal point Trailing zeroes are only significant if they are after a decimal point Use scientific notation if it might be ambiguous as to how many of the trailing zeroes in a recorded number are significant Defined conversion factors and counted numbers are considered exact and have an infinite number of significant figures. Examples: The population of the United States is 333 290 000 5 sig figs (rules 1 and 4. Should be reported as 3.3329 × ﷐10﷮8﷯) 2408 Joules 4 sig figs (rules 1 and 2) 0.000 000 000 000 000 000 000 000 000 000 911 kg (mass of an electron)
0.000 000 000 000 000 000 000 000 000 000 911 kg (mass of an electron) 3 sig figs (rules 1 and 3) 1141 pages in our textbook Exact number (rule 5) Significant Figures in Calculations When we add, subtract, multiply, divide two numbers that have significant figures there are certain rules we must use otherwise we will incorrectly express the final numerical result. (there are also rules for logarithms) Multiplication and Division The calculated result should not be expressed to more significant figures than the factor with the least number of significant figures. Example: Potential energy of a snowball at the top of a hill The equation is: ﷐𝐸﷮𝑝﷯=𝑚𝑔ℎ Mass of snowball is 2.5 ×﷐10﷮−2﷯ 𝑘𝑔 Gravitational acceleration constant = 9.81 m∙﷐𝑠﷮−2﷯ (not an exact number) Height of hill is 21 m ﷐𝐸﷮𝑝﷯=﷐2.5 ×﷐10﷮−2﷯ 𝑘𝑔﷯﷐9.81 𝑚∙﷐𝑠﷮−2﷯﷯﷐21 𝑚﷯= 5.15025 𝑘𝑔∙﷐𝑚﷮2﷯∙﷐𝑠﷮−2﷯
= 5.2 J In this answer we only need 2 sig figs because the mass and height are only given to 2 sig figs. The units are best expressed as Joules Note the rounding rule. The third digit is a 5, so we round the second digit up and discard the rest. Also 1 kg∙﷐m﷮2﷯∙﷐s﷮−2﷯=1 J Addition and Subtraction (different rule) When adding or subtracting, the result should have the same number of decimal places as the number with the fewest decimal places Example: Total mass of an apple, an orange, and a kernel of popcorn Apple = 125. g Orange = 145. g Popcorn kernel = 0.4 g ----------- 170.4 g The mass should be reported as 170. grams or 1.70 ×﷐10﷮2﷯ The kernel of popcorn's mass really doesn't matter here. Weird huh? Make sure you understand this rule. Example 2: 2796.8 kJ - 2795 kJ
Example 2: 2796.8 kJ - 2795 kJ The answer is not 1.8 kJ. It is 2 kJ by the addition and subtraction rule. When performing calculations it is best to perform all calculations to extra significant figures first then trim the final answer to the correct number. This prevents rounding errors. Dimensional Analysis Chemical calculations that involve multiple conversions or involve lots of units are best done using dimensional analysis. Units should cancel out when you perform a dimensional analysis to give you the units you seek in the end. You may need to use the reciprocal of the conversion factor that you are given. It is worthwhile to plan your conversion before you start. Aktiv Chemistry will help you practice this skills ﷟HYPERLINK "https://youtu.be/CRQ3HliPesY?si=3SCqgUk_B3xyS2PW"How to Use Aktiv Chemistry for Dimensional Analysis How to Use Aktiv Chemistry for Dimensional Analysis Press enter to activate, • . CONVERTlNG ΙΙΝΙΤ5 τυτ0ΑφΙ •
How to Use Aktiv Chemistry for Dimensional Analysis Press enter to activate, • . CONVERTlNG ΙΙΝΙΤ5 τυτ0ΑφΙ • For units that have units on the top and bottom (compound units) you may need to deal with both of them. Density (g/mL) is an example of a compound unit as is speed (m/s) When you use unit conversions that are squared or cubed you need to also square or cube the conversion factor number After you have your fully worked analysis, to plug it into your calculator, you'll want to multiply all the numbers on the top, and divide all the numbers on the bottom. Ignore all of the 1's (as that won't change your answer) Questions 35-46, 63, 64, 66-68, 71-73, 76-79, and 83 in your textbook are great for practicing this skills. Example 1: 1.259 x 103 J to kJ Example 2: 5.5 MJ to kJ Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
The absolute exponential distance between kJ and MJ is 103. We can solve the same problem in 1 step now. Always place the 1 with the larger unit and the absolute exponential distance with the smaller For more on this method go to this website: ﷟HYPERLINK "https://chemteam.info/Metric/Metric.html"ChemTeam: Metric System and do tutorials 2 and 3. It takes a little effort to learn this but it will save you a lot of time. Example 3: 2.0 m3 to mL Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
The conversion factor must be cubed here. Example 4: 175 pounds (lb) to kilograms Example 5: How many minutes does it take for light to travel from the sun to the earth, given that the sun is about 93 million miles from the earth? Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Example 6: The density of air at sea level and 98°F is about 1.20 g·L–1. The volume of the adult human lungs in the expanded state is about 6.0 liters. Given that air is 20% oxygen by mass, compute the number of grams of oxygen in your lungs. Example 7: The density of pure gold is 19.3 g·cm–3 at 20°C. A quantity of what appears to be gold has a mass of 465 grams and a volume of 26.5 milliliters. Is the substance likely to be pure gold? Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
The density of pure gold is 19.3 g·cm–3 at 20°C. A quantity of what appears to be gold has a mass of 465 grams and a volume of 26.5 milliliters. Is the substance likely to be pure gold? Please write the following and turn in before you leave for the day: Name (First and Last) One thing you learned today One thing you want to learn more about One thing you liked or didn't like about lecture Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings

 

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