Chapter 3 Scientific Measurement Unit 2 Chapter 3 Scientific Measurement

Today… Turn in: Nothing Our Plan: Daily Challenge Scientific Notation, Accuracy, Precision, Error Notes Worksheet #1 Wrap Up – Rally Robin Homework (Write in Planner): Complete WS #1 by next class

Daily Challenge The number 602200000000000000000000 is used so frequently in chemistry that it has its own name; Avogadro’s number. What would be a better way of writing it?

Scientific Notation To write a number in scientific notation: Move the decimal so that the number is between 1 and 10. The exponent is the number of tens places you moved the decimal Moving the decimal right = - exponent Moving the decimal left = + exponent

Examples 65000 m = 0.0000156 s = 0.24 m/s = 6.7 mm = 6.5 x 104 m 1.56 x 10-5 s 2.4 x 10-1 m/s 6.7 x 100 mm

To Write a number in Standard Form Change it from scientific notation to a standard number by moving the decimal. Example 1.4 x 106 = 1,400,000 2.6 x 10-4 = 0.00026

Adding & Subtracting Change the numbers to the same exponent. Add or subtract the numbers Example: 4.1 x 106 + 8.5 x 107 0.41 x 107 + 8.5 x 107 = 8.91 x 107

Multiplication Multiply the numbers Add the exponents Example: (4 x 106)(2 x 108) 8 x 1014

Division Divide the numbers Subtract the exponents Example: (9 x 107)/(3 x 104) 3 x 103

Try It Out! 3.5 x 104 + 5.1 x 105 (5.7 x 108)(3.5 x 106) (6.9 x 106)/(4.5 x 103)

Answers 5.45 x 105 1.995 x 1015 1.53 x 103

Or… Use your scientific calculator. The EE button means x10^ Do the Try it Out problems again using your calculator and see if you get the correct answers!

Accuracy & Precision Accuracy – compare to the CORRECT value Precision – compare to the values of two or more REPEATED MEASUREMENTS

Accurate, Precise, Both, Neither?

Accurate, Precise, Both, Neither?

Accurate, Precise, Both, Neither?

Accurate, Precise, Both, Neither?

Accurate, Precise, Both, Neither?

Accurate, Precise, Both, Neither?

Percent Error Percent Error = |experimental - actual| actual value The absolute value is present so that percent error is always POSITIVE! X 100

Example 5.59% Percent Error = |2.85 – 2.699| 2.699 X 100 = Working in the laboratory, a student finds the density of a piece of pure aluminum to be 2.85 g/cm3.  The accepted value for the density of aluminum is 2.699 g/cm3.  What is the student's percent error? Percent Error = |2.85 – 2.699| 2.699 5.59% X 100 =

Try It Out 1.75% Percent Error = |196.5 – 200.00| 200.00 X 100 = A student takes an object with an accepted mass of 200.00 grams and masses it on his own balance.  He records the mass of the object as 196.5 g.   What is his percent error? Percent Error = |196.5 – 200.00| 200.00 1.75% X 100 =

STOP! Complete Worksheet #1 by next class Worksheets are… A completion grade (i.e. You do not get a grade until it is 100% finished) 10 points on time -2.5 points each day it’s late

Wrap Up Rally Robin Pair up with your shoulder partner. Divide a deck of cards in half. Take turns asking each other the questions on the cards. Be sure to cover the answer with your finger.

Today… Turn in: Get out WS#1 to Check Our Plan: Scientific Notation Clicker Review Scientific Notation Quiz Notes – Significant Figures/Units of Measurement WS #2 Bluff Homework (Write in Planner): Complete WS #2 by next class (9/12) QUIZ OVER SIG FIGS NEXT TIME!

Units in Chemistry When you add or subtract two numbers, they must have the same units. The answer then has those units as well. Example: 4 m + 12 m = 16 m When you multiply, you also multiply the units. Examples: 4 m x 5 m = 20 m2 2 g x 3 s = 6g·s When you divide, you also divide the units. 4 m / 2 s = 2 m/s 8 g / 2 mL = 4g/mL

What does the word “significant” mean? Challenge! What does the word “significant” mean?

Significant Figures The numbers that are known, plus a digit that is estimated

RULES 3 6 Zeros between nonzero numbers are significant. ***All nonzero numbers are significant*** 125, 689 has 6 significant figures (sig figs) 156 has 3 sig figs Zeros between nonzero numbers are significant. 40.7 mL has ______ sig figs 870,009 g has _____ sig figs 3 6

RULES Zeros in front of nonzero numbers are not significant 2 3 0.00011 s has _____ sig figs 0.956 g/mL has _____ sig figs 2 3

RULES Zeros at the end of a number and to the right of a decimal are significant 85.0000 kg has _____ sig figs 2.00000000 L has _____ sig figs 6 9

RULES Zeros at the end of a number are NOT significant. If there is a decimal at the end, they ARE. 2000. m/s has _____ sig figs 2000 m/s has _____ sig figs 4 1

Memorize! EASY RULE! Decimal No Start at the first nonzero number on the left and count every number right Start at the first nonzero number on the right and count every number left

Unlimited Significant Figures Counting – There are 23 students in the classroom Could also be expressed as 23.0 or 23.00000000000000 etc. Conversion Factors – 60 min = 1 hour Exact quantities do not affect the process of rounding

Try It Out How many sig figs? 0.00125 1.12598000 3 3,000 0.0100103 9 5,500. 1.23 x 105 3 9 1 6 4 3

Rounding Round the following numbers so that they have 3 significant figures: 1.36579 = 120 = 145,256,987 = 0.0001489651 = 1.37 1.20 x 102 OR 120. 145,000,000 0.000149

To Multiply & Divide Sig Figs… Count the number of sig figs in each number Round the answer so that it has the same number of sig figs as the number in the problem with the fewest.

Example 1 16.19 g / 4.2 mL = 3.8547619 g/mL 3.9 g/mL 16.19 has 4 sig figs 4.2 has 2 sig figs, so the answer should have 2 sig figs 3.9 g/mL

Example 2 9.3 m x 0.00167 m = 0.015531m2 9.3 m has 2 sig figs, 0.00167 has 3 sig figs Therefore, the answer must have only 2 sig figs. 0.016 m2

Try It Out! (1.23)(0.011) = 12.63000/100 = (1.23 x 106)(3.5 x 104) = 0.0045912/6.570 = 0.014 0.1 4.3 x 1010 6.988 x 10-4

Stop Complete Worksheet #2

Bluff 1A. How many sig figs are in 0.001023? 1B. Solve 456 x 3.2 2A. How many sig figs would the answer have if you calculated 2.1 x 0.01? 2B. How many sig figs are in 123,000? 3A. Solve 2.7 x 3 3B. How many sig figs would the answer have if you calculated 1.4/3.789?

Bluff 4A. What is 235,489 rounded to 2 sig figs? 4B. Solve 1/236 5A. Solve 3.7914/9.2 5B. What is 1,926,560 rounded to 1 sig fig? 6A. How could you write 230 with 3 sig figs? 6B. What is 0.00056798 rounded to 4 sig figs?

Today… Turn in: Get out WS#2 to Check Our Plan: Sig Fig Race Sig Fig Quiz Notes – Significant Figures in Measurement Practical Lab - Measurement Wrap Up – Measure Up Homework (Write in Planner): Fill out p. 9 – top of 11 using your text by next class!

Sig Figs in Measurements When doing any measurements in chemistry, it is important that you use the correct precision. All measurements should be made by writing all units you know and estimating the last unit.

Examples 54 70 10 30 50 20 40 60 38 10 30 50 70 20 40 60 13.9 2 4 6 8 10 12 14

More Examples! 3.4 2 4 6 1.16 0.5 1 1.5 72 20 40 60

Units of Measurement Every measurement in chemistry MUST HAVE A UNIT! Without a unit, the number means nothing! We will use SI units in class

Wrap Up – Clicker! 5.3 2 4 5 6 1.58 0.5 1 1.5 43 20 40 60

Today Before Class: Get out Note Booklet, Calculator, & Pencil Our Plan: Mix/Group Review (#1-11) Challenge Notes - Conversions WS #3 Wrap Up – Practice Problem from the Worksheet Homework (Write in Planner): Try out some of the problems on the worksheet

Review Time Open up your notebooklet to p. 11. Answer questions 1 – 6. Get up and move around the classroom. When the instructor says “group by the answer to #___” you have to form a group of students that is the same as the answer to the problem!

Review Time Now answer questions 7 – 11 on your own. When you are finished pair up with your face partner and share your answers.

Mix/Group How many sig figs: 102.32500 560. 0.0012501 What is the exponent?: 420= 36,000,000 60 =

Think-Pair-Share Round these numbers so that they have 3 sig figs: 103,250 567.9 0.0012561 100 Read the measurement below correctly. 103,000 or 1.03 x 105 568 or 5.68 x 102 0.00126 or 1.26 x 10-3 100. or 1.00 x 102 43 20 40 60

Challenge Would you be breaking the speed limit in a 40 mi/h zone if you were traveling at 60 km/h? http://www.youtube.com/watch?v=Qhm7-LEBznk

Challenge How old are you, in minutes?

Conversion Factors Definition: a ratio of equivalent units It is always equal to 1 When multiplying by a conversion factor, the numerical value is changed, but the actual size of the quantity remains the same

Conversion Factors When working with conversion factors, we use the Factor-Label Method (dimensional analysis) The factor is the number that explains the relationship between two things The labels are its’ units

Examples 1 dollar = 1 4 quarters = 1 OR 4 quarters 1 dollar Factor Label

Examples 12 months = 1 1 year 1 foot = 1 12 inches

Rules for using Conversion Factors Always start by writing what you know from the problem. Multiply by a conversion factor so that the units cancel out (same unit in numerator and denominator) Continue converting until your answer is in the desired units.

Example 1 – your age in minutes Checklist: I started by writing what I knew All units cancel My answer is in minutes

Example 1 – your age in minutes 16 years x 365 days 1 year x 24 hours 1 day x 60 minutes 1 hour = 8,409,600 minutes Checklist: I started by writing what I knew All units cancel My answer is in minutes

Mrs. C’s top 4 reasons for NOT using the Factor-Label Method You’re super-intelligent and enjoy solving relatively simple problems in the most complex manner. You're tired of always getting the correct answers.

Mrs. C’s top 4 reasons for NOT using the Factor-Label Method You’re artistic, and rather than using Mrs. C’s concrete-sequential method of solving problems you want to use your own random method such that you create abstract patterns and designs on paper that you might be able to sell as artwork.

Mrs. C’s top 4 reasons for NOT using the Factor-Label Method Let's say that you have no interest in going to the prom or making the soccer team, and you don't mind being unpopular, unattractive, ignorant, insecure, uninformed, and unpleasant. Otherwise, You Need the Factor-Label Method!

Testimonials "I was a South High School student who dozed off while Mrs. C taught us the Factor-Label method in chemistry. I never quite got the hang of it. It irritated me... all of those fractions. I never really liked fractions. Although my grades had been pretty high, I got a D in chemistry and subsequently did not take any more high school science classes. It was not long before I started on drugs, and then used crime to support my drug habit. I have recently learned the factor-label method and realize how simply it could have solved all of my problems. Alas, it is too late. I won't get out of prison until 2022 and even then, my self image is permanently damaged. I attribute all of my problems to my unwillingness to learn the factor-label method." -Jane

Testimonials "I thought I knew everything and that sports was the only thing that mattered in high school. When Mrs. C taught our class the factor-label method, I didn't care about it at all. I was making plans for the weekend with my girlfriend who loved me because I was a running back and not because of chemistry. While other kids were home solving conversion problems, I was practicing making end sweeps. Then one day I was hit hard. Splat. My knee was gone. I was a total loser. My girl friend deserted me. My parents, who used to brag about my football stats, stopped loving me and started getting on my case about grades. I decided to throw myself into my school work. But I couldn't understand anything. I would get wrong answers all of the time. I now realize that my failure in school came from never having learned the factor-label method. I thought everyone else was smarter than me. After the constant humiliation of failing I finally gave up. I am worthless. I have no friends, no skills, no interests. I have now learned the factor-label method, but it is too late." -Bill

Example 2 How many dollars do you have if you have 38 quarters?

Example 3 How many nanoseconds are in one week? 600,000,000,000,000 nanoseconds

Example 4 How many milligrams are in 12 g? 12,000 mg

TRY IT OUT! Now try the next three problems in your notes on your own. Checklist: I started by writing what I knew All units cancel My answer is in desired units

The Answers… 790,000,000 seconds 6.71 x 103 grams 5.3 x 103 mL

STOP! Start Worksheet #3. You must show work and you must use the factor-label method!

Today… Turn in: Get WS #3 out On Mrs. C’s birthday she will be 1.041 x 109 seconds old. How many years old will she be? Our Plan: Pass the Paper Work on Worksheet #3 Notes - Density WS #4 Wrap Up – Density Problem Homework (Write in Planner): Complete WS #3 &#4 by next class QUIZ OVER BOTH WORKSHEETS NEXT TIME!

Review Pass the Problem Each student has a problem to solve. The first student will do step 1 (write what you know) and pass the paper to the next student who will complete the second step. Continue passing the paper until you get the answer. Example: How many days are in 60 seconds?

Pass the Paper Answers 569 96,400 8 1,000,000

Density Review Density = Mass/Volume Volume of liquids is measured in liters or milliliters Volume of solids is length x width x height

Do formulas confuse you? Try this visual approach…

Example A bar of silver has a mass of 68.0 g and a volume of 6.48 cm3. What is the density of silver? 10.5 g/cm3

Example A copper penny has a mass of 3.1 g and the density of copper is 8.8571 g/cm3. What is the volume of the penny? 0.35 cm3

Try It Out What is the mass of a pure silver coin that has a volume of 1.3 cm3? The density of silver is 10.5 g/cm3. 14 g

STOP! Complete Worksheet #4

Wrap Up - Density Review (p. 15 Notes) Four graduated cylinders each contain a different liquid: A, B, C, and D. Liquid A: mass = 18.5 g; volume = 15.0 mL Liquid B: mass = 16.5 g; volume = 8.0 mL Liquid C: mass = 12.8 g; volume = 10.0 mL Liquid D: mass = 20.5 g; volume = 12.0 mL Examine the information given for each liquid, calculate the density, and predict the layering of the liquids if they were carefully poured into a larger graduated cylinder.

Density Review Density = Mass/Volume A – 1.23 g/mL C – 1.28 g/mL D – 1.71 g/mL B – 2.1 g/mL

Today… Turn in: Get WS #3 & #4 out to be graded Our Plan: Which Word Am I? Conversions/Density Quiz Lab Wrap Up – High Five Homework (Write in Planner): Missing Work

Review – Which Word Am I (p. 15 Notes) Mass divided by volume The numbers that are known in a measurement plus one estimated digit How close your measurements are to the true value How close your measurements are to each other Convert 3.69 meters into inches. What is the volume of a cube that has a mass of 7.9 g and a density of 9.45 g/cm3?

Wrap Up What questions do you have on the lab?

Today… Turn in: Get Lab Packet Out, Calculator, Pencil Our Plan: LAB – DUE TODAY Work Day Missing Work Test Review Homework (Write in Planner): Test Review due next class TEST NEXT TIME!

Today… Turn in: Get out Test Review to check Turn in Measurement Lab if you haven’t yet! Our Plan: Worksheet Race Go over Test Review, then turn it in Unit 3 Test Periodic Table Basics Activity Homework (Write in Planner): PT BASICS DUE NEXT MONDAY!

After the Test PT BASICS HELP