Pages 3 to 33 “Quantum Chemistry” Target Completion Date: October 1

1. Chemistry Review Section Pages 3 to 33 “Quantum Chemistry” Target Completion Date: October 1

2. Pages with a PINK background are supplementary . Not material for a test! About Slide Icons important information. • You should either note or highlight items from this slide. Some items from this slide WILL be on tests! Very Important Sample Problems • Always hand-copy important sample problems in your note book, and refer back to them when doing assignments. Similar problems will be on tests! Look at this! (usually charts, diagrams or tables) • You don’t need to copy or memorize this, but you must read and understand the diagrams or explanations here. Concepts will be tested, but not the details. Information only. Don’t copy! • This is usually background information to make a topic more interesting or to fill in details, or to give examples of how to use a table. Not directly tested. Review Stuff • Not part of the material you will be tested on, but you are expected to remember this from grade 10. It may be indirectly tested. Supplementary stuff • Not material covered this year. R

3. R Conversions • You must be able to do ALL standard metric conversions, especially: • Litres to millilitres, millilitres to litres • Grams to kilograms, kilograms to grams • Other conversions you will learn during the course of the year: • Temperature: degrees celcius (℃) to kelvins (K) • Pressure: kilopascals (kPa) to millimetres (mmHg)

4. Quick Conversions The table on the left gives the eight most commonly used prefixes in the metric system. It also includes five rows that do not have prefixes. The middle row is for the unit: metre, litre, gram, newton, or any other legal metric unit. This table can be used to quickly convert from one metric amount to an equivalent. Make a copy of this table on the margin of the front cover of your notebook, and learn how to use it. Lets do an example. Let’s find how many centimetres there are in 2.524 km Conversion: 2.524 km  ? cm 00 cm Add extra zeros if necessary 2 524 km There are five steps in the table between “kilo” and “centi”, so we have to move the decimal five places to the right. If we were going up the table we would move left. Answer: 2524 km = 252 400 cm

5. R Density • Density is the relationship between the volume of an object and its mass. Density is an important characteristic property of matter. • This is a review formula from last year: ρ V m or Where: ρ= the density of the object, in g/cm3 or g/mL m = the mass of the object, in g V = the volume of the object, in cm3 or mL The density of water is 1 g/mL. This is not true of other substances. Objects with less density than water will float. Objects with greater density will sink. ρw= 1 g/mL = 1 g/cm3

6. Solving Problems • When solving Chemistry problems on a test or exam, it is important not only to find the correct answer, but to justify it. While solving the problem you should: • Show your data, the information you used to solve the problem. • Show your work, including the formulas you used and the substitutions you made. • Write an answer statement, a sentence that clearly states your final answer. • Include the correct units for your answer. Never just give a number—you must specify what the number means!

7. Suggested Solution Method Problem: A block of material has a length of 12.0 cm, a width of 5.0 cm, and a height of 2.0 cm. Its mass is 50.0 g. Find its density. Arrange your solution like this: List all the information you find in the problem, complete with units, and the symbols. Data: l = 12 cm. w = 5.0 cm h =2.0 cm m =50g V = ? To Find: ρ(density) Write down all the formulas you intend to use: Formulas: V = lwhρ= Show the substitutions you make, and enough of your calculations to justify your solution: Calculations: V =12cm x 5cm x 2 cm = 120 cm3 𝜌= 50 g / 120 cm3 = 0.417g/cm3 Always state your answer in a complete sentence, with appropriate units. Answer: The density of the block is 0.417 g/cm3 (or 0.417 g/mL)

8. Problems on Conversions and Density • Convert the following: • 125 mL to L d) 30 mL to L g) 75 mL to L • 450 g to kg e) 4500 mL to L h) 0.035L to mL • 2.5 L to mL f) 1.35 kg to g i) 0.56L to mL • Find the density of a 4cm x 3cm x 2cm block that has a mass or 480 g. Justify your solution. • Find the width of a cube whose density is 5 g/cm3 and whose mass is 135 g. Justify your solution. Also: Do the worksheets entitled “Density” and “Metric Conversions”

9. Overview: UncertaintyInherent Errors in Measuring Devices In chemistry we often use instruments to measure quantities. Unfortunately, all instruments have some degree of inaccuracy or error. I prefer to call this error “uncertainty”, since it is not a mistake on the observer’s part, but an unavoidable inaccuracy that comes from the instrument. In this section we will see how to write measurements that show we recognize the limitations of our instruments.

10. Absolute Uncertainty (AU) App.5 Page 394 In math, numbers are considered pure, abstract things. In math, 2.00, 2.0 and 2 are considered the same, they all represent perfect number 2. In science, numbers are considered to be measurements, and all measurements have some degree of uncertainty. They are seldom considered perfect! In science, 2 mL, 2.0 mL and 2.00 mL are different! All instruments that we use to make measurements have an inherent error or absolute uncertainty. On some instruments, the absolute uncertainty is marked, on other instruments we make the following assumption: Assumption: The absolute uncertainty of a measurement is usually* one half of a measuring instrument’s smallest graduation. *at university level, or when using high-quality equipment AU measurements may be expected to be one fifth of the measure between the smallest marking instead of one half!

11. Example of Uncertainty. App.5 Page 394 • At first glance, the two graduated cylinders here seem identical, but look closer. • The first one has a measurement of 32.0 ± 0.5 mL • The second one 32.5 ± 0.5 mL • It is NOT correct to say that the first measurement is just 32 mL!

12. How to Record Absolute Uncertainty Unit Plus-minus sign () 32 .5 ±0.5 mL A pair of parenthesis may be placed around the measurement. • When you first look at a graduated cylinder, it appears to contain 32 mL of liquid. • Looking closer, you see it is about halfway between 32 and 33 mL, so you record the .5 • If you had seen it was just below the 32 instead of just above it, you would record 31.5. If you still see it as exactly 32 even after a closer look, then record it as 32.0 • Then you write the absolute uncertainty, the allowable error of the instrument – usually* half the measure between the smallest markings. • In this case, the smallest markings represent one millilitre, so half the measure ( 0.5 mL) is the uncertainty. Doubtful, but Significant digit Absolute Uncertainty

13. Adding and Subtracting with Absolute Uncertainties • Frequently we make two measurements and subtract them to find a difference (Δ). When we subtract numbers that have an uncertainty we must ADD the absolute uncertainty values! • Eg. While doing a density experiment we add an object to a graduated cylinder. The reading of the cylinder changes from (20.5±0.5)mL to (24.0±0.5)mL. The volume difference (ΔV) is (3.5±1.0)mL • When adding two numbers with uncertainties, we also ADD the uncertainty. AUT = ΣAU orAUT = AU1 +AU2+…

14. Relative Uncertainty App.5 Page 394 • Sometimes it is useful to know how much uncertainty we have compared to the original measurement. To do this we can calculate the relative uncertainty (RU). • RU of a measurement equals the absolute uncertainty divided by the absolute value of the original measurement. • The resulting decimal number is often converted to a percentage Click here for details on UNCERTAINTY.

15. Example of Relative Uncertainty App.5 Page 394 • The graduated cylinder has a reading of (32.5±0.5) mL (absolute) • To find its relative uncertainty, divide: 0.5 ÷ 32.5 = 0.01538461 • Round off to a reasonable number of decimal places and convert to a percent: 0.015 x 100 = 1.5% • Write it like this: 32.5 ml ±1.5% The nice thing about relative uncertainties it that they show you how small your error actually is. Parenthesis isNOTused for Relative Uncertainty

16. Multiplying and Dividing with Uncertainties Not in TEXT! • When you multiply and divide measurements, you cannot use Absolute Uncertainties. • Instead, we must add the Relative Uncertainties after we multiply or divide. • Example: an object weighs (58.3±1.0)g and has a volume of (32.5±0.5)mL. Find its density. • (58.3±1.0) g ÷ (32.5±0.5) mL = • find percents: 1.0 ÷ 58.3 x 100 =1.7%, 0.5 ÷ 32.5 x 100=1.5% • 58.3 g ±1.7% ÷ 32.5 mL ±1.5% = 1.79g/mL ± 3.2% • Answer: The density is 1.79g/mL ± 3.2% Can’t do it this way! Use RU

17. Correct precision • It is considered improper in science to imply that a measurement is more precise than it really is. • If you have a graduated cylinder that is marked in 1 mL increments, you can record it to between the two smallest marks: eg. 32.0 ±0.5 mL or 32.5 ±0.5 mL are acceptable readings. • With the same graduated cylinder, it would be wrong to write 32 ±0.5 mL or 32 ±0.5 mL or even 32.00 ±0.5 mL • In science 32 mL, 32.0 mL and 32.00 mL have different meanings with respect to precision.

18. Exercise on Uncertainty • Do the sheet “uncertainty” • The sheet will be corrected in class. • Procedures for an in-class exercise • Make sure your first and last name are on the sheet. • Complete as much of the sheet as you can in the time allotted. Use a pencil or dark colour pen. • When the time is up, follow the teacher’s instructions regarding corrections. Correct with a red pen. • When the sheet has been corrected, put it into your assignment folder or duotang. Keep it here until at least the end of the current term.

19. Overview: Significant FiguresKnowing how much to round an answer. In the sciences, we have an particular way of determining how much precision we need in the observations and answers we record. The method of rounding is called significant digits or significant figures. There is a detailed section in the appendix to your textbook on pages 394 to 397. Unfortunately, a few of the details given there are, well… I won’t say wrong, let’s just call them “uncertain”.

20. Significant Figures(A.K.A. Significant Digits) App.5 Page 395 • In science, we use significantdigits as a guide to how precise an observation is, and as a guide to how much we should round off the results we obtain by doing math with those observations.

21. Rules for Significant Figures Interpreting Significant Digits App.5 Page 395 • All non-zero digits are ALWAYS significant • Zeros between significant digits are ALWAYS significant. • Zeros at the beginning of a number are NEVER significant. • Zeros at the end of a number MAY be significant. • Exponents, multiples, signs, absolute errors etc. are NEVER significant.

22. Examples of Rule 1, 2 and 3 Rule 1. Non-zero digits are ALWAYS significant. 1.234 has 4 significant digits 145 has 3 significant digits 19567.2 has 6 significant digits Rule 2. Zeros between significant digits ARE significant. • has 4 significant digits 5007.4 has 5 significant digits 20000.6 has 6 significant digits Rule 3. Zeros at the beginning are NEVER significant. 007 has 1 significant digit 0.0000005 has 1 significant digit 0.025 has 2 significant digits

23. Explaining Rule 4 Rule 4. Zeros at the end of a number MAY be significant. Your textbook says that they are ALWAYS significant, but this is contrary to what most textbooks say. If there is a decimal point, there is no problem. All textbooks agree, the zeros are ALL significant. 3.00000 has 6 significant digits 5.10 has 3 significant digits 10.00 has 4 significant digits If there is NO decimal, the situation is ambiguous, and a bit of a JUDGEMENT CALL. If you trust the source to be precise, then you count all the zeros at the end. If you have reason to believe the person was estimating, then you don’t count the zeros at the end. 5000 has 1 or 4 significant digits 250 has 2 or 3 significant figures 123 000 000 has 3 or 9 significant figures In a test situation, assume the numbers are precise, unless something in the question states otherwise. Trusted precise source Estimated source

24. Rule 5 Rule 5: Exponents and their bases, perfect multiples, uncertainties (error values), signs etc. are NEVER significant. 6.02x 1023 has 3 significant digits 504.1 mL x 3has 4 significant digits 5.3±0.5 mL has 2 significant digits – 5.432x 10-5has 4 significant digits In each case, the blue part is significant, the greenpart is NOT significant. Note: The term Significance in this usage is not the same as importance. A digit may be “insignificant” but still very important. The significant digits guide you to the correct way of rounding numbers to show precision. The insignificant digits may serve as “placeholders”, making sure the decimal point is in the right place. An important job indeed, but not one that adds to the precision of the answer.

25. Avoiding Ambiguity Not in TEXT! • We mentioned before that measurements ending in zeros with no decimal were ambiguous. Their accuracy depends on how they were measured, and that doesn’t always show up in the number. • For example, if you measure 200 mL in a cylinder with markings of 1 mL it will be more accurate than if you measured it in one with markings 10 mL apart, and much better than a beaker whose markings were 100 mL apart. How can we show someone reading our lab notes the number of what our 200 mL really means? One answer is Scientific Notation!

26. Same Number, Different Precision Avoid using numbers like 200 mL.Instead write them in scientific notation. 2.0x102 mL means you measured it to the nearest 10 mL (2 S.D.) 2.00 x 102 mL means you measured it to the nearest 1 mL (3 S.D.) 2.0000 x102 mL means you measured it to the nearest 0.01 mL… a very fine level of accuracy indeed! *This could represent one significant digit, or two significant digits, or three significant digits depending on how precise the measuring equipment was. If I am careless enough to write a number like this on a test, you should assume I mean 3 S.D., but you have my permission to point out my mistake! Another way of showing the difference is to include the absolute uncertainty!

27. Math with Significant Figures • Adding and Subtracting: • All units must be the same (can’t add different units!) • Line up all the measurements at their decimal points. • Round off all numbers to match the shortest number of decimals. • Add or subtract as normal. Decimals lined up Cut off Example: add the following measurements. 5345.8 mL 5345.7 6 mL 5.34576 L This unit is not the same as the others! (litres vs. millilitres) 55.1 43mL 55.1 mL 55.1 43mL 547.1 mL 547.1 mL 5984.0 mL The answer is 5984.0 mL. Note that the answer has 5 sig. digits, even though one of the measurements had only 4 sig. digits. This can happen with addition.

28. Math with Significant Figures • Multiplication and Division: • Different units may be multiplied or divided if there is a formula to justify it. • The main rule in multiplying and dividing is that you cannot have an answer with more significant digits than your “weakest” measurement (the one with fewest significant digits) • After doing the math, round off your answer to match the weakest measurement. Weakest measurement only 3 S.D. You are the weakest link. Goodbye! Justification: m=ρV Multiply 2.53 g/mL by 75.35 mL 2.53 x 75.35 = 190.6355 About the unit: x mL = g Answer has only 3 S.D. =191 g

29. Math with Significant Figures • Perfect numbers • Occasionally we consider a number to be perfect. For example, if you are told to “double a quantity” the 2 you multiply by is considered perfect. It does not affect the significant digits of your answer, neither increasing or decreasing them. Mole ratios in stoichiometry are also considered perfect, as are constants like pi. Perfect numbers have no units. • Other operations • Generally, use the same rule as for multiplying for square roots, exponents etc. That is, your answer can have no more significant digits than your weakest measurement. • Mixed operations • When doing mixed operations in science, you will usually do the additions or subtractions first (there should be brackets around them), then the other operations.

30. Problems on Significant Figures • How many significant digits are in each measurement: • 123.45 mL c) 007 spiese) 0.0023 m • 4.500 x103 mL d) times 5 f) 4000 kg • A Coulter counter is a device which counts the blood cells in a sample as they pass through a beam of light. A laboratory technician records 20000 wbc in a blood sample. At a demonstration a reporter says there were 20000 protesters. Both numbers are the same, which one has more significant figures? Why? • Find the volume of a cube that measures 2.3 cm by 3.55 cm by 2.14159 cm. • Add the measurements: 2.500 kg, 354.2 g, 153.78 g Also: Do the worksheet entitled “Significant Figures”

31. Review 1 Periodic Classification Overview The periodic table is a useful arrangement of the elements, into regions, families and periods that have important meanings. It is also a source of much additional information about the elements. With careful interpretation of the table, we can find the number of protons an atom has, the approximate number of neutrons, and the arrangement of electrons in the atom and in its ions.

32. Page 4 R Topic 1: Organization of Matter 0.1.1 O O C H • 0.1.1 Atoms and Molecules • All matter is composed of atoms. • The atoms that make up most matter are assembled into molecules. • A molecule may contain one atom, or it may contain several thousand atoms, or any number between. • A molecule is represented by its formula • Water molecules, for example, are represented by the formula H2O, shown below: • A few large molecules have abbreviations, not formulas, like DeoxyriboNucleicAcid CO2 H N NH3 H One atom Ne Ne Cl Cl S several thousand atoms O DNA 2 atoms of hydrogen 1 atom of oxygen SCl2 32 H2O H H

33. Page 4 Cl– Cl Na Na+ cation anion 0.1.2 • Chemical Formulas and Ions • Some matter is formed from ions instead of normal atoms or molecules. • For the most part, we treat ions like regular atoms, and ionic compounds like molecules but there are a few very technical differences. • Ions are atoms or clusters of atoms that have become positively or negatively charged by losing or gaining one or more electrons. • Positive ions are called cations (ca+ions), • Negative ions are called anions (aNions) • Metals always form cations (+), non-metals usually form anions (-) Notice the slightly stronger wording with respect to metals than nonmetals! 33

34. Differences between ionic and covalent compounds 34

35. Sample Ions Metal Ions (+) + Cations – Anions Non-Metal Ions (-) Notice that some elements can form more than one type of ion. Compounds of the same element can differ quite a bit, for example, red iron oxide (rust) has Fe3+ ions, black iron oxide (wustite) contains Fe2+ ions. Note also, that most negative ions have the name ending changed to –ide. 35

36. 2– O Big Fat Ions + H O S O N H O H O O 3– P H – O O Cl O • Polyatomicions are ions that are composed of a cluster of atoms, instead of a single atom. • For example, the nitrate ion (NO3–) looks like this: • But it acts like a single, negatively charged particle in reactions. • Polyatomic ions are sometimes called radicals. • They are not the same as molecules. O N- O O O Na+ Na+ + NO3- NaNO3 N- O O

37. Common Polyatomic Ions (see p.422) 3- 2- 1- 1- 37 This information is important when naming ternary ionic compounds. Click to skip ahead to Ionic Naming Rules

38. Review 2 Representation of Atoms Overview Since the time of classical Greece, humans have tried to represent what matter was made of. Because the particles of matter are too small to see, we have used models to represent our concepts of atoms and molecules.

39. R Representation of Atoms 0.2.0 H • Early Representations • Democritus (c.450 BCE) first suggested that matter was made of particles. • John Dalton (1800) represented the atoms as spheres (like microscopic bowling balls) • J.J. Thomson represented the atom as a “plum pudding” of positive charge with negative charged electrons scattered inside “like rasins” • You studied the historic importance of these models last year, so you will not be tested on them this year. We will concentrate on the three most widely used representations on the slides that follow. C N O P S Cl Dalton models Original and Modern + - - - - - 39

40. R Page 5 0.2.1 Page 5 Rutherford-Bohr Model • Rutherford discovered that the atom has a dense nucleus containing positively charged protons. • Negatively charged electrons move around this nucleus in paths that resemble an orbit. • Later, Bohr calculated that there were different orbital energy levels or “shells” that could hold different numbers of electrons. • A pattern of “Bohr numbers” corresponds to the formula 2n2 where n is a whole number. • Bohr numbers: 2,8, 18, 32, 50… Early Rutherford model Revised Bohr model 40

41. Page 5 0.2.2 Page 6 The Simplified Atomic Model • The simplified atomic model that we often use today adds neutrons (discovered by James Chadwick after the Bohr-Rutherford model had been proposed)to the protons in the nucleus. • We often draw this in a simplified way, showing the nucleus as a full circle, and the electron “shells” as half-circles. Symbol: The symbol of the element Electrons: 2 in first shell, 8 in 2nd 1 in 3rd 11p+ 12n0 Na The Atomic Number, Z, is the number of protons in the element. The configuration is the arrangement of the electrons in the shells 2e- 8e- 1e- Nucleus: If asked for a complete simplified model, give the #protons and #neutrons (if known) in the nucleus. Otherwise, just draw a full circle. Z=11, configuration: 2,8,1 41

42. WARNING • Be careful how you draw them! • The diagram must show the nucleus! Unacceptable! Unacceptable! Nucleus is not shown. Nucleus is confused with 1st shell Nucleus shown as solid circle. Labelled with element symbol beside. Nucleus shown as full circle. Labelled with #protons and neutrons. ACCEPTABLE ACCEPTABLE

43. Page 6 The Sub-atomic Particles nucleons 43

44. R 0.2.3 Page 7 Lewis Model: (AKA Lewis electron dot notation) • Lewis notation is a way of drawing a representation of the valence electrons of an atom • When sketching an atom, write the symbol, and then arrange dots around it to represent its valence electrons. • Example: N has 5 valence electrons N • The “odd” or unpaired electrons are available for the purpose of bonding. • Because there are 3 electrons available for bonding, we say nitrogen has a valence of 3. • When bonding, atoms gain, lose or share electrons in order to get a total of 8* electrons around each atom. 2 paired electrons 1 5 3 “odd” unpaired electrons 4 2 3 44

45. The preferred way of drawing Lewis diagrams of the first ten elements is shown below: However, the dots may be moved around to show different arrangements. All of the drawings of Beryllium shown below might be correct in some circumstances. Sometimes electrons are removed from one atom to others in order to get 8 Sometimes showing the bonding between atoms requires clever sharing of dots, as in the drawing of a nitrogen molecule (N2) shown here: 45

46. The Modern Model(Optional Enrichment) • The Modern Model of the Atom • Of course, the Rutherford-Bohr model and the Simplified Model do not perfectly represent what happens inside the atom. No model can! • A more complete model, The Modern or Electron-Cloud model exists, but is more complicated and extremely difficult to draw. • The Modern Model more accurately explains the relationship between the atom and the periodic table, and allows you to produce simplified models of elements in the transition area of the periodic table. 46

47. The Modern Model(Optional Enrichment) • The 2-8-8 vs. 2-8-18 problem. • You have probably been taught how to draw Simplified Models for the first 20 elements • If so, you have noticed that for the elements potassium and calcium, the third shell only holds 8 electrons—but Bohr said it should hold up to 18! • The models you have been taught can’t explain why, but the modern model includes a concept called “orbitals” or subshells, and a filling pattern called the “aufbaudiagram” that explain this . 47

48. The Modern Model(Optional Enrichment) • You are not required to learn the Aufbau diagram or the modern electron cloud model, but if time permits, I will show you how it works near the end of the review section. In the meantime: • You must know that the third shell CAN hold up to 18 electrons, but often doesn’t. • And you must learn how the periodic table can be used to figure out the electron arrangement of many elements past the first 20. • But that is part of the next lesson… 48

49. Atomic Model Exercises • Draw Simplified Models of the first 20 elements. • Draw Lewis Models of the first 20 elements. • Convert the following: • 125 cm to m d) 320 mL to L g) 750 mL to L • 280 g to kg e) 45000 mm to km h) 0.0035km to cm • 4.63 L to mL f) 5.52 kg to g i) 0.45L to mL

50. Review 3 Periodic Classification Overview The periodic table is a useful arrangement of the elements, into regions, families and periods that have important meanings. It is also a source of much additional information about the elements. With careful interpretation of the table, we can find the number of protons an atom has, the approximate number of neutrons, and the arrangement of electrons in the atom and in its ions.