1. Chemistry is where you learn 2 + 2 = 10 or something. —Dennis Rodman Chemistry Math With Chemistry-specific graphs

2. Chemistry = Memorization? http://www.magazine-agent.com/officials-logic-problems/magazine Look at the following numbers. How easy would it be to memorize this list and regenerate it in a week or so on a quiz? Look at the following numbers. How easy would it be to memorize this list and regenerate it in a week or so on a quiz? 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845 Pretty hard? Pretty Easy? Why? Pretty hard? Pretty Easy? Why? Easy huh? OK, what’s the next number in the sequence? How about the next 5 numbers? Easy huh? OK, what’s the next number in the sequence? How about the next 5 numbers?

3. 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845 http://www.antiqueradiomuseum.org/RR%20Rule%20Book%20for%20CMSP&P%20RR.jpg The numbers don’t seem to follow any kind of pattern. The numbers don’t seem to follow any kind of pattern. But, what if you knew a rule? It wouldn’t just be memorization then. But, what if you knew a rule? It wouldn’t just be memorization then. OK, good point! The rule is: OK, good point! The rule is: Start with 1. Start with 1. Double and add 1. Double and add 1. Double and subtract 1. Double and subtract 1. And so on. And so on. You just wish it was that EASY!

4. Learn HOW to do the problem; don’t just memorize the answer! http://familyfun.go.com/Resources/printable-previews/previews/beaver_memorygame_august2.jpg Doesn’t “knowing the rule” make the list easier to memorize? Doesn’t “knowing the rule” make the list easier to memorize? You don’t have to memorize a bunch of unrelated numbers. You don’t have to memorize a bunch of unrelated numbers. IF YOU KNOW the rule, you can generate the number list on the test easily. Anytime! Anywhere! IF YOU KNOW the rule, you can generate the number list on the test easily. Anytime! Anywhere! Don’t

5. Can you make sense out of NONSENSE? ForceHourUponNeigh ForceHourUponNeigh KoranForceCisShun KoranForceCisShun HeavenFodderCount HeavenFodderCount YeBratAnent YeBratAnent SagoFarceAnew SagoFarceAnew Figured it out yet? Figured it out yet?

6. The Gettysburg Address http://www.old-picture.com/defining-moments/pictures/Abraham-Lincoln-Antietam-Battlefield.jpg http://en.wikipedia.org/wiki/Gettysburg_Address “Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.” “Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.” Being able to look at something new, and make sense of it is an important skill for the rest of this course. Being able to look at something new, and make sense of it is an important skill for the rest of this course. Yes, Ms Rackley, I know this was Antietam, but it’s a nice picture.

7. Unfortunately (for you) I’m not Bill Nye http://www.tvgasm.com/newsgasm/Bill-nye.jpg In Chemistry, when we have numbers, much of the time we do one of three things: In Chemistry, when we have numbers, much of the time we do one of three things: Multiple 2 x 3 Multiple 2 x 3 Divide 2 / 3 Divide 2 / 3 Divide 3 / 2 Divide 3 / 2 If you can figure out which operation to do when, you can actually solve the problem. That’s our goal. If you can figure out which operation to do when, you can actually solve the problem. That’s our goal. What would Bill Nye do?

8. Units TELL you the right ANSWER If your units don’t work out right, your answer is wrong. If your units don’t work out right, your answer is wrong. Don’t just ignore wrong units. It is a big clue for you. Don’t just ignore wrong units. It is a big clue for you. LISTEN to the units! LISTEN to the units!

9. Variables Independent Independent Variable “I” change Variable “I” change Graphed on “x” axis Graphed on “x” axis Dependent Dependent Variable which “Depends” on independent variable Variable which “Depends” on independent variable Tested during experiment Tested during experiment Graphed on “y” axis Graphed on “y” axis Control Control Variables you control so they do not change and mess up your experiment Variables you control so they do not change and mess up your experiment Never graphed Never graphed

10. Graphing Variables Slope = rise/run Slope = mass/volume Slope = density We don’t graph just to graph; the graph and the data tells us something meaningful.

11. Line of Best Fit Real data never (almost never) falls exactly on the line! The line is an “average” Once you know the line of best fit, you can use it to predict other values. The line represents the data.

12. We never “connect the dots” in a graph. Don’t connect the dots. The line of best fit doesn’t have to go through ANY of the data points. However, some points might be exactly on the line. Ideally the points above the line = the points below the line

13. y = mx + b To graph without your calculator, you need 2 points to define a line. To graph without your calculator, you need 2 points to define a line. Use the y-intercept for the first point (x = 0 when y = b) Use the y-intercept for the first point (x = 0 when y = b) Set y = 0 to find the second point (x = − b/m when y = 0). Set y = 0 to find the second point (x = − b/m when y = 0). Use a RULER to draw your lines! Use a RULER to draw your lines!

14. Accuracy & Precision Accuracy is how close you are to the true value. Think of a “bullseye” in darts. Accuracy is how close you are to the true value. Think of a “bullseye” in darts. Precision is how close all your measurements are to each other. Precision is how close all your measurements are to each other. Can you be accurate but not precise? Can you be accurate but not precise? Can you be precise but not accurate? Can you be precise but not accurate?

15. Helpful Formulas Unit 1 Density Density D = m/V D = m/V Temperature Conversions Temperature Conversions K = °C + 273 (note K does not have a ° symbol) K = °C + 273 (note K does not have a ° symbol) °C = K − 273 °C = K − 273 °C = (°F − 32) ÷ 1.8 °C = (°F − 32) ÷ 1.8 ΔT = T 2 − T 1 orΔT = T final − T initial ΔT = T 2 − T 1 orΔT = T final − T initial

16. Directly Proportional Directly proportional means that as one goes up, the other goes up too. Directly proportional means that as one goes up, the other goes up too. For matter, kinetic energy (KE) is directly proportional to Kelvin temperature (K) For matter, kinetic energy (KE) is directly proportional to Kelvin temperature (K) If you graph these variables, you will get a straight line with a POSITIVE slope. If you graph these variables, you will get a straight line with a POSITIVE slope.

17. Inversely Proportional Inversely proportional means that as one goes up, the other goes down (and vice versa). Inversely proportional means that as one goes up, the other goes down (and vice versa). For any gas, pressure (P) is inversely proportional to volume (V) For any gas, pressure (P) is inversely proportional to volume (V) If you graph these variables, you will get a straight line with a NEGATIVE slope. If you graph these variables, you will get a straight line with a NEGATIVE slope.

18. Let’s Do Some Math! Density Density If a marble weighs 10.0 g and has a volume of 5.0 mL what is the density of the marble? Use correct units. If a marble weighs 10.0 g and has a volume of 5.0 mL what is the density of the marble? Use correct units. Another marble with the same density has a mass of 15.0 g. What is the volume of that marble? Use correct units. Another marble with the same density has a mass of 15.0 g. What is the volume of that marble? Use correct units. A different marble has a density of 3.0 g/mL. If that marble has a volume of 10.0 mL, what is the mass of that marble? Use correct units. A different marble has a density of 3.0 g/mL. If that marble has a volume of 10.0 mL, what is the mass of that marble? Use correct units.

19. Let’s Do Some Math! Temperature Temperature If it is 104°F in Fredericksburg, what is the temp in °C? If it is 104°F in Fredericksburg, what is the temp in °C? What is the temp in K? What is the temp in K? If it is -40°F in Fredericksburg, what is the temp in °C? If it is -40°F in Fredericksburg, what is the temp in °C? What is the temp in K? What is the temp in K? If a sample of matter is 298K, what is the temp in °C? If a sample of matter is 298K, what is the temp in °C?

20. Helpful Formulas Unit 1 How to Figure out your Quiz Grade: How to Figure out your Quiz Grade: Your Grade ÷ 25 × 100 = SCORE Your Grade ÷ 25 × 100 = SCORE Calculating Error Calculating Error Error = |Your Number − True Number| Error = |Your Number − True Number| % Error = Error ÷ True Number × 100 % Error = Error ÷ True Number × 100

21. Let’s Do Some Math! Error Analysis Error Analysis The accepted value for the density of a penny is 7 g/cm 3. The accepted value for the density of a penny is 7 g/cm 3. You measure 5 pennies and calculate the density as You measure 5 pennies and calculate the density as 7.50 g/cm 3 7.50 g/cm 3 7.20 g/cm 3 7.20 g/cm 3 6.90 g/cm 3 6.90 g/cm 3 7.40 g/cm 3 7.40 g/cm 3 6.90 g/cm 3 6.90 g/cm 3 What is the average density? What is the error? What is the percent error? What is the average density? What is the error? What is the percent error?

22. Let’s Do Some Math! What is the average density? 7.18 g/cm 3. What is the average density? 7.18 g/cm 3. What is the error? |7.18 − 7| = 0.18 g/cm 3. What is the error? |7.18 − 7| = 0.18 g/cm 3. What is the percent error? 0.18 ÷ 7 x 100 = 2.57142857 What is the percent error? 0.18 ÷ 7 x 100 = 2.57142857 You should record your final answer as 2.6% after rounding. You should record your final answer as 2.6% after rounding.

23. Helpful Formulas Unit 1 SI Units and Conversions SI Units and Conversions Need to know what these prefixes mean Need to know what these prefixes mean Kilo (k)ex 1 kg = 1000 g Kilo (k)ex 1 kg = 1000 g Centi (c)ex 100 cm = 1 m Centi (c)ex 100 cm = 1 m Milli (m)ex 1,000 mL = 1 L Milli (m)ex 1,000 mL = 1 L Micro (μ)ex 1,000,000 μg = 1 g Micro (μ)ex 1,000,000 μg = 1 g Nano (n)ex 1,000,000,000 nm = 1 m Nano (n)ex 1,000,000,000 nm = 1 m

24. Dimensional Analysis The base unit can change, but the prefix means the same thing The base unit can change, but the prefix means the same thing 100 cm = 1 m 100 cm = 1 m 100 cg = 1 g 100 cg = 1 g 100 cL = 1 L 100 cL = 1 L Centi ALWAYS means that there are 100 divisions of the base unit. Centi ALWAYS means that there are 100 divisions of the base unit.

25. Let’s Do Some Math! Convert 45 cm to mm? Convert 45 cm to mm? To do this you need to know the conversion factors To do this you need to know the conversion factors 100 cm = 1 m 100 cm = 1 m 1,000 mm = 1 m. 1,000 mm = 1 m. First step: convert cm to meters. First step: convert cm to meters. Second step: convert meters to mm. Second step: convert meters to mm. To find the answer: cancel out units until you have the units you are looking for. To find the answer: cancel out units until you have the units you are looking for.

26. Let’s Do Some Math! Convert 45 cm to mm? Convert 45 cm to mm? 45 cm × 1 m × 1,000 mm = ? 45 cm × 1 m × 1,000 mm = ? 100 cm 1 m 100 cm 1 m 45 cm × 1 m × 1,000 mm = 450 mm 45 cm × 1 m × 1,000 mm = 450 mm 100 cm 1 m 100 cm 1 m

27. Let’s Do Some Math! Convert 345 μg to kg? Convert 345 μg to kg? Convert 14.6 mL to L? Convert 14.6 mL to L? Convert 1 hour to seconds? Convert 1 hour to seconds? Convert 100 cm 3 to mL Convert 100 cm 3 to mL Convert 500 nm to mm? Convert 500 nm to mm?

28. Let’s Do Some Math! Answers: Answers: Convert 345 μg to kg? 3.45 x 10 -7 kg Convert 345 μg to kg? 3.45 x 10 -7 kg Convert 14.6 mL to L? 0.0146 L Convert 14.6 mL to L? 0.0146 L Convert 1 hour to seconds? 3,600 sec Convert 1 hour to seconds? 3,600 sec Convert 100 cm 3 to mL 100 mL Convert 100 cm 3 to mL 100 mL Convert 500 nm to mm? 5 x 10 -4 mm Convert 500 nm to mm? 5 x 10 -4 mm

29. Some Other Chemistry Graphs Phase Diagrams Heating Curves Radioactive Decay Reaction Progress Not all chemistry graphs will be straight lines. But most will. Let’s see some distinctive ones which aren’t.

30. Phase Diagram for H 2 O A phase is a “state” of matter. Solid phase Liquid phase Gas phase We don’t “do” plasma. Critical Point Triple Point

31. Phase Diagram for H 2 O The triple point is the only point on the graph where all 3 phases are at equilibrium. The critical point is the END of the graph. Critical Point Triple Point

32. Phase Diagram for H 2 O The lines show the pressure/temperature points where the phase changes from one to the other. When P = 1 atm, you can read the MP and BP right off the graph. Boiling Point Melting Point

33. Heating Curve for H 2 O Solid between A&B, liquid between C&D, gas between E&F

34. Heating Curve for H 2 O Melts between B & C Boils between D & E Why doesn’t the temp rise when water is melting?

35. Radioactive Decay After 1 half life, 50% remains. After 2 half lives, 25% remains. HALF of whatever is left decays during each half life.

36. From the Pretest… The point where vapor pressure crosses atmospheric pressure (101.3kPa) = boiling point. The lower the vapor pressure, the higher the boiling point.

37. Rxn Progress Rxn Progress The reaction is exothermic (products have less energy than reactants). Enzyme = biological catalyst. Rxn = abbreviation for reaction

38. Rxn Progress This reaction is endothermic. Products are higher than reactants (have more potential energy).

39. Significant Figures aka Sig figs If you didn’t know the exact amount of coffee, is adding one more drop significant? If you didn’t know the exact amount of coffee, is adding one more drop significant? In other words, by adding one more drop, do you now know that it’s exactly 200.05mL? In other words, by adding one more drop, do you now know that it’s exactly 200.05mL?

40. Sig Fig Rules 1. All digits except for zero are ALWAYS significant. 1. All digits except for zero are ALWAYS significant. How many sig figs does 12.34 have? How many sig figs does 12.34 have? How many sig figs does 45.6 have? How many sig figs does 45.6 have? 2. Zero is SOMETIMES significant. 2. Zero is SOMETIMES significant. 0’s between other numbers are significant. 0’s between other numbers are significant. 100.3 has 4 sig figs. 100.3 has 4 sig figs. 10101010101 is totally significant. Every one of the digits is significant. Make sense? 10101010101 is totally significant. Every one of the digits is significant. Make sense? 0’s at the end of a number are significant IF they are also to the right of the decimal point. 0’s at the end of a number are significant IF they are also to the right of the decimal point.

41. Sig Fig Rules 0’s at the end of a number are significant IF they are also to the right of the decimal point. 0’s at the end of a number are significant IF they are also to the right of the decimal point. 14.50 has 4 sig figs (end of the number AND right of the decimal point). 14.50 has 4 sig figs (end of the number AND right of the decimal point). 1,450 has 3 sig figs (zero is at end of the number BUT to the LEFT of the decimal point). 1,450 has 3 sig figs (zero is at end of the number BUT to the LEFT of the decimal point). 0.02345 has 4 sig figs (zero is to the right of the decimal point, BUT NOT at the end of the number). 0.02345 has 4 sig figs (zero is to the right of the decimal point, BUT NOT at the end of the number). BOTH conditions must be true. Must be at the END of the number AND to the RIGHT of the decimal. BOTH conditions must be true. Must be at the END of the number AND to the RIGHT of the decimal. 3. 0’s at the BEGINNING of a number are never significant. 3. 0’s at the BEGINNING of a number are never significant.

42. Sig Figs How many sig figs do each of the following have How many sig figs do each of the following have 1234.0 1234.0 0.000000000000000000001 0.000000000000000000001 0.000100 0.000100 50 50 50.0 50.0 60 min = 1 hour 60 min = 1 hour How many sig figs does 60 have? How many sig figs does 60 have? How many sig figs does 1 have? How many sig figs does 1 have?

43. Rules for Sig Figs if you take the measurement yourself All of the digits you can read directly off the measuring instrument are significant. All of the digits you can read directly off the measuring instrument are significant. The first digit you can ESTIMATE is also significant. The first digit you can ESTIMATE is also significant. Suppose you have water in a graduated cylinder. The meniscus is EXACTLY on 20 mL. The next mark up is 21 mL. What should you record the volume as. Suppose you have water in a graduated cylinder. The meniscus is EXACTLY on 20 mL. The next mark up is 21 mL. What should you record the volume as. Suppose the meniscus was between 20 and 21 mL. What then? Suppose the meniscus was between 20 and 21 mL. What then?

44. Scientific Notation Put the following in scientific notation. Put the following in scientific notation. 150,000 150,000 0.000045 0.000045 Put the following in regular notation Put the following in regular notation 4.05 x 10 8 4.05 x 10 8 2.34 x 10 -4 2.34 x 10 -4

45. The End