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Chapter 2 Measurement and Calculations

Chapter 2 Measurement and Calculations. Chapter 2 Measurement and Calculations. The marshmallow test. http://youtu.be/ QX_oy9614HQ. The marshmallow test study description and conclusions http://www.youtube.com/watch?v=amsqeYOk--w&NR=1. 2.1 The Scientific Method.

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Chapter 2 Measurement and Calculations

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  1. Chapter 2 Measurement and Calculations

  2. Chapter 2 Measurement and Calculations The marshmallow test http://youtu.be/QX_oy9614HQ The marshmallow test study description and conclusions http://www.youtube.com/watch?v=amsqeYOk--w&NR=1

  3. 2.1 The Scientific Method Observing and Collecting Data • Qualitative: Use descriptions to explain data • Ex: small, white, puffy, smells good, quiet, wiggly • Quantitative: Use numbers to describe data • Ex: 4 cm, 5.30 grams, 15.65 minutes

  4. 2.1 System – a specific portion of matter in a given region of space that has been selected for study during an experiment. Example: In Marshmallow Test, the system is the child, the marshmallow, the plate, and everything in the room. Surroundings – everything outside of the system. Example: In the Marshmallow Test, the surroundings are everything outside of the room.

  5. The Scientific Method – a review 2.1

  6. 2.1 Formulating Hypotheses • A hypothesis is a testable statement (it really is not just an educated guess) • A hypothesis is often written as an if – then statement • Ex. If phosphorus stimulates plant growth, then plants treated with phosphorus fertilizer should grow faster than plants not treated with phosphorous fertilizer (all other variables held constant). • Sometimes we add more detail to the hypothesis: • Plants that receive more phosphorus should grow faster than those that receive less phosphorus.

  7. 2.1 Testing Hypotheses In Science, there is a commitment to follow the evidence, wherever it leads. If a hypothesis is not supported by data, it must be rejected. So, was the hypothesis about phosphorus fertilizer correct? There must also be a willingness to accept that new evidence may require us to modify or change our ideas about what we thought to be true.

  8. 2.1 Theorizing In everyday language, the word “theory” is often misused when a more accurate term would be “hypothesis.” Example: I have a theory that it always rains after I wash my car. This is really a hypothesis. It has not been, but could be tested. A theory would have already been vigorously tested, generated consistent results, and would offer an explanation of why the event occurs.

  9. 2.1 Theorizing A theory is a broad generalization that explains a body of facts or observations. Theories are well documented and provedbeyond reasonable doubt. Scientists continue to tinker with the component parts of each theory in an attempt to make them more exact. Theories can be tweaked, but they are seldom, if ever, entirely replaced.

  10. The SI Units of Measurement(le Système International, SI) 2.2 You do not need to be concerned with Amperes and candelas this year

  11. 2.2 Units of Measurement Quantitative Measurements • Always contain two parts • number • unit • Both parts must be present for the measurement to be meaningful.

  12. 2.2 The SI Units of Measurement(le Système International, SI) Prefixes are added to these base units to show quantities in larger or smaller amounts. (you will have the ones you need on a handout) Here are a few of them: Tera T 1012 1 000 000 000 000 Giga G 109 1 000 000 000 Mega M 106 1 000 000 Milli m 10-3 1/1000 Nano n 10-9 1/1 000 000 000

  13. 2.2 SI Measurement A quantity is something that has magnitude, size or amount. The units of measurement must be standardized for the measurement to make sense to everyone. • A standardized system of measurement is one in which everyone agrees upon the size of the unit. Early systems of measurement were based upon the size of the king’s foot, or length of arm, for example. • But this type of system has problems: • What happens if you want to communicate measurements to someone in another country? • What happens when you get a new king?

  14. SI Base Units 2.2 • Mass- • a measure of the amount of matter in an object • standard unit is the kilogram (but we often use grams) • not the same as weight Remember this? Weight is a measure of the pull of gravity on the object, so the stronger the gravitational pull, the higher the weight.

  15. SI Base Units 2.2 • Length- • a measure of distance • standard unit is the meter • we often use mm, cm

  16. SI Base Units 2.2 • Volume- • the amount of space an object takes up • standard unit for liquids is the liter (L) but we often use mL (1/1000 of a liter) • we also use cm3 (for solids)

  17. 2.2 Used for solids Used for liquids It is very helpful to know that 1 mL and 1 cm3 are equal volumes 1 cm3 = 1mL

  18. Density 2.2 Density is a measure of how packed together the molecules are. The more packed together it is, the more dense it is. Density = mass divided by volume Which material below is most dense? A B

  19. 2.2 M V M D = D V Density • Density - mass per unit volume (g/cm3 for solidsand g/mL for liquids)

  20. 2.2 D = M V 18 g = 9 g cm3 2 cm3 Density is a ratio of mass to volume. Does changing the size of the sample (like cutting it in half) change the density? Example: a 2 cm3 piece of copper weighs 18 g. What is the density of the copper? What is the density of a piece of copper that is half the size? Density for a material does not depend on the size of the sample! Half the size: 9 g = 9 g cm3 1 cm3

  21. 2.2 M D V Density Practice Problem 1 • An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g ) x (825 cm3) cm3 M = 11,220 g

  22. 2.2 WORK: V = M D V = 25 g 0.87 g/mL M D V Density Practice Problem 2 • A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g V = 28.73563218 mL

  23. 2.2 WORK: D = M V D = 620 g 753 cm3 M D V Density Practice Problem 3 • You have a sample with a mass of 620 g & a volume of 753 cm3. Find density. GIVEN: M = 620 g V = 753 cm3 D = ? D = 0.823373174 g/cm3

  24. 2.2 Derived SI Units Multiplying or dividing SI units creates a “derived unit” (derived units are generated by calculation, not by a direct measurement) Example: measuring the volume of a shoebox You measure these directly Volume = length x width x height Volume =__ cm x __cm x __cm a derived unit that came from a calculation Volume = __cm3

  25. Lab: How do you find the mass of an object? Put it on a balance and weigh it! How do you find the volume of an object? If it is rectangular, you can multiply length x width x height For irregular shaped objects, slide it into water and notice how much the water level rises

  26. Scientific Notation - a quick review (2.3) exponent 8.6 x 1018 coefficient Scientific notation allows us to talk about numbers that are very, very large or very, very small 0.0081 = 8.1 x 10-3 36 000 = 3.6 x 104

  27. Why do we need scientific notation in chemistry? (2.3) Example 1: one electron weighs 0.000000000000000000000000009109 grams (that’s 27 zeros after the decimal point) Its much easier to write the mass of an electron in scientific notation as…9.109 x 10-28 grams Example 2: 12.0 grams of carbon contains 602000000000000000000000 atoms of carbon That’s…………..6.02 x 1023 atoms

  28. (2.3) Write in Scientific Notation If the number is GREATER than 1, the exponent is POSITIVE If the number is LESS than 1, the exponent is NEGATIVE • 98,500,000 = • 64,100,000,000 = • 279,000,000 = • 4,200,000 = • 0.0054 = 9.85 x 107 6.41 x 1010 2.79 x 108 4.2 x 106 5.4 x 10-3 Note that we put only one digit in front of the decimal.(This makes it a number between 1 and 10) This is proper scientific notation form.

  29. (2.3) Write in Decimal notation If the exponent is +, move the decimal to the RIGHT If the exponenet is -, move the decimal to the LEFT • 6.27 x 106 = • 9.01 x 104 = • 2.65 x 10 -3 = • 6,270,000 • 90,100 • 0.00265

  30. What’s wrong with these? 30 x 106 0.1 x 10-3 10.1 x 1012 0.72 x 10-9 (2.3) 3.0 x 107 1 x 10-4 1.01 x 1013 7.2 x 10-10 Improper form! Can you fix them? There should be one digit in front of the decimal

  31. Scientific Notation Math Multiplying scientific notation: Multiply the coefficients Add the exponents Make sure the new coefficient is a number between 1 and 10 (2.5 x 104) x (4.5 x 103) (11.25 x 107) (1.125 x 108) Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent. }

  32. Scientific Notation Math • Dividing scientific notation: • Divide the coefficients • Subtract the exponents • Make sure the new coefficient is a number between 1 and 10 • (2.5 x 104) ÷ (4.5 x 103) • (.5555… x 101) • (5.6 x 100) Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent. }

  33. Scientific Notation Adding Scientific notation: Set both notations to the same exponent. Add the coefficients Exponent stays the same Make sure the new coefficient is a number between 1 and 10 (3.4 x 104) + (5.7 x 107) (3.4 x 104) + (5700.0 x 104) 5703.4 x 104 5.7034 x 107 Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent.

  34. Scientific Notation Subtracting Scientific notation: Set both notations to the same exponent. Subtract the coefficients Exponents stay the same Make sure the new coefficient is a number between 1 and 10 (3.4 x 104) - (5.7 x 107) (3.4 x 104) - (5700.0 x 104) -5696.6 x 104 -5.6966 x 107 Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent.

  35. (2.3) Scientific Notation And Your Calculator To key in the number 4.2 x 103…. Type 4.2 (the base) Press EE or EXP (this takes care of the x 10 part) Type 3 (the exponent) Don’t Type 4.2 X 10 ^ 3 (don’t use the evil ^ button!) DON’T hit the x (times button) if you are using the EE or EXP button

  36. (2.3) Try out your calculator (3.1 x 103)(4.8 x 102) Answer: 1.488 x 106 calculator may say 1.488 E 6 calculator may say1.4886 If you didn’t get these answers, let’s examine your calculator to see what buttons you should press. It is important to learn how your individual calculator works. Borrowing a calculator from a friend is not a good idea because you may make input errors if theirs works differently from the one you are used to. or 1 488 000

  37. Try out your calculator again (8 x 10-7) x (4 x 10-1) Answer: 3.2 x 10-7 or 0.00000032 calculator may say 3.2 E -7 If you didn’t get this answer, get help NOW! (2.3)

  38. Powers of Ten slide show http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/ The video http://www.powersof10.com/

  39. (2.3) For more scientific notation practice: Scientific notation practice site http://science.widener.edu/svb/tutorial/sigfigurescsn7.html messing with the exponents in sci notation http://www.ucel.ac.uk/rlos/essentialmaths/M1/1E.Int3.htm decimal sci notation conversions http://academic.umf.maine.edu/~magri/tools/DSconversion.html Sci notation pracrtice http://www.aaamath.com/dec71i-dec2sci.htm l Sci notation practice http://janus.astro.umd.edu/astro/scinote/ Sci notation practice with quiz http://janus.astro.umd.edu/cgi-bin/astro/scinote.p l Quick Tutorial on Scientific Notation: http://www.swtc.edu:8082/mscenter/mthsci/science/1tools/p02csnot.pps

  40. Scientific Notation Practice Worksheet 1 Scientific Notation Practice Worksheet 2

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