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SCIENTIFIC MEASUREMENT

SCIENTIFIC MEASUREMENT. CHEM IH: CHAPTER 3. Stating a Measurement. In every measurement there is a Number followed by a Unit from a measuring device The number should also be as precise as the measuring device. Ex: Reading a Meterstick.

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SCIENTIFIC MEASUREMENT

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  1. SCIENTIFIC MEASUREMENT • CHEM IH: CHAPTER 3

  2. Stating a Measurement In every measurement there is a • Number followed by a • Unit from a measuring device The number should also be as precise as the measuring device.

  3. Ex: Reading a Meterstick . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm First digit (known) = 2 2.?? cm Second digit (known) = 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported =2.75 cm or 2.74 cm or 2.76 cm

  4. UNITS OF MEASUREMENT Use SI units — based on the metric system Length Mass Volume Time Temperature Meter, m Kilogram, kg Liter, L Seconds, s Celsius degrees, ˚C kelvins, K

  5. Metric Prefixes

  6. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 hr. = 60 min Factors: 1 hr. and 60 min 60 min 1 hr.

  7. How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 min 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

  8. Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x ___min x ____ s = 1 day hr min ANSWER: 120,960 s.

  9. Significant Figures (Honors only) • The numbers reported in a measurement are limited by the measuring tool • Significant figures in a measurement include the known digits plus one estimated digit

  10. Counting Significant Figures: Non-Zero Digits (Honors Only) RULE 1. All non-zero digits in a measured number ARE significant. #of Significant Figures 38.15 cm 4 5.6 ft 2 65.6 lb ___ 122.55 m___

  11. Counting Significant Figures:Leading Zeros (Honors Only) RULE 2. Leading zeros in decimal numbers are NOT significant. #of Significant Figures 0.008 mm 1 0.0156 oz 3 0.0042 lb ____ 0.000262 mL ____

  12. Counting Significant Figures:Sandwiched Zeros (Honors Only) RULE 3. Zeros between nonzero numbers ARE significant. (They can not be rounded unless they are on an end of a number.) # of Significant Figures 50.8 mm 3 2001 min 4 0.702 lb ____ 0.00405 m ____

  13. Counting Significant Figures:Zeros @ the End of a # & to the Right of a Decimal (Honors Only) RULE 4. Trailing zeros at the end of a number and to the right of a decimal numbers ARE significant. # of Significant Figures 43.00 m. 4 200.00 yr 5 1.10 gal ____ 0.04500 g ____

  14. Counting Significant Figures:Trailing Zeros (Honors Only) RULE 5. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. # of Significant Figures 25,000 in. 2 200. yr 3 48,600 gal ____ 25,005,000 g ____

  15. Counting Significant Figures:Unlimited Sig Figs (Honors Only) RULE 6. 2 instances in which there are an unlimited # of sig figs. • Counting. Ex: 23 people in our classroom. • Exactly defined quantities. Ex: 1hr = 60 min. • Both are exact values. There is no uncertainty. • Neither of these types of values affect the process of rounding an answer.

  16. Learning Check (Honors Only) A. Which answers contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105

  17. Learning Check (Honors Only) In which set(s) do both numbers contain the samenumber of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000

  18. Significant Numbers in Calculations (Honors Only) • A calculated answer cannot be more precise than the measuring tool. • A calculated answer must match the least precise measurement. • Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing • If you must round to obtain the right # of sig figs, do so after all calcs are complete

  19. Adding and Subtracting (Honors Only) The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2one decimal place + 1.34two decimal places 26.54 answer 26.5one decimal place

  20. Learning Check (Honors Only) In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.8 3) 257 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7

  21. Multiplying and Dividing (Honors Only) Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

  22. Learning Check (Honors Only) A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1)61.582) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041

  23. What is Scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • For very large and very small numbers, scientific notation is more concise.

  24. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x

  25. Examples • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer:2.898 x 108 (how many sig figs? Honors only) • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer:5.67 x 10-4 (How many sig figs? Honors only)

  26. CHEMICAL QUANTITIES: THE MOLEchemIh: Chapter 3 & 10

  27. MEASURING MASS • A mole is a quantity of things, just as… 1 dozen = 12 things 1 gross = 144 things 1 mole = 6.02 x 1023 things • “Things” usually measured in moles are atoms, molecules, ions, and formula units

  28. You can measure mass, or volume, or you can count pieces • We measure mass in grams • We measure volume in liters • We count pieces in MOLES

  29. A MOLE… • is an amount, defined as the number of carbon atoms in exactly 12 grams of carbon-12 • 1 mole = 6.02 x 1023of the representative particles • Treat it like a very large dozen 6.02 x 1023is called: Avogadro’s number

  30. Similar Words for an amount: • Pair: 1 pair of shoelaces = 2 shoelaces • Dozen: 1 dozen oranges = 12 oranges • Gross: 1 gross of pencils= 144 pencils • Ream: 1 ream of paper= 500 sheets of paper

  31. What are Representative Particles (“RP”)? • The smallest pieces of a substance: • For a molecular compound: it is the molecule. • For an ionic compound: it is the formula unit (made of ions) • For an element: it is the atom • Remember the 7 diatomic elements? (made of molecules)

  32. Practice Counting Particles • How many oxygen atoms in the following? • CaCO3 3 atoms of oxygen • Al2(SO4)3 12 (4 x 3) atoms of oxygen • How many ions in the following? • CaCl2 • 3 total ions (1 Ca2+ ion and 2 Cl1- ions) • NaOH • 2 total ions (1 Na1+ ion and 1 OH1- ion) • Al2(SO4)3 • 5 total ions (2 Al3+ + 3 SO4 ions)

  33. CONVERSION FACTOR • MOLES = RPs x ____1 mole___ 6.02 x 1023 RPs

  34. EXAMPLES: ATOMS  MOLES • How many moles of B are in 3.15 x 1023 atoms of B? • Conversion: 1 mole B = 6.02 x 1023 atoms B (b/c the atom is the RP of boron) 1 mole B 6.02 x 1023 atoms B = 3.15 x 1023 atoms of B 0.532 mole

  35. EXAMPLES: MOLES  ATOMS • How many atoms of Al are in 1.5 mol of Al? • Conversion: 1 mole = 6.02 x 1023 atoms 1.5 mol of Al 6.02 x 1023 atoms Al 1 mole Al 9.03 x 1023 atoms of Al =

  36. CAUTION: Identify RPs Carefully! • See next slide!

  37. EXAMPLES: MOLECULES  MOLES How many atoms of H are there in 3 moles of H2O? (HINT: Are atoms the RP for water?) Conversions: 1 mole = 6.02 x 1023 molecules (b/c molecules are the RP for H2O) H2O molecule = 2 atoms of Hydrogen 6.02 x 1023molecH2O 1 mole H2O 2 atoms H 1 H2O molecule 3 moles of H2O = 3.612 x 1024 atoms H

  38. MOLAR MASS Def: The mass of a mole of representative particles of a substance. Each element& compound has a molar mass.

  39. 20 Ca 40.08 MOLAR MASS OF AN ELEMENT Determined simply by looking at the periodic table Molar mass (g) = Atomic Mass (amu) * Thus, 1 mol Ca = 40 g 1 atom of Ca weighs 40.08 amu 1 mole of Ca atoms weighs 40.08grams

  40. MOLAR MASS FOR COMPOUNDS • To calculate the molar mass of a compound, find the number of grams of each element in one mole of the compound • Then add the masses within the compound Example: H2O H= 1.012 (1.01) + 1 (15.999)= 18.02 g/mol O= 15.999

  41. SOME PRACTICE PROBLEMS • How many atoms of O are in 3.7 mol of O? • 2.2 X 1024 atoms of oxygen • How many atoms of P are in 2.3 mol of P? • 1.4 x 1024 atoms of phosphorus • How many atoms of Ca are there in 2.5 moles of CaCl2? • 1.5 x 1024 atoms Ca • How many atoms of O are there in 1.7 moles of SO4? • 4.1 x 1024 atoms of oxygen

  42. Remember!!!! • The molar mass of any substance (in grams) equals 1 mole • This applies to ALL substance: elements, molecular compounds, ionic compounds • Use molar mass to convert between mass and moles • Ex: Mass, in grams, of 6 mol of MgCl2 ? mass of MgCl2 = 6 mol MgCl2 92.21 g MgCl2 1 mol MgCl2 = 571.26 g MgCl2

  43. VOLUME AND THE MOLE • Volume varies with changes in temperature & pressure • Gases are predictable, under the same physical conditions • Avogadro’s hypothesis helps explain: equal volume of gases, at the same temp and pressure contains equal number of particles • Ex: helium balloon

  44. Gases vary at different temperatures, makes it hard to measure • Because of variation use STP • Standard Temperature and Pressure • Temperature = 0° C • Pressure = 1 atm (atmosphere) or 101.3 kPal

  45. Molar Volume • At STP:1 mole, 6.02 x 1023 atoms, of any gas has a volume of 22.4 L 1 mole gas = 22.4 L gas • Called Molar Volume • Used to convert between # of moles and vol of a gas @ STP • Ex: what is the vol of 1.25 mol of sulfur gas 1.25 mol S 22.4 L = 28.0 L 1 mol

  46. MOLAR MASS FROM DENSITY • Different gases have different densities • Density of a gas measured in g/L @ a specific temperature • Can use the following formula to solve : grams = grams X 22.4 L mole L 1 mole • Ex: Density of gaseous compound containing oxygen and carbon is 1.964 g/ L, what is the molar mass? • grams = 1.964 g X 22.4 L then you solve mole 1 L 1 mole = 44.o g/mol

  47. Atoms, molecules, etc.

  48. Molarity • Def: the concentration of a solution. How many moles/liter • Can be used to calculate # of moles of a solute • Ex: Household laundry bleach is a dilute aqueous solution of sodium hypochlorite (NaClO). How many moles of solute are present in 1.5 L of 0.70 M NaClO?

  49. Calculating Percent Composition of a Compound • Like all percent problems: a part ÷ the whole • Find the mass of each of the components (the elements) • Next, divide by the total mass of the compound • Then X 100 % = percent Formula: % Composition = Mass of element X 100% Mass of compound

  50. Method #1: % Comp When Actual Masses are Given A compound is formed when 9.03 g of Mg combines completely with 3.48 g of N. What is the percent composition of the compound? • First add the 2 mass of the 2 compounds to reach the total mass 9.03 g Mg + 3.48 g N = 12.51 g Mg3N2 • Find the % of each compound % Mg= 9.03 g Mg X 100% = 72.2 % 12.51 g Mg3N2 % N= 3.48 g N X 100% = 27.8 % 12.51 g Mg3N2

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