Measurements and Calculations. Chapter 2

Transcription

1 Measurements and Calculations Chapter 2

2 Qualitative Observations: General types of observations. Easy to determine. Not necessarily precise. I have many fingers, the speed limit is fast, class is long, acceleration due to gravity is large. It is hot. It is blue. It is magnetic. There was a precipitate.

3 Quantitive Observation: involving the measurement of quantity or amount. I have 10 fingers, the speed limit is 55 miles per hour, class is 1 hour long, acceleration due to gravity is 9.8 m/s 2, it is 85 O F. These are all numbers, and usually with units to give them physical significance.

4 Qualitative red far from the earth microscopic burns quickly hot Quantitative 700 nm wavelength 300 million light years smaller than 1 nm burns at 1 cm candle/min 350 degrees C

5 Scientific Approach: Developing a Model Observations : Use the senses to obtain information. Qualitative: descriptive noise Quantitative: numerical 30 mph

6 Hypothesis: Testable statement. Revised if not supported Experiment: Procedure to test hypothesis; measures one variable at a time. by experiment.

7 Model (Theory): Explanation of how phenomena occur and how data or events are related. Revised if not supported by experiment. Further Experiment: Tests predictions based on model.

8 Chemists must make careful observations and calculations to work through the prior sequence.

9 The Tools Of Chemistry.

10 Rounding.64 Rounds down to.6 4 or less rounds down.

11 .66 Rounds up to.7 6 or more rounds up.

12 .65 Rounds down to.6 Even number followed by a 5 keep it even.

13 .55 Rounds up to.6 Odd number followed by a 5 round up to even.

14 Why this rounding method? Half the time the number in front of the 5 will be even and rounded down. Half the time the number following the 5 will be odd and rounded up. The error caused by rounding should be balanced out.

15 Scientific Notation Used for very large and very small numbers. M x 10 n where 1 M < 10 and n = any integer n indicates how many spots to move the decimal point and which direction.

16 +n indicates that the originalnumber is greater than one. -n indicates that the originalnumber is less than one.

17 Scientific Notation Examples: x x 10 3 Original number > 1 Positive exponent Original number < 1 Negative exponent

18 6.02 x exponent Original number is > 1 Therefore: 602

19 6.02 x exponent Original number is < 1 Therefore: Zeros can be.0602 added to fill decimal spots.

20 Scientific Notation on the Calculator Discuss the scientific notation options on personal calculators and do sample calculator problems.

21 Scientific Notation Key Access

22 Scientific Notation Key Access

23 Scientific Notation Key Access

24 Scientific Notation Key Access

25 Much scientific knowledge comes from careful measurements. All measurements are comparisons to a standard.

26 BASE UNIT - meter (m) - LENGTH. Up until 1983 the meter was defined as 1,650, wavelengths in a vacuum of the orange-red line of the spectrum of krypton-86. And since then it is determined to be the distance traveled by light in a vacuum in 1/299,792,450 of a second. BASE UNIT - second (s) - TIME The second is defined as the duration of 9,192,631,770 cycles of the radiation associated with a specified transition of the cesium-133 atom.

27 Science is different than much math in that science uses quantities while math uses numbers.

28 Quantity: number and a standard unit. Math: 2+2 = 4 Science: 2 yds + 2 ft 4 of anything. Only like quantities can be added or subtracted or compared.

29 Common Every Day Units Gallons liters milligrams Calories Pounds miles/hour psi seconds - minutes - hours

30 An international comparison rather than a case of downsizing. The Pepsi can to the left is a standard American size containing 12 US fl oz or 355ml and sold in the USA, Canada and SE Asia. The Pepsi can to the right is a metric size and contains 330ml, the equivalent of 11.2 US fl oz.

31 Metric ( SI) Base Units Quantity Name Symbol Length Meter m Mass Time Kilogram kg Seconds s Amount Mole mole Temperature Kelvin K

32 The F. P. And B.P. of Water B.P. = 100 O C A F.P. = 0 O C A O C K O F

33 a

34 Metric Prefixes Prefix Symbol Meaning Kilo K 1000 Deci d tenth Centi c hundreth Milli m thousandth

35 Prefixes Used with SI Units Prefix Prefix Symbol Number Word Exponential Notation tera T 1,000,000,000,000 trillion giga G 1,000,000,000 billion 10 9 mega M 1,000,000 million 10 6 kilo k 1,000 thousand 10 3 hecto h 100 hundred 10 2 deka da 10 ten one 10 0 deci d 0.1 tenth 10-1 centi c 0.01 hundredth 10-2 milli m thousandth 10-3 micro µ millionth 10-6 nano n billionth 10-9 pico p trillionth femto f quadrillionth 10-15

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37 Factor Label Method of Conversions Utilizes comparisons of units to solve a problem.

38 Simple Examples of Factor Label 10 students attend a concert and pay $5 for a ticket. What is the total cost? 10 students x 10 tickets x student $ 5.00 ticket = $50.00

39 If you baby sit for 3 hours and earn $4 per hour, how much do you earn? 3 hours x $ 4.00 = $12.00 hour

40 If you baby sit for 225 minutes and earn $4 per hour, how much do you earn? 225 min X1 hour x 60 min $ 4.00 hour = $15.00

41 More Factor Label Convert 175 inches to feet. 175 in x 1 foot = 14.6 feet 12 in

42 Convert 25.0 cm to feet. Cm ---> inches ---> feet 25.0 cm x 1 inch x 2.54 cm 1 foot = 12 inches 0.82 feet

43 Convert 25.0 gal to milliliters. Gallons ---> liters ---> ml 25.0 gal x 3.8 liters x 1000 ml = 1 gal 1 liter ml

44 Convert 48 oz to kilograms. oz ---> lbs ---> grams ---> kg 48.0 oz x 1 lb x 16 oz 454 g x 1lb 1 kg = 1.36 kg 1000 g

45 How many seconds have you been alive? years ---> days ---> hours ---> sec 17 yrs x 365 days x 1 yr 24 hrs x 1 day 3600 sec = 5.36 x 10 8 sec 1 hr

46 Double Decker Factor Label Light travels 3 x 10 8 meters per second. How many miles does light travel in (per) one year?

47 Area and Volume Factor Label Area conversions: How many cans of paint for a room? How much fabric? How many gallons of driveway sealer? Volume Conversion: How much dirt, gravel, mulch

48 Convert 125 ft 2 to in ft x ( 12 in ) 2 = ( ) in 2 1 ft The squares goes with the number and the unit.

49 Convert 1250 cm 3 to ft cm x ( 1 in ) 3 x( 1 ft ) 3 = ( 2.54 cm) 3 ( 12 in) ft 3 The cubes goes with the number and the unit.

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51 Density Density is a measure of mass per unit volume. Property of matter. Identify unknowns. Density Weight (Heavy). Size is not a factor. Large - low density - Boat

52 Small - high density - Penny Density = Mass Volume Units for Density: grams cm 3 Solids Or Liquids or gases grams ml

53 Mass: Lab Balance - Units - Grams Volume: Shape Formulas - Cube - L x W x H Units: cm 3

54 Odd Shaped Objects - Water Displacement Units: ml Density of 1 kg of lead is ( > = < ) Density of 1 kg of feathers. Density of 1 kg of lead is ( > = < ) Density of 1 gram of lead.

55 Density of Water Water (H 2 O) has a density of 1.0 gram/ml. Object Density > DensityH 2 O -the object sinks.

56 Object Density < DensityH 2 O -the object floats.

57 How Things Stack Up

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61 D = M V Cover what you re solving for to get the equation.

62 Density Problems Calcium has a density of 1.54 g/cm 3. What is the mass of 6.0 cm 3 of calcium? M = D x V 1.54 grams X 6.0 cm 3 = 9.24 cm 3 grams

63 Cobalt has a density of 8.9 g/ml. What volume would a 10.0 gram sample occupy? V = M / D 10.0 g = 1.1 ml 8.9 g ml

64 A cubical object has a mass of 100 grams. It measures 10.0 cm by 5.0 cm by 0.20 m. What is the density of the object?

65 Density =? M = 100 g D = M V V =??? V = 10 cm X 5 cm X 20 cm = 0.20 m x 100 cm 1 m 1000 cm 3

66 D = M V D = 100 gram = 1000 cm g/cm 3

67 An odd shaped object has a mass of 10.0 grams. When placed in a graduated cylinder, the volume changes from 25.8 ml to 30.8 ml. What is the density of this object?

68 Density =? M = 10.0 g D = M V V =??? V = 30.8 ml 25.8 ml = 5.0 ml

69 D = M V D = 10.0 gram = 5.0 ml 2.0 g/ml

70 What is the mass of 75.0 ml of a 3% hydrogen peroxide solution that has a density of 1.1 g/ml? M = D x V 1.1 grams X ml 75.0 ml = 82.5 grams

71 Significant Digits These are a PAIN!!! The greater the number of significant digits in a measurement, the greater the certainty.

72 Q Q Q Q Q Q Q Q Q Q Q Q

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75 1 cm 2 cm 1.6 cm Certain Uncertain

76 1.35 cm 1 cm 2 cm Certain Uncertain

77 1.72 cm 1 cm 2 cm Certain Uncertain

78 1.60 cm 1 cm 2 cm Certain Uncertain

79 1 cm 2 cm 2.00 cm Certain Uncertain Measurements ALWAYS contains one uncertain digit.

80 Area = L X W 12 X 21 2 Uncertain Digits x 10 2

81 Rules For Significant Digits

82 1. All nonzero digits are significant. 2. For numbers larger than 1 (one) that contain zeros. A. Zeros to the left of an UNDERSTOOD decimal point are NOT significant contains 2 sig. figs.

83 B. Zeros to the left of an EXPRESSED decimal point ARE significant Contains 4 sig. figs. Exactness Zeros 3. Zeros between nonzero digits are significant all have four sig.figs.

84 4. For numbers smaller than 1 (one) that contain zeros: A. Zeros to the right of a decimal but to the left of a nonzero digit are NOT significant has two sig. figs.

85 B. Zeros to the right of a decimal and to the right of a nonzero digit ARE significant has four significant digits. Exactness Zeros

86 5. Coefficients in Scientific Notation are significant. 4.5 x 10 23

87 6. Exact numbers or definitions- numbers with no uncertainty. These have as many significant digits as the calculation requires. 60 min = 1 hr 1000 mg = 1 g Typically factor label conversions.

88 Math Operations and Sig. Figs. 1. Multiplication and Division The number with the least certainty limits the certainty of the result.

89 The answer can only have as many sig. figs as contained in the number with the least number of sig. figs. EX: X 1267 = 29,141,000 = 29,000,000

90 9.2 cm x 6.8 cm x cm = cm 3 or 23 cm 3

91 2. Addition and Subtraction The answer should be as accurate as the number with the lesser accuracy.

92 Adding two numbers: (+/- 100) (+/- 10) = /- 100 Subtracting two volumes: ml ml ml = ml

93 Measurements and Uncertainty It is not possible to know the exact measurement of anything. There is always going to be some guess work involved when measuring.

94 When Measuring Anything: Determine what the markings on the equipment mean. These are the certain digits.

95 Doubtful Digits in Measurements With any analog scientific tool the measurement can only be estimated to one spot past the certain digit. This estimated digit is also called the doubtful digit and is significant!!!

96 . T E N S U N I T S T E N T H S H U N D R E T H S T H O U S A N D T H S

97 Graduated Cylinders Meniscus: Dip in a liquid caused by attractions between the liquid and the cylinder.

98 Reading Graduated Cylinders Always read the bottom of the meniscus.

99 Determine the following volumes. 24mL Doubtful Digit

100 23.3 ml Doubtful Digit

101 52.8 ml

102 5.90 ml

103 36.5 ml

104 Buret

105 20.38 ml Uncertain Digit

106 0.60 ml

107 25.05 ml

108 Beaker 47 ml Uncertain Digit Beakers are not good for measuring when a specific amount of liquid is needed.

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110 Balance grams

111 62.40 grams

112 grams

113 25.38 grams

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115 a O C 32.3 O C A a

116 Ruler 4⅛ inches

117 Percent Error Theoretical Value Experimental Value x 100 Theoretical Value Theoretical Value = Actual Value

118 During an experiment, you collect 15.5 grams of NaCl. Upon reviewing the chemical reaction, you calculate that the reaction could have produced 18.5 grams NaCl. What was the percentage error that you experienced during the completion of your lab? Theoretical Experimental 18.5 grams 15.5 grams X 100 = 18.5 grams 16.2 %

119 Precision and Accuracy When making measurements in the laboratory you need to know how good is the measurement. Precision indicates degree of reproducibility of a measured number.

120 Accuracy indicates how close your measurements are to the true value.

121 Precision and Accuracy in the Lab Precise and Accurate Precise but not Accurate

122 Not accurate but precise Accurate but low precision

123 XXX XXX XXX XXX XXX XXX

124 XXX XXX XXX XXX XXX XXX XXX XXX

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126 When you make measurements in science you want them to be both precise and accurate. When we measure quantities in science, particularly for the very first time, it is always difficult to know if the measurement is accurate.

127 A

128 D

129 B

130 D

131 B

132 Precision and Accuracy in the Lab Random Error Systematic Error

133 Systematic Error: Error that is either all higher or all lower than the actual value. Error that is part of the experimental system faulty measuring device or a consistent mistake in taking the reading.

134 Systematic error can be avoided or taken into account through calibration of the measuring device. Compare to a known standard.

135 X X X X X X X X X X X x

136 Random Error: Error that is both higher and lower than the actual value. Always occurs but its magnitude depends on the reading skills of the experimenter and the precision of the equipment.

137 X X X X X X X X X X X x

138 Precise measurements have low random error. Accurate measurements have low systematic error and low random error.

139 The End