2 Measurement Quantitative Observation Comparison Based on an Accepted Scalee.g. Meter StickHas 2 Parts – the Number and the UnitNumber Tells ComparisonUnit Tells Scale2
3 Scientific NotationTechnique Used to Express Very Large or Very Small NumbersBased on Powers of 103
4 Writing Numbers in Scientific Notation 1. Move the decimal point so there is only one non-zero number to the left of it. The new number is now between 1 and 92. Multiply the new number by 10nwhere n is the number of places you moved the decimal point3. Determine the sign on the exponent nIf the decimal point was moved left, n is +If the decimal point was moved right, n is –If the decimal point was not moved, n is 04
5 Writing Numbers in Standard Form Determine the sign of n of 10nIf n is + the decimal point will move to the rightIf n is – the decimal point will move to the leftDetermine the value of the exponent of 10Tells the number of places to move the decimal pointMove the decimal point and rewrite the number5
6 Standard to Scientific Notation 75,000,0008,031,000,000
7 Scientific to Standard Notation 2.75 x 10-75.22 x 1047.10 x 10-59.38 x 1012
8 More practice Change to scientific notation 41080.642 1.8732 Change to standard notationx 106391 x 10-2
10 Related Units in the Metric System All units in the metric system are related to the fundamental unit by a power of 10The power of 10 is indicated by a prefixThe prefixes are always the same, regardless of the fundamental or basic unit6
13 Length SI unit = meter (m) About 3½ inches longer than a yard 1 meter = one ten-millionth the distance from the North Pole to the Equator = distance between marks on standard metal rod in a Paris vault = distance covered by a certain number of wavelengths of a special color of lightCommonly use centimeters (cm)1 m = 100 cm1 cm = 0.01 m = 10 mm1 inch = 2.54 cm (exactly)7
14 Figure 2.1: Comparison of English and metric units for length on a ruler.
15 VolumeMeasure of the amount of three-dimensional space occupied by a substanceSI unit = cubic meter (m3)Commonly measure solid volume in cubic centimeters (cm3 (cm x cm x cm))1 m3 = 106 cm31 cm3 = 10-6 m3 = m3Commonly measure liquid or gas volume in milliliters (mL)1 L is slightly larger than 1 quart1 L = 1 dL3 = 1000 mL = 103 mL1 mL = L = 10-3 L1 mL = 1 cm38
17 Mass Measure of the amount of matter present in an object SI unit = kilogram (kg)Commonly measure mass in grams (g) or milligrams (mg)1 kg = pounds, 1 lbs.. = g1 kg = 1000 g = 103 g, 1 g = 1000 mg = 103 mg1 g = kg = 10-3 kg, 1 mg = g = g9
18 Figure 2.4: An electronic analytical balance used in chemistry labs.
19 Metric conversions250 mL to Liters1.75 kg to grams88 daL to mL
20 Metric conversions475 cg to mg328 hm to MmnL to cL
21 Uncertainty in Measured Numbers A measurement always has some amount of uncertaintyUncertainty comes from limitations of the techniques used for comparisonTo understand how reliable a measurement is, we need to understand the limitations of the measurement10
22 Reporting Measurements To indicate the uncertainty of a single measurement scientists use a system called significant figuresThe last digit written in a measurement is the number that is considered to be uncertainUnless stated otherwise, the uncertainty in the last digit is ±111
23 Rules for Counting Significant Figures Nonzero integers are always significantHow many significant figures are in the following examples:275389.6590.28112
24 Significant Figures Zeros Captive zeros are always significantHow many significant figures are in the following examples:1001.4
25 Significant Figures Zeros Leading zeros never count as significant figuresHow many significant figures are in the following examples:
26 Significant Figures Zeros Trailing zeros are significant if the number has a decimal pointHow many significant figures are in the following examples:22,00063,850.100,000
27 Significant Figures Scientific Notation All numbers before the “x” are significant. Don’t worry about any other rules.7.0 x 10-4 g has 2 significant figures2.010 x 108 m has 4 significant figures
28 Rules for Rounding Off Round 87.482 to 4 sig figs. If the digit to be removedis less than 5, the preceding digit stays the sameRound to 4 sig figs.is equal to or greater than 5, the preceding digit is increased by 1Round to 3 sig figs.13
29 Rules for Rounding OffIn a series of calculations, carry the extra digits to the final result and then round offEx: Convert 80,150,000 seconds to yearsDon’t forget to add place-holding zeros if necessary to keep value the same!!Round 80,150,000 to 3 sig figs.
30 Multiplication/Division with Significant Figures Count the number of significant figures in each measurementRound the result so it has the same number of significant figures as the measurement with the smallest number of significant figurescm x cm =3.7 x 103 x =16
31 Calculations with Significant Figures Calculators/computers do not know about significant figures!!!Exact numbers do not affect the number of significant figures in an answerAnswers to calculations must be rounded to the proper number of significant figuresround at the end of the calculation15
32 Exact Numbers Exact Numbers are numbers known with certainty Unlimited number of significant figuresThey are eithercounting numbersnumber of sides on a squareor defined100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm1 kg = 1000 g, 1 LB = 16 oz1000 mL = 1 L; 1 gal = 4 qts.1 minute = 60 seconds14
33 Problem Solving and Dimensional Analysis Many problems in chemistry involve using equivalence statements to convert one unit of measurement to anotherConversion factors are relationships between two unitsConversion factors generated from equivalence statementse.g. 1 inch = 2.54 cm can give or18
34 Problem Solving and Dimensional Analysis Arrange conversion factor so starting unit is on the bottom of the conversion factorYou may string conversion factors together for problems that involve more than one conversion factor.19
35 Converting One Unit to Another Find the relationship(s) between the starting and final units.Write an equivalence statement and a conversion factor for each relationship.Arrange the conversion factor(s) to cancel starting unit and result in goal unit.20
36 Converting One Unit to Another Check that the units cancel properlyMultiply all the numbers across the top and divide by each number on the bottom to give the answer with the proper unit.Round your answer to the correct number of significant figures.Check that your answer makes sense!21
37 English Units Conversions 28.5 inches to feet4.0 gallons to quarts48.39 minutes to hours155.0 pounds to grams2.00 x 108 seconds to hours
38 More Difficult Conversions 682 mg to pounds3.5 x 10-4 L to cm30.091 ft2 to inches247.1 mm3 to kL
39 Complex Conversion Problems 25 miles per hour to feet per second4.70 gallons per minute to mL per year5.6 x 10-6 centiliters per square meter (cL/m2) to cubic meters per square foot (m3/ft2)
40 Temperature Scales Fahrenheit Scale, °F Celsius Scale, °C Water’s freezing point = 32°F, boiling point = 212°FCelsius Scale, °CTemperature unit larger than the FahrenheitWater’s freezing point = 0°C, boiling point = 100°CKelvin Scale, KTemperature unit same size as CelsiusWater’s freezing point = 273 K, boiling point = 373 K22
41 Temperature Conversions Fahrenheit to Celsius oC = 5/9(oF -32)Celsius to Fahrenheit oF = 1.8(oC) +32Celsius to Kelvin K = oC + 273Kelvin to Celsius oC = K – 273
42 Figure 2.6: Thermometers based on the three temperature scales in (a) ice water and (b) boiling water.
43 Figure 2.7: The three major temperature scales.
44 Figure 2.8: Converting 70. 8C to units measured on the Kelvin scale.
45 Figure 2.9: Comparison of the Celsius and Fahrenheit scales.
46 Temperature Conversion Examples 86oF to oC-5.0oC to oF352 K to oC12oC to K248 K to oF98.6oF to K
47 DensityDensity is a property of matter representing the mass per unit volumeFor equal volumes, denser object has larger massFor equal masses, denser object has small volumeSolids = g/cm31 cm3 = 1 mLLiquids = g/mLGases = g/LVolume of a solid can be determined by water displacementDensity : solids > liquids >>> gasesIn a heterogeneous mixture, denser object sinks23
50 Spherical droplets of mercury, a very dense liquid.
51 Density Example Problems What is the density of a metal with a mass of g whose volume occupies cm3?What volume, in mL, of ethanol (density = g/mL) has a mass of 2.04 lbs?What is the mass (in mg) of a gas that has a density of g/L in a 500. mL container?
52 Figure 2. 10: (a) Tank of water Figure 2.10: (a) Tank of water. (b) Person submerged in the tank, raising the level of the water.
53 Volume by displacement To determine the volume to insert into the density equation, you must find out the difference between the initial volume and the final volume.A student attempting to find the density of copper records a mass of 75.2 g. When the copper is inserted into a graduated cylinder, the volume of the cylinder increases from mL to 58.5 mL. What is the density of the copper in g/mL?
54 Percent ErrorPercent error – absolute value of the error divided by the accepted value, multiplied by 100%.% error = measured value – accepted value x 100%accepted valueAccepted value – correct value based on reliable sources.Experimental (measured) value – value physically measured in the lab.
55 Percent Error ExampleIn the lab, you determined the density of ethanol to be 1.04 g/mL. The accepted density of ethanol is g/mL. What is the percent error?The accepted value for the density of lead is g/cm3. When you experimentally determined the density of a sample of lead, you found that a 85.2 gram sample of lead displaced 7.35 mL of water. What is the percent error in this experiment?