Chapter 3 Scientific measurement 1 Types of measurement Quantitative- (quantity) use numbers to describe Qualitative- (quality) use description without numbers 4 meters Quantitative extra large Qualitative Hot Qualitative 100ºC Quantitative 2 Which do you Think Scientists would prefer Quantitative- easy check Easy to agree upon, no personal bias The measuring instrument limits how good the measurement is 3 How good are the measurements? Scientists use two word to describe how good the measurements are Accuracy- how close the measurement is to the actual value Precision- how well can the measurement be repeated 4 Differences Accuracy can be true of an individual measurement or the average of several Precision requires several measurements before anything can be said about it examples 5 Let’s use a golf anaolgy 6 Accurate? No Precise? Yes 7 Accurate? Yes Precise? Yes 8 Precise? No Accurate? NO 9 Accurate? Yes Precise? We cant say! 10 Reporting Error in Experiment Error • A measurement of how accurate an experimental value is • (Equation) Experimental Value – Accepted Value • Experimental Value is what you get in the lab • accepted value is the true or “real” value • Answer may be positive or negative 11 Reporting Error in Experiment • % Error = • | experimental – accepted value | x 100 accepted value OR | error| accepted value • Answer is always positive 12 x 100 Example: A student performs an experiment and recovers 10.50g of NaCl product. The amount they should of collected was 12.22g on NaCl. 1. Calculate Error Error = 10.50 g - 12.22 g = - 1.72 g 2. Calculate % Error 13 % Error = | -1.72g | x 100 12.22g = 14.08% error Scientific Notation 2.5 is the coefficient Example: 2.5x10-4 (___) -4 and ( ___) is the power of ten Convert to Scientific Notation And Vise Versa 5.5 x 106 5500000 = ____________ 0.0344 3.44 x 10-2 = ____________ 2.16 x 103 = ____________ 2160 1.75 x 10-3 0.00175 = ____________ 14 Multiplying and Dividing Exponents using a calculator 9.00 x 102 (3.0 x 105) x (3.0 x 10-3) = _________________ 2.475 x 1017 (2.75 x 108) x (9.0 x 108) = ________________ (5.50 x (8.0 x 15 10-2) 108) x (1.89 x / (4.0 x 10-23) 10-2) -24 1.04 x 10 = ____________ 10 2.0 x 10 = ________________ Adding and Subtracting Exponents using a calculator 7.5 x 107 + 2.5 x 109 9 2.575 x 10 = __________________ 5.498 x 10-2 5.5 x 10-2 - 2.5 x 10-5 = _________________ 16 Significant figures (sig figs) How many numbers mean anything When we measure something, we can (and do) always estimate between the smallest marks. 4.5 inches 1 17 2 3 4 5 Significant figures (sig figs) Scientist always understand that the last number measured is actually an estimate 4.56 inches 1 18 2 3 4 5 Sig Figs What is the smallest mark on the ruler that measures 142.15 cm? Tenths place 142 cm? Ones place 140 cm? Yikes! Here there’s a problem does the zero count or not? They needed a set of rules to decide which zeroes count. All other numbers do count 19 Which zeros count? Those at the end of a number before the decimal point don’t count 12400 = 3 sig figs If the number is smaller than one, zeroes before the first number don’t count 0.045 = 2 sig figs 20 Which zeros count? Zeros between other sig figs do. 1002 = 4 sig figs zeroes at the end of a number after the decimal point do count 45.8300 = 6 sig figs If they are holding places, they don’t. If they are measured (or estimated) they do 21 Sig Figs Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12 A a piece of paper is measured 11 inches tall. Being able to locate, and count significant figures is an important skill. 22 Sig figs. How many sig figs in the following measurements? 458 g = 3 sig figs 4085 g = 4 sig figs 4850 g = 3 sig figs 0.0485 g = 3 sig figs 0.004085 g = 4 sig figs 40.004085 g = 8 sig figs 23 Sig Figs. 405.0 g = 4 sig figs 4050 g = 3 sig figs 0.450 g = 3 sig figs 4050.05 g = 6 sig figs 0.0500060 g = 6 sig figs 24 Question 50 is only 1 significant figure if it really has two, how can I write it? A zero at the end only counts after the decimal place. 50.0 = 3 sig figs Scientific notation 5.0 x 101 now the zero counts. 25 Adding and subtracting with sig figs The last sig fig in a measurement is an estimate. Your answer when you add or subtract can not be better than your worst estimate. have to round it to the least place of the measurement in the problem 26 For example 27.93 + 6.4 First line up the decimal places 27.93 + 6.4 34.33 27 Find the estimated numbers in the problem Then do the adding This answer must be rounded to the tenths place Rounding rules look at the number behind the one you’re rounding. If it is 0 to 4 don’t change it If it is 5 to 9 make it one bigger round 45.462 to four sig figs = 45.46 to three sig figs = 45.5 to two sig figs = 45 to one sig fig = 50 28 Practice 4.8 + 6.8765 = 11.6756 = 11.7 520 + 94.98 = 614.98 = 615 0.0045 + 2.113 = 2.1175 = 2.118 6.0 x 102 - 3.8 x 103 = 3198 = 3.2 x 103 5.4 - 3.28 = 2.12 = 2.1 6.7 - .542 = 6.158 = 6.2 500 -126 = 374 6.0 x 10-2 - 3.8 x 10-3= 0.0562 = 5.6 x 10-2 29 Multiplication and Division Rule is simpler Same number of sig figs in the answer as the least in the question 3.6 x 653 2350.8 3.6 has 2 s.f. 653 has 3 s.f. answer can only have 2 s.f. 2400 30 Multiplication and Division practice 4.5 / 6.245 = 0.720576 = 0.72 4.5 x 6.245 = 28.1025 = 28 9.8764 x .043 = 0.4246852 = 0.42 3.876 / 1983 = 0.001954614 = 0.001955 16547 / 714 = 23.17507 = 23.2 31 The Metric System Easier to use because it is …… a decimal system Every conversion is by some power of …. 10. A metric unit has two parts A prefix and a base unit. prefix tells you how many times to divide or multiply by 10. 32 Base Units Length - meter more than a yard - m Mass - grams - a bout a raisin - g Time - second - s Temperature - Kelvin or ºCelsius K or C Energy - Joules- J Volume - Liter - half f a two liter bottle- L Amount of substance - mole - mol 33 Prefixes Kilo K 1000 times Hecto H 100 times Deka D 10 times deci d 1/10 centi c 1/100 milli m 1/1000 kilometer - about 0.6 miles centimeter - less than half an inch millimeter - the width of a paper clip wire 34 Converting K H D d c m King Henry Drinks (basically) delicious chocolate milk how far you have to move on this chart, tells you how far, and which direction to move the decimal place. The box is the base unit, meters, Liters, grams, etc. 35 Conversions k h D d c m Change 5.6 m to millimeters starts at the base unit and move three to the right. move the decimal point three to the right 56 00 36 Conversions k h D d c m convert 25 mg to grams = 0.025 g convert 0.45 km to mm = 450,000 mm convert 35 mL to liters = 0.035 L It works because the math works, we are dividing or multiplying by 10 the correct number of times (homework) 37 Volume calculated by multiplying L x W x H Liter the volume of a cube 1 dm (10 cm) on a side so 1 L = 10 cm x 10 cm x 10 cm or 1 L = 1000 cm3 1/1000 L = 3 1 cm Which means 1 mL = 1 cm3 38 Volume 39 1 L about 1/4 of a gallon - a quart 1 mL is about 20 drops of water or 1 sugar cube weight is a force, Mass is the amount of matter. 1gram is defined as the mass of 1 cm3 of water at 4 ºC. 1 ml of water = 1 g 1000 g = 1000 cm3 of water 1 kg = 1 L of water 40 Mass Mass 1 kg = 2.5 lbs 1 g = 1 paper clip 1 mg = 10 grains of salt or 2 drops of water. 41 Density how heavy something is for its size the ratio of mass to volume for a substance M D=M/V D 42 V Density is a Physical Property The density of an object remains constant at constant temperature _________ _______ ________ Therefore it is possible to identify an unknown by figuring out its density. 43 Story & Demo (king and his gold crown) What would happen to density if temperature decreased? As temperature decreases molecules slow _____ down ______ And come closer together therefore making decrease volume _________ STAYS ____ THE _______ SAME The mass ______ INCREASE Therefore the density would _______ WATER, because it expands. Exception _____________________ Therefore Density decreases ICE FLOATS 44 Units for Density 45 1. Regularly shaped object in which a g/cm3 ruler is used. ______ 2. liquid, granular or powdered solid in g/ml which a graduated cylinder is used ______ 3. irregularly shaped object in which the water displacement method must be used _____ g/ml Sample Problem: What is the density of a sample of Copper with a mass of 50.25g and a volume of 6.95cm3? D = M/V D = 50.25g / 6.95 cm3 = 7.2302 = 7.23 cm3 46 Sample Problem 2. A piece of wood has a density of 0.93 g/ml and a volume of 2.4 ml What is its mass? M D V M=DxV M = 0.93 g/ml x 2.4 ml = 2.232 = 2.2 g 47 Problem Solving or Dimensional Analysis 48 Identify the unknown What is the problem asking for List what is given and the equalities needed to solve the problem. Ex. 1 dozen = 12 Plan a solution Equations and steps to solve (conversion factors) Do the calculations Check your work: Estimate; is the answer reasonable UNITS All measurements need a NUMBER & A UNIT!! Dimensional Analysis dimensions to help analyze Use the units (__________) solve the problem. (______) Conversion Factors: Ratios of equal measurements. Numerator measurement = Denominator measurement Using conversion factors does not change the value of the measurement 12 in (_________) equality Examples; 1 ft = _____ 1 ft__ 12 in 49 or 12 in 1 ft (_____________ Conversion __________) factors What you are being asked to solve for in the problem will determine which conversion factors need to be used. 50 Common Equalities and their conversion factors: 16 1 lb = _____oz 5280 1 mi = ______ft 1 yr = ______days 365 24 1 day = ____hrs 60 1 hr = ____min 60 1 min = ____sec Sample Problems using Conversion Factors: How many inches are in 12 miles? Equalities: 1 mi = 5280 ft 1 ft = 12 in 12miles X 5280 ft X 12 in = 760,320 inches 1 ft 1 mi 51 sig figs = 760,000 inches 2. How many seconds old is a 17 year old? Equalities: 1 yr = 365 days; 1 day = 24 hrs; 1 hr = 60 min; 1 min = 60 sec 17 yrs X 365 day X 24 hrs X 60 min X 60 sec 1 yr 1 day 1 hr 1 min = 536,112,000 sec Sig figs = 540,000,000 sec 52 3. How many cups of water are in 5.2 lbs of water? Equalities: 1 lb = 16 oz; 8 oz = 1 cup 83.2 cup 16 oz 1 cup 5.2 lbs X X = 8 1 lb 8 oz 53 = 10.4 cups Sig figs = 1.0 x 101 cups 3. If the density of Mercury (Hg) at 20°C is 13.6 g/ml. What is it’s density in mg/L? Equalities: 1 g = 1000 mg; 1 L = 1000 ml 13.6 g X 1000 mg X 1000 ml = 1 ml 1g 1L 13,600,000 mg/L 13.6 x 107 mg/L 54