Scientific measurement Chapter 3 Scientific measurement

Types of measurement Quantitative- (quantity) use numbers to describe Qualitative- (quality) use description without numbers 4 meters extra large Hot 100ºC Quantitative Qualitative Qualitative Quantitative

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

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

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

Let’s use a golf anaolgy

Accurate? No Precise? Yes

Accurate? Yes Precise? Yes

Precise? No Accurate? NO

Accurate? Yes Precise? We cant say!

Reporting Error in Experiment 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

| experimental – accepted value | x 100 Reporting Error in Experiment % Error = | experimental – accepted value | x 100 accepted value OR | error| x 100 Answer is always positive

Example: A student performs an experiment and recovers 10.50g of NaCl product. The amount they should of collected was 12.22g on NaCl. Calculate Error Error = 10.50 g - 12.22 g = - 1.72 g Calculate % Error % Error = | -1.72g | x 100 12.22g = 14.08% error

Convert to Scientific Notation And Vise Versa Example: 2.5x10-4 (___) is the coefficient and ( ___) is the power of ten 2.5 -4 Convert to Scientific Notation And Vise Versa 5500000 = ____________ 3.44 x 10-2 = ____________ 2.16 x 103 = ____________ 0.00175 = ____________ 5.5 x 106 0.0344 2160 1.75 x 10-3

Multiplying and Dividing Exponents using a calculator (3.0 x 105) x (3.0 x 10-3) = _________________ (2.75 x 108) x (9.0 x 108) = ________________ (5.50 x 10-2) x (1.89 x 10-23) = ____________ (8.0 x 108) / (4.0 x 10-2) = ________________ 9.00 x 102 2.475 x 1017 1.04 x 10-24 2.0 x 1010

Adding and Subtracting Exponents using a calculator 7.5 x 107 + 2.5 x 109 = __________________ 5.5 x 10-2 - 2.5 x 10-5 = _________________ 5.498 x 10-2

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 2 1 3 4 5

Significant figures (sig figs) Scientist always understand that the last number measured is actually an estimate 4.56 inches 1 2 3 4 5

Sig Figs What is the smallest mark on the ruler that measures 142.15 cm? 142 cm? 140 cm? 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 Tenths place Ones place Yikes!

Which zeros count? Those at the end of a number before the decimal point don’t count 12400 If the number is smaller than one, zeroes before the first number don’t count 0.045 = 3 sig figs = 2 sig figs

Which zeros count? Zeros between other sig figs do. 1002 zeroes at the end of a number after the decimal point do count 45.8300 If they are holding places, they don’t. If they are measured (or estimated) they do = 4 sig figs = 6 sig figs

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.

Sig figs. How many sig figs in the following measurements? 458 g

Sig Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g = 4 sig figs

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. Scientific notation 5.0 x 101 now the zero counts. 50.0 = 3 sig figs

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

For example 27.93 6.4 + First line up the decimal places 27.93 6.4 + 27.93 6.4 Find the estimated numbers in the problem Then do the adding 34.33 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 to three sig figs to two sig figs to one sig fig = 45.46 = 45.5 = 45 = 50

Practice = 11.6756 = 11.7 4.8 + 6.8765 520 + 94.98 0.0045 + 2.113 6.0 x 102 - 3.8 x 103 5.4 - 3.28 6.7 - .542 500 -126 6.0 x 10-2 - 3.8 x 10-3 = 614.98 = 615 = 2.1175 = 2.118 = 3198 = 3.2 x 103 = 2.12 = 2.1 = 6.158 = 6.2 = 374 = 0.0562 = 5.6 x 10-2

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

Multiplication and Division practice 4.5 / 6.245 4.5 x 6.245 9.8764 x .043 3.876 / 1983 16547 / 714 = 0.720576 = 0.72 = 28.1025 = 28 = 0.4246852 = 0.42 = 0.001954614 = 0.001955 = 23.17507 = 23.2

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.

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

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

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.

k h D d c m Conversions 5 6 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 5 6

k h D d c m Conversions convert 25 mg to grams convert 0.45 km to mm convert 35 mL to liters It works because the math works, we are dividing or multiplying by 10 the correct number of times (homework) = 0.025 g = 450,000 mm = 0.035 L

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 = 1 cm3 Which means 1 mL = 1 cm3

Volume 1 L about 1/4 of a gallon - a quart 1 mL is about 20 drops of water or 1 sugar cube

Mass 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

Mass 1 kg = 2.5 lbs 1 g = 1 paper clip 1 mg = 10 grains of salt or 2 drops of water.

Density how heavy something is for its size the ratio of mass to volume for a substance D = M / V M D V

Density is a Physical Property The density of an object remains _________ at _______ ________ Therefore it is possible to identify an unknown by figuring out its density. Story & Demo (king and his gold crown) constant constant temperature

What would happen to density if temperature decreased? As temperature decreases molecules ______ _____ And come closer together therefore making volume _________ The mass ______ ____ _______ Therefore the density would _______ Exception _____________________ Therefore Density decreases ICE FLOATS slow down decrease STAYS THE SAME INCREASE WATER, because it expands.

Units for Density 1. Regularly shaped object in which a ruler is used. ______ 2. liquid, granular or powdered solid in which a graduated cylinder is used ______ 3. irregularly shaped object in which the water displacement method must be used _____ g/cm3 g/ml 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

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 M = D x V D V M = 0.93 g/ml x 2.4 ml = 2.232 = 2.2 g

Problem Solving or Dimensional Analysis 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 Use the units (__________) to help analyze (______) the problem. Conversion Factors: Ratios of equal measurements. Numerator measurement = Denominator measurement Using conversion factors does not change the value of the measurement Examples; 1 ft = _____ (_________) 1 ft__ or 12 in (_____________ __________) 12 in 1 ft dimensions solve 12 in equality Conversion factors

What you are being asked to solve for in the problem will determine which conversion factors need to be used. Common Equalities and their conversion factors: 1 lb = _____oz 1 mi = ______ft 1 yr = ______days 1 day = ____hrs 1 hr = ____min 1 min = ____sec 16 5280 365 24 60 60

Sample Problems using Conversion Factors: How many inches are in 12 miles? Equalities: 1 mi = 5280 ft 1 ft = 12 in 12miles X X = sig figs = 760,000 inches 760,320 inches 12 in 1 ft 5280 ft 1 mi

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 X X X = 536,112,000 sec Sig figs = 540,000,000 sec 365 day 1 yr 24 hrs 1 day 60 min 1 hr 60 sec 1 min

3. How many cups of water are in 5.2 lbs of water? Equalities: 1 lb = 16 oz; 8 oz = 1 cup 5.2 lbs X X = = 10.4 cups Sig figs = 1.0 x 101 cups 83.2 cup 8 16 oz 1 lb 1 cup 8 oz

Equalities: 1 g = 1000 mg; 1 L = 1000 ml X X = 13.6 g 1 ml 1000 mg 1 g 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 X X = 13.6 g 1 ml 1000 mg 1 g 1000 ml 1 L 13,600,000 mg/L 13.6 x 107 mg/L