Scientific measurement

Number vs. Quantity UNITS MATTER!! Quantity - number + unit Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

2.1 Types of measurement Quantitative- use numbers to describe Qualitative- use description without numbers 4 feet extra large Hot 100ºF

2.1 Scientists prefer.. Quantitative - easy to check Easy to agree upon, no personal bias The measuring instrument limits how good the measurement is.

2.2 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

Accuracy vs. Precision Systematic errors: reduce accuracy Scientists repeat experiments many times to increase their accuracy. Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy Random errors: reduce precision (instrument) (person)

2.2 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 10

Accurate? Yes Precise? Yes 12

Precise? No Accurate? Maybe? 13

Accurate? Yes Precise? We cant say! 18

REVIEW: Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

2.3 Scientific Notation 65,000 kg  6.5 × 104 kg Converting into Scientific Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig figs. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

2.3 Converting Numbers to Scientific Notation 0 . 0 0 0 0 2 2 0 5 2.205 x 10-5 1 2 3 4 5 In scientific notation, a number is separated into two parts. The first part is a number between 1 and 10. The second part is a power of ten.

Form: (# from 1 to 9.999) x 10exponent 800 = 8 x 10 x 10 = 8 x 102 2531 = 2.531 x 10 x 10 x 10 = 2.531 x 103 0.0014 = 1.4 / 10 / 10 / 10 = 1.4 x 10-3

2.3 Scientific Notation Practice Problems 1. 2,400,000 g 2. 0.00256 kg 3. 7  10-5 km 4. 6.2  104 mm 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Using the Exponent Key on a Calculator

EE or EXP means “times 10 to the…” How to type out 6.02 x 1023: How to type out 6.02 x 1023: 6 EE . 3 2 6 EE . 3 2 Don’t do it like this… WRONG! 6 y x . 3 2 WRONG! …or like this… x 1 6 . 2 EE 3 …or like this: TOO MUCH WORK. y x 3 2 x 1 6 .

Example: 1.2 x 105 2.8 x 1013 = 1 . 2 EE 5 3 8 Type this calculation in like this: 4.2857143 –09 Calculator gives… 4.2857143 E–09 or… This is NOT written… 4.3–9 4.3 x 10–9 But instead is written…

Scientific Notation Type on your calculator: EXP EE EXP EE EXE 5.44 7 Calculating with Scientific Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EE EXP EE ENTER EXE 5.44 7 8.1 ÷ 4 = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

How to Use a Scientific Calculator Divide: (5.44 x 107) / (8.1 x 104) 671.604938 54400000. 5.44 8.1 00 07 00 04 How to enter this on a calculator: . 5.44 7 8.1 4 EE . EE ENTER OR . 5.44 7 8.1 4 EXP . EXP = 671.6049383 rounded to 6.7 x 102 Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52

2.3 How reliable are Measurements? How do you make a measurement? With most measuring devices, you should be able to estimate to one decimal place more than the smallest division on the device. The smallest division is a _____ of a centimeter, so you can guess to the _____________ (or ___ decimal places like 1.24). tenth hundredth 2

Using A Ruler = 1.94 cm = 3.00 cm = 1.5 cm

1 2 3 1 = 5.73 2 = 3.0 3 = .35

2.3 Significant Figures 1.19 cm Indicate precision of a measurement. Recording Sig. Figs. Sig. figs. in a measurement include the known digits plus a final estimated digit 1.19 cm Centimeters 1 2 3 4 5 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

2.3 Measurement – Significant Figures All of the known digits plus the estimated digit are significant – they are not placeholders. When we measured the volume of cylinder 1 on the last slide we got: 5.73 mL known estimated This would mean 3 significant figures.

100 200 300 100 200 300 120 mL 120 mL

Significant Figures 100 200 300 100 200 300 What is the smallest mark on a graduated cylinder that measures 142.15 cm? 242 mL? 240 mL? Here there’s a problem… does the zero count or not?

2.3 Measurement – Significant Figures Significant Figure Rules Every nonzero is significant. 123.2 g 4 sig figs Zeros between nonzero digits are significant. 1004 m 4 sig figs Zeros to left of nonzero are NOT significant. 0.01 g 1 sig fig Zeros to the right of a nonzero number if there is no decimal point are NOT significant 1200 g 2 sig figs

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

Significant Figures Counting Sig Figs REVIEW Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Significant Figures Practice Counting Sig. Figs. Examples 1. 23.50 1. 23.50 4 sig figs 2. 402 2. 402 3 sig figs 3. 5,280 3. 5,280 3 sig figs 4. 0.080 4. 0.080 2 sig figs Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Sig Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g Next we learn the rules for calculations

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

Rounding Practice Round the following to 3 significant figures 55.8954 m 527,254 g 4.998 mL 959,600 m

Scientific Notation Quiz Write in Standard form 1. 6.32 x 105 2. 5.05682 x 103 Write in Scientific Notation 3) 9384000 g 4) 0.00000034623 m Calculate~ Answers need to be in scientific notation! 5. (6.02 X 1023) X (9.54 x 10-13) 6. (5.23 X 10-21) / (1.23 X 1023)

2.5 Significant Figures in Calculations An answer can’t have more significance than the measurements upon which it is based. YOUR ANSWER IS ONLY AS GOOD AS YOUR WORST MEASUREMENT!

Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 3 SF 324 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Multiplication and Division Same rules for division Practice 4.5 / 6.245 4.5 x 6.245 9.8764 x .043 3.876 / 1983 16547 / 714

Significant Figures 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350 g  7.9 mL Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

For example 27.93 6.4 + First line up the decimal places 27.93 6.4 + 27.93 6.4 Then do the adding Find the estimated numbers in the problem 34.33 This answer must be rounded to the tenths place

Significant Figures 2. 18.9 g - 0.84 g 18.06 g Practice Problems 1. (15.30 g) ÷ (6.4 mL) 4 SF 2 SF = 2.390625 g/mL  2.4 g/mL 2 SF 2. 18.9 g - 0.84 g  18.1 g 18.06 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Problems 500 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 102 Now the zero counts.

Practice 1. 4.8 + 6.8765 2. 520 + 94.98 3. 0.0045 + 2.113 4. 6.0 x 102 - 3.8 x 103 5. 5.4 - 3.28 6. 6.7 - .542 7. 500 -126 8. 6.0 x 10-2 - 3.8 x 10-3

Significant Figures Calculating with Sig Figs (con’t) Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

2.5 Significant Figures in Calculations REVIEW Addition Subtraction Round your answer to the same number of decimal places as your least significant number. Think of it as the leftmost uncertainty. 124.0 m + .12 m 420 m 544.12 m 540 m

2.5 Significant Figures in Calculations REVIEW Multiplication and Division Round answer to the same number of significant digits as the measurement with the least number of significant digits. 238.63 m × 12.0 m 5 3 2863.56 m2 2860 m2

2.6 Units of Measurement – Metric 2. Metric – Developed in France in 1790. Simple base units Interchangeable prefixes Decimal (base 10) system

Metric Prefixes Prefix Symbol Meaning kilo- k hecto- h deca- da deci- centi- c milli- m 1 km = 1000 m 1 hm = 100 m 1 dam = 10 m 10 dm = 1 m 100 cm = 1 m 1000 mm = 1 m

2.1 Units of Measurement – SI Base Units Quantity Unit Symbol Length meter m Mass kilogram kg Time second s Temperature kelvin K Amount of Substance mole mol Electrical current ampere A Luminous intensity candela cd

No Cussing! Inch Mile Foot Pint Yard Acre Metric The following 4-Letter words are forbidden here: Inch Mile Foot Pint Yard Acre And we never swear the BIG F (useoC) Please keep it clean and Metric

Metric Conversions kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) 1000 100 10 1/10 1/100 1/1000 To convert from 1 prefix to another, just move the decimal to the left or right that many places!

5000 cg How many centigrams (cg) are in 5dag? 1 2 3 kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) How many centigrams (cg) are in 5dag? Just move the decimal ___ places to the ________! 5 3 right 5000 cg

.012 km 1 2 3 left How many kilometers (km) are in 12 meters m? kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) How many kilometers (km) are in 12 meters m? Just move the decimal ___ places to the ________! 1 2 3 left .012 km

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 1 L = 1000 cm3 1/1000 L = 1 cm3 1 mL = 1 cm3

Measuring Volume: Tank of Water Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 143

Person Submerged in Water Archimedes Principle: water displacement method to find the volume of an irregularly shaped object. The volume the water level increased is equal to the volume of the submerged object. Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 143

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

Density M V D = M M = D x V ass D V M D V = ensity olume

Density of Some Common Substances Substance Density (g / cm3) Air 0.0013* Lithium 0.53 Ice 0.917 Water 1.00 Aluminum 2.70 Iron 7.86 Lead 11.4 Gold 19.3 *at 0oC and 1 atm pressure

Consider Equal Volumes Mass Density = Volume Equal volumes… …but unequal masses The more massive object (the gold cube) has the _________ density. Question: Which weighs more a ton of feathers or a ton of bricks? (They weigh the same) Question: Which occupies a larger volume; a ton of feathers or a ton of bricks? (the feathers will occupy a larger volume) GREATER aluminum gold Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71

Consider Equal Masses Equal masses… …but unequal volumes. The object with the larger volume (aluminum cube) has the smaller density. gold aluminum Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71

Density An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Density A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK: V = M D V = 25 g 0.87 g/mL V = 29 mL Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

2.12 Temperature Heat – type of energy transferred because of a difference in temperature. Can’t be measured directly Temperature – measure of the average kinetic energy of the particles in a sample of matter. Determines the direction of heat transfer

2.12 Temperature What does your body sense? temperature or heat What contains more heat? a glass of boiling water or an iceberg What does your body sense? temperature or heat

2.12 Temperature Scales Celsius (C) – based on water Fahrenheit (F) – zero based on equal mix of snow and ammonium chloride. 32F = freezing point of water 212F = boiling point of water Celsius (C) – based on water 0C = freezing point of water 100C = boiling point of water

2.12 Temperature Scales 0 K = all particle motion stops Kelvin (K) - only temperature scales that is proportional to the speed of the particles. 0 K = all particle motion stops 273 K = freezing point of water 373 K = boiling point of water

2.12 Temperature Conversion T(K) = t(C) + 273 What is 25C (room temp.) in kelvin? T(K) = 25C + 273 = 298 K t(C) = T(K) – 273

Accuracy is very important when making measurements in the lab. In order to evaluate the accuracy of a measurement, you must be able to compare the experimental value to the accepted value. Accepted value = the true or correct value based on reliable references Experimental value = the measured value determined in the experiment in the lab.

Percent Error Indicates accuracy of a measurement expressed as a percentage Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Percent Error % error = 2.94 % A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.94 % Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem