Scientific Method Measurement Significant Figures Scientific Notation Density Edward Wen, PhD We use Chemistry Everywhere Human body involves chemical reactions (mental/physical) Electric vehicle utilizes battery (chemistry <-> electricity) Cooking process is chemical change The scientific approach to understanding nature Observations Hypothesis is
revised if experimental results do not support it. Hypothesis Tentative proposal that explains observations Experiment Procedure to test hypothesis; measures one variable at a time Model (Theory) Model is altered if predicted events do not support it.
Natural phenomena and measured events; can be stated as a natural law if universally consistent Further Experiment Set of conceptual assumptions that explains data from accumulated experiments; predicts related phenomena Tests predictions based on model How to study Chemistry effectively and with joy? From the basic psychological fact: the
forgetting curve Do homework/review regularly and frequently, especially at the beginning review after review everyday 1 day for 2 days Chemistry is in our everyday life review everyday for 3 days 4 Chapter Outline
Measurement, Metric system (SI) Conversion factor Scientific Notation Significant figures in Measurement/Calculation Conversion involving units raised to powers Density What is a Measurement? Quantitative observation comparison to an agreed upon standard Every measurement has a number and a unit: 77 Fahrenheit: Room temperature 7.5 pounds: Average newborn body weight in the US:
55 grams: amount of sugar in one can of Coca Cola UNIT: what standard you are comparing your object to the number tells you 1. what multiple of the standard the object measures 2. the uncertainty in the measurement () 6 Big Numbers, Small Numbers : Scientific Notation Very Large vs. Very Small numbers: The suns diameter is 1,392,000,000 m; An atoms diameter is 0.0000000003 m
the suns diameter is 1,392,000,000 m Comparison with everyday data: The diameter of the Sun = 818 million times of Dr. Eddies height an atoms Dr. Eddies height = 5.67 billion times of the average diameter is size of an Atom 0.000 000 000 3 m Scientific Notation: 1.392 x 109 m & 3 x 10-10 m Scientific Notation (SN) Power of 10 (Math language): 10 x 10 = 100 100 = 102 (2nd power of 10) 10 x 10 x 10 = 1,000 1,000 = 103 (3rd power of 10)
each Decimal Place in our number system represents a different power of 10 24 = 2.4 x 101 = 2.4 x 10 365 = 3.65 x 100 = 3.65 x 102 1,000,000,000 (1 billion) = 109 0.0000000001 (1/10 billionth ) = 10-10 Easily comparable by looking at the power of 10 8 Exponents 10Y exponent when the exponent on 10 (Y) is positive, the number 1.23 x10-8 is that many powers of 10 larger decimal part exponent part suns diameter = 1.392 x
109 m = 1,392,000,000 m 1.23 x 105 > 4.56 x 102 4.56 x 10-2 > 7.89 x 10-5 7.89 x 1010 > 1.23 x 1010 when Y is negative, the number is that many powers of 10 smaller avg. atoms diameter = 3 x 10-10 m = 0.0000000003 m 9 Writing Numbers in SN Exponent > 0, Number > 10 12,340,000
Exponent < 0, Number < 1 0.0000234 1.234 x 10 7 2.34 x 10 -5 10 Writing a Number in Standard Form Negative exponent: move the decimal point to the left. if you run out of digits, add zeros
1.234 x 10-6 = Positive exponent: move decimal point to the right and add trailing zeros: 1.234 x 1010 = 11 0.000 001 234; 1.2340000000 Practice Convert the following numbers to SN: 149,000,000 0.00000000844 Convert the following SN to standard form: 4.45 x 1012 1.45 x 10-7 Unit in Measurement: The Standard Units (SI units)
Scientists have agreed on a set of international standard units for comparing all our measurements Systme International = International System Quantity Length Mass Time Temperature Unit meter kilogram second kelvin Symbol m
kg s K 13 Some Standard Units in the Metric System Quantity Measured Name of Unit Abbreviation Mass gram
g Length Volume meter liter m L Time seconds s
Temperature Kelvin K 14 Related Units in the SI System All units in the SI system are related to the standard unit by a power of 10 1 kg = 103 g 1 km = 103 m 1 m = 102 cm The power of 10 is indicated by a prefix The prefixes are always the same, regardless of the standard unit 15
Common Prefixes in the SI System Prefix Symbol Decimal Equivalent Power of 10 mega- M 1,000,000 Base 106
kilo- k 1,000 Base 103 deci- d 0.1 Base 10-1 centi-
c 0.01 Base 10-2 milli- m 0.001 Base 10-3 micro- m or mc
0.000 001 Base 10-6 nano- n 0.000 000 001 Base 10-9 16 Standard Unit vs. Prefixes Using meter as example: 1 km = 1000 m = 103 m 1g = 10 dm = 100 cm
= 102 cm = 1000 mm = 103 mm = 1,000,000 mm = 106 mm = 1,000,000,000 nm = 109 nm 1 = 10d = 100c = 1000m = 106 m = 109 n 17 Length: Km, m, cm, mm, Two-dimensional distance an object covers SI unit: METER (abbreviation as m)
About 3 inches longer than a yard 1 m = 10-7 the distance from the North Pole to the Equator Commonly use centimeters (cm) 1 m = 100 cm = 1.094 yard 1 cm = 0.01 m = 10 mm 1 inch = 2.54 cm (exactly) What is your measurement? 2.42 ~ 2.44 cm 18 Mass: Kg, g, mg,
Amount of matter present in an object SI unit: kilogram (kg) about 2 lbs. 3 oz. Commonly measure mass in grams (g) or milligrams (mg) 1 kg = 1000 g = 103 g, 1 g = 1000 mg = 103 mg 1 g = 0.001 kg = 10-3 kg, 1 mg = 0.001 g = 10-3 g 1 kg = 2.2046 pounds (1 lbs. = 0.45359) 19 Volume: M , L, mL, 3 Amount of three-dimensional space occupied SI unit = cubic meter (m3)
a Derived Unit (not the BASIC) Cubic centimeters (cm3, or cc) 1 m3 = 106 cm3 1 cm3 = 10-6 m3 = 0.000001 m3 Milliliters (mL) 1 L is slightly larger than 1 quart 1 L = 1 dm3 = 1000 mL = 103 mL 1 mL = 0.001 L = 10-3 L 1 mL = 1 cc = 1 cm3 20 Prefixes Used to Modify Standard Unit kilo = 1000 times base unit = 103 1 kg = 1000 g = 103 g deci = 0.1 times the base unit = 10-1 1 dL = 0.1 L = 10-1 L; 1 L = 10 dL centi = 0.01 times the base unit = 10-2
1 cm = 0.01 m = 10-2 m; 1 m = 100 cm milli = 0.001 times the base unit = 10-3 1 mg = 0.001 g = 10-3 g; 1 g = 1000 mg micro = 10-6 times the base unit 1 mm = 10-6 m; 106 mm = 1 m nano = 10-9 times the base unit 1 nL = 10-9L; 109 nL = 1 L 21 Common Units and Their Equivalents Length 1 kilometer (km) = 0.6214 mile (mi) 1 m = 39.37 in = 1.094 yard 1 inch (in.) = 2.54 cm exactly Mass 1 pound (lb) = 453.59 grams (g) 1 ounce (oz) = 28.35 (g) Volume
1 U.S. gallon (gal) = 3.785 liters (L) 22 Use of Units Always write every number with its associated unit Always include units in your calculations you can do the same kind of operations on units as you can with numbers cm cm = cm2 cm + cm = cm cm cm = 1 using units as a guide to problem solving 23 Conversion Factor
Relationships to Convert one unit of measurement to another: meter to cm, cm to inch, etc. Conversion Factors: Relationships between two units Both parts of the conversion factor have the same number of significant figures Conversion factors generated from equivalence statements 1in 2.54cm e.g. 1 inch = 2.54 cm can give 1in or 2.54cm 24 We have been using the Conversion Factor ALL THE TIME! How are we converting #cents into #dollars? Why? From 1 dollar = 100 cents
45,000 cents x 1 dollar dollar = 450 dollars 100 cents cents Conversion Factor 25 How to Use Conversion Factor Arrange conversion factors so starting unit cancels Arrange conversion factor so starting unit is on the bottom of the conversion factor unit 1 x
unit 2 unit 1 = unit 2 Conversion Factor To convert 5.00 inches to cm (1 in = 2.54 cm): 26 Example: Conversion among Units (1 = 10d = 100c = 1000m = 106 m = 109 n) 3.78 L = ? nL 1.2 mm = ? m 8.0 in = ? cm
? nL 3.78L ?L ?m 1.2mm ? mm ?? cm 8.0in ? in Measurement: Estimate the Last Digit
for instruments marked with a scale, you get the last digit by estimating between the marks mentally divide the space into 10 equal spaces, then estimate how many spaces over the indicator is 2.25 cm 2.26-2.28 cm 2.2 cm 2.3 cm
Reporting Measurements measurements are written to indicate the Uncertainty in the measurement the system of writing measurements we use is called Significant Figures when writing measurements, all the digits written are known with certainty except the last one, which is an estimate 45.872 certain estimated 29 Practice: Measurements
(digitals and units) 2.2 cm; 2.222 cm; 2.50 cm; 103.4 F Significant Figures (Sig. Fig., SF) Definition: The non-place-holding digits in a reported measurement some zeros in a written number are only there to help you locate the decimal point What is Sig. Fig. for? Range of values to expect for repeated measurements, aka Certainty the more significant figures in a measurement, the smaller the range of values is, more precise. 12.3 cm
has 3 sig. figs. and its range is 12.2 to 12.4 cm 12.30 cm has 4 sig. figs. and its range is 12.29 to 12.31 cm 31 Counting Significant Figures 1. All non-zero digits are significant 1.5 : 2 Sig. Fig.s 2.
Interior zeros are significant 1.05 : 3 Sig. Fig.s 3. Trailing zeros after a decimal point are significant 1.050 : 4 Sig. Fig.s. Leading zeros are NOT significant 0.001050 : 4 Sig. Fig.s Place-holding zeros = SN : 1.050 x 10-3 32 Counting Significant Figures (Contd) 4. Exact numbers has infinite () number of significant
figures: example: 1 pound = 16 ounces 1 kilogram = 1,000 grams = 1,000,000 milligrams 1 water molecule contains 2 hydrogen atoms 5. Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation. if 150 has 2 sig. figs. then 1.5 x 102 but if 150 has 3 sig. figs. then 1.50 x 102 33 Example How many Sig. Figs? 1.080 L 23,000 students
0.200 cm . 2.970 105 kg 1 dozen = 12 4; ambiguous or 2; 3; 4; both exact34 Practice: How many significant figures vs. Decimal places? 2.2 cm (2 SF, 1 dp); 2.50 cm (3 SF, 2 dp); 2.222 cm (4 SF, 3 DP) 35 Sig. Fig. in Multiplication/Division When multiplying or dividing measurements
with Sig. Fig., the result has the same number of significant figures as the measurement with the fewest number of significant figures Rounding 5.02 89,665 3 Sig. Fig.. 0.10 = 45.0118 =______ 5 Sig. Fig.. 2 Sig. Fig.. 2 sig. figs.
5.892 6.10 = 0.96590 = ________ 4 sig. figs. 3 sig. figs. 3 sig. figs. 45 0.966 36 Sig. Fig. in Multiplication/Division: Scientific notation Occasionally, scientific notation is needed to present results with proper significant figures. 5.89 6,103 = 35946.67 = _______ 3 sig. figs. 4 sig. figs.
3 sig. figs. (5.020 10-4) (8.665 106) = 43.4983 10(-4+6) = __________ 4 Sig. Fig.. 4 Sig. Fig.. 4 sig. figs. 2.50 0.20 500.0 0.04 = 62,500 = _______ 3 SF 2 SF 4 SF 3.59 104 1 SF 4.350 103 result should have 1 Sig. Fig.
6 104 37 Sig. Fig. in Multiplication/Division: Scientific notation Occasionally, scientific notation is needed to present results with proper significant figures. 5.89 6,103 = 35946.67 = Sometimes, trailing zero(s) is added to present results with proper significant figures. 4.500 500. = 0.009 = 3.59 104; 0.00900 38
Sig. Fig. in Addition/Subtraction when adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places 5.74 + 2 dp 4.865 3 dp 0.823 + 2.651 = 9.214 3 dp 3 dp 3.965 = 0.9 3 dp
= 2 dp = 3 dp 9.21; 0.900 39 Sig. Fig. in Combined Calculations Do and/or , then + and/or 3.489 5 .67 2.3 3 dp 3 Sig. Fig. 2 Sig. Fig. = 3.489 13 3 dp
0 dp = -9.511 = _________ 0 dp (2 sig. fig.) Parentheses (): Do calculation in () first, then the rest 3.489 (5.67 2.3) 2 dp 1 dp = 3.489 4 Sig. Fig. 3.4 = 11.8628 = _______ 2 Sig. Fig. 2 Sig. Fig. -10; 12
40 Practice: Calculation with Proper Significant Figures a. 12.99 + 2.09 x 1.921 = b. 2.00 x 3.5 - 1.000 = 2.54 12.46 c. 3.75 d. (0.0025 6.7) 8.8 41 How to solve Unit Conversion Problems 1) Write down Given Amount and Unit 2) Write down what you want to Find and Unit
3) Write down needed Conversion Factors or Equations 4) Design a Solution Map for the Problem order Conversions to cancel previous units or arrange Equation so Find amount is isolated. Example: from Equation A = b c to solve for b 42 Solution Map for Unit Conversion 4) Apply the Steps in the Solution Map check that units cancel properly multiply terms across the top and divide by each bottom term Example: 2.54 g 12.46 g 15.00g 2
1 . 9 g / cm 3.1cm 2.5cm 7.75cm 2 5) Check the Answer to see if its Reasonable correct size and unit 43 Good practice: Convert 7.8 km to miles
Given: 7.8 km Find: ? mi Conv. Fact. 1 mi = 5280 ft 1 foot = 12 in km m cm in 1 in = 2.54 cm (exact) ft mi
= 4.8 mi 44 Know Your Scientific Calculator 45 Inputting Scientific Notation into a Calculator input decimal part of the number if negative press +/- key () on some press EXP key EE on some input exponent on 10 press +/- key to
Press +/- -1.23 -03 Simple test: Using SN to Calculate 1.008 6.022 1023 = ANS: 1.67410-24 46 Mass & Volume M a ss D e n sit y Mass & Volume: V o lu m e two main characteristics of matter even though mass and volume are individual
properties - for a given type of matter they are related to each other! Density (ratio of mass vs. volume): for a certain matter, its density is one of the characteristic to distinguish from one another 47 M a ss D e n sit y V o lu m e Unit for density Solids = g/cm3 1 cm3 = 1 mL Liquids = g/mL: Density of water = 1.00 g/mL Gases = g/L: Density of Air ~ 1.3 g/L Volume of a solid can be determined by water
displacement Density : solids > liquids >>> gases except ice and dry wood are less dense than liquid water! 48 Density of Common Matters 49 About Density Temperature affects the density: Heating objects causes objects to expand, density The Lava Lamp: heating/cooling In a heterogeneous mixture, the denser object sinks Why do hot air balloons rise?
The Gold Rush: Extracting gold particle from sand Density of gasoline changes over the day! 50 Density and Volume Styrofoam vs. Quarter: Both of these items have a mass of 23 grams, but they have very different volumes; therefore, their densities are different as well. 51
Density and Buoyancy Average density of human body = 1.0 g/cm3 Average density of sea water = 1.03 g/mL Density of mercury, liquid metal, = 13.6 g/mL Density of copper penny = 8.9 g/cm3 52 M Using Density in Calculations D V
M ass Density Volume Both sides multiplied by Volume M a s s D e n s ity V o lu m e Solution Maps: m, V D m V, D Both sides divided by Density
Mass Volume Density m, D V 53 Application of Density A geologist found a piece of golden color mineral. He decided to measure the density to help identify if it is gold. He first measured the mass of mineral as 10.20 grams. Then he measured its volume as 2.01 cm3. What is
the density of this mineral? Is it gold? (photo credit: https://www.analyticalsci.com/store/p415/Fools_Gold.html) Data: Density pure gold = 19.3 g/cm3 54 Test results Given: Mass = 10.20 grams Volume = 2.01 cm3 Density Au = 19.3 g/cm3 Find: Density in grams/cm3 Density 5.08 g/cm3
Density as a Conversion Factor Between mass and volume!! Density H2O = 1 g/mL \ 1 g H2O 1 mL H2O Density lead = 11.3 g/cm3 11.3 g lead 1 cm3 lead 1.00 g 1 mL or 1 mL 1.00 g 11.3 g 1 mL or 1 mL 11.3 g
56 Density as a Conversion Factor I: Volume One piece of aluminum foil weighs 4.545 g. The density of aluminum is 2.70 g/cm3. What is the volume of this piece of aluminum foil in liter? Given: 4.54 kg Find: Volume in L Conversion Factors: 2.70 grams/cm3 1 L = 1000 cc 0.00168 L
Density as a Conversion Factor II: Mass A truck driver fills 100. L gasoline into the tank. How many kilograms does the gasoline weigh? Density of gasoline = 0.77 g/mL Given: V = 100. L Find: mass in kg Solution Map: D,V gram kg Mass = 77 kg 58 Example: Conversion between nonstandard Units
(1 = 10d = 100c = 1000m = 106 m = 109 n) 3.78 nL = ? mL 1.2 mm = ? km The Meaning of Temperature Temperature is a measure of the average kinetic energy of the molecules in a sample Not all molecules have in a sample the same amount of kinetic energy a higher temperature means a ______ average kinetic energy 60
Celsius Temperature Scale Two reference points: Freezing point of distilled water (0C) Boiling point of distilled water (100C) more reproducible standards most commonly used in science Room temperature is about 25C 61 Fahrenheit vs. Celsius a Celsius degree is 1.8 times larger than a Fahrenheit degree Conversion between Fahrenheit and Celsius C
F F ______ C _______ 62 The Kelvin Temperature Scale Kelvin scale is an absolute scale, meaning it measures the actual temperature of an object 0 K = Absolute Zero: all molecular motion would stop 0 K is theoretically the lowest temperature in the universe 0 K = -273C = -459F Absolute Zero is a theoretical value 63 Kelvin vs. Celsius
the size of a degree on the Kelvin scale is the same as on the Celsius scale though technically, call the divisions on the Kelvin as kelvins, not degrees that makes 1 K 1.8 times larger than 1F the 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale K C _______ 64 Example: Convert -80 F into Celsius and Kelvin 1.8 C 32 F K 273 C
C = -62 C (round to 2 significant 65 figures) Practice Convert the following numbers to SN: 149,000,000 0.00000000844 Convert the following SN to standard form: 4.45 x 1012 1.45 x 10-7 More practice on Conversion 1. Proper dosage of a drug is 3.5 mg/kg of body weight. Calculate the milligrams of this drug for a 138-lb individual? (1 lb = 454 g). KEY: 2.2102 mg (2SF) 2. 100. mg ibuprofen/5 mL Motrin. Calculate the
grams of ibuprofen in 1.5 teaspoons of Motrin. (1 teaspoon = 5.0 mL) KEY: 0.15 g (2SF) 67 Density as a Conversion Factor I: Volume One piece of aluminum foil weighs 4.545 g. The density of aluminum is 2.70 g/cm3. What is the volume of this piece of aluminum foil in liter? Given: 4.54 kg Find: Volume in L Conversion Factors: 2.70 grams/cm3
1 L = 1000 cc Volume = Mass / Density Or conversion factor: 4.545 g x 1 (exact) cm3 /2.70 g = 1.68 cm3 1.68 cm3 x 1 L/1000cm3 = 0.00168 L 0.00168 L Practice: Calculation involving Density 1. The density of air at room temperature and sea level is 1.29 g/L. Calculate the mass of air in a 5.0-gal bottle (1 gal = 3.78 L). KEY: 24 g (2SF) 2. A driver filled 15.60 kg of gasoline into his car. If the density of gasoline is 0.788 g/mL, what is the volume of gasoline in liters? KEY: 19.8 L (3SF)
69 Density as a Conversion Factor II: Mass A truck driver fills 100. L gasoline into the tank. How many kilograms does the gasoline weigh? Density of gasoline = 0.77 g/mL Given: V = 100. L Find: mass in kg Solution Map: D,V gram kg Mass = Volume x Density Or conversion factor: 100. L x 1000mL/1 L = 1.00 x 105 mL 1.00 x 105 mL x 0.77 g/mL = 7.7 x 104 g
7.7 x 104 g x 1 kg/1000 g = 77 kg Mass = 77 kg 70 (self-reading material): Sig. Fig. In Multiplication/Division: Why there is such a rule? To measure the density of a solid, a student weighed 2.01 g of solid and measured its volume as 1.1 mL. What does the above data mean? Mass of solid: (precision 0.01 g, or to the centigram) 2.00 g ~ 2.02 g Volume of solid: (precision 0.1 mL) 1.0 mL ~1.2 mL 71
(contd): Why there is such a rule? Mass 2.01 g ( 0.01g, aka between 2.00 and 2.02 g) Volume 1.1 mL ( 0.1mL, aka between 1.0 mL and 1.2 mL). Then the density of this sample would have such a range: lower end: 2.00 g Density 1.66666... g / mL 1.2 mL higher end: Density 2.02 g 2.0 g / mL 1.0 mL How many significant figures are for the density? 72 Sig. Fig. In Addition/Substraction:
Why there is such a rule? To measure the volume of a solid, a student weighed the empty beaker as 197.55 grams. After adding the solid into the beaker, the combined mass is 252.0 grams. What does the above data mean? Mass of empty beaker: (precision 0.01 g, or to the centigram) 197.54 g ~ 197.56 g Mass of beaker + solid: (precision 0.1 g) 251.9 g ~ 252.1 g 73 (contd.): Why there is such a rule? Mass of empty beaker: 197.04 g ~ 197.06 g Mass of beaker + solid: 251.9 g ~ 252.1 g Then the mass of the solid would have such a range: lower end: 251.9 g 197.56 g = 54.34 g higher end: 252.1 g 197.54 g = 54.56 g
What is the uncertainty of mass? (How many decimals should be kept?) 74 Study of Making Best Cookies: Scientific Method Introduction: https://www.youtube.com/watch?v=GKGtkzgKfkc PBS documentary on Chemistry: part 1: https://www.youtube.com/watch?v=lYoFis_v4yk Part 2: https://www.youtube.com/watch?v=yG0G_NkwOMc Part 3: https://www.youtube.com/watch?v=TKt3VuMMH_E Chemistry demystified: https://www.youtube.com/watch?v=YdkPt6DUKuI Practice: Calculation with Sig. Fig. 2.54
cm 12.46 cm 3.121 min Area of a circle with diameter of 1.00 m Volume of a cube with length of the edge at 3.21 cm 4.806 cm/min;0.785 m2; 33.1 cm3 76
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