Section 2.1 Units and Measurements Pages 32-39 International System of Units (SI System) In 1960, the metric system was standardized in the form of the International System of Units (SI). These SI units were accepted by the international scientific community as the system for measuring all quantities. SI Base Units are defined by an object or event in the physical world. The foundation of the SI is seven independent quantities and their SI base units. You must learn the first 5 quantities listed! Quantity Time Length Mass Temperature Amount of a Substance Electric Current Luminous Intensity Base Unit second (s) meter (m) kilogram (kg) Kelvin (K) mole (mol) ampere (A) candela (cd) SI Prefixes SI base units are not always convenient to use so prefixes are attached to the base unit, creating a more convenient easier-to-use unit. You must memorize these! Prefix Kilo ---Deci Centi Milli Micro Nano Symbol k ---d c m u n Numerica Power of l Value 10 1000 103 1 100 0.1 10-1 0.01 10-2 0.001 10-3 0.000001 10-6 0.000000001 10-9 Temperature Temperature is a measure of the average kinetic energy of the particles in a sample of matter. Kelvin C 273 o The Fahrenheit scale is not used in chemistry. SI Derived Units • • In addition to the seven base units, other SI units can be made from combinations of the base units. Area, volume, and density are examples of derived units. Volume (m3 or dm3 or cm3 ) length length length 1 cm3 = 1 mL 1 dm3 = 1 L Density Density (kg/m3 or g/cm3 or g/mL) is a physical property of matter. m D= V m = mass V = volume Density An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: WORK: V = 825 cm3 D = 13.6 g/cm3 m=? m = DV m D V m = (13.6 g/cm3)(825cm3) m = 11,220 g m = 11,200 g (correct sig figs) Density A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: WORK: D = 0.87 g/mL V=? m = 25 g V=m D m D V V = 25 g = 28.736 mL 0.87 g/mL V = 29 mL (correct sig figs) Non SI Units The volume unit, liter (L), and temperature unit, Celsius (C), are examples of non-SI units frequently used in chemistry. SI & English Relationships • One meter is approximately 3.3 feet. • One kilogram weighs approximately 2.2 pounds at the surface of the earth. Remember: Mass (amount of material in the object) is constant,but weight (force of gravity on the object) may change. • One liter or one dm3 is slightly more than a quart, 1.06 quart to be exact. Section 2.2 Scientific Notation Pages 40-43 Scientific Notation Scientific Notation In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 ??????????????????????????????????? Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n • M is a number between 1 and 10 • n is an integer 2 500 000 000 . 9 8 7 6 5 4 3 2 1 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n 2.5 x 9 10 The exponent is the number of places we moved the decimal. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n 5.79 x -5 10 The exponent is negative because the number we started with was less than 1. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION Review: Scientific notation expresses a number in the form: M x 1 M 10 n 10 n is an integer 4 x 106 6 + 3 x 10 7 x 106 IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 106 6 10 4 x - 3 x 6 1 x 10 The same holds true for subtraction in scientific notation. 106 4 x + 3 x 105 If the exponents are NOT the same, we must move a decimal to make them the same. 6 10 4.00 x 4.00 x 6 5 + .30 x 10 + 3.00 x 10 6 4.30 x 10 Move the decimal on the smaller number! 6 10 A Problem for you… -6 10 2.37 x -4 + 3.48 x 10 Solution… -6 002.37 2.37 x 10 -4 + 3.48 x 10 Solution… -4 0.0237 x 10 -4 + 3.48 x 10 -4 3.5037 x 10 PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION Multiplication and Division Multiplication 4.0 x 106 Exponents do NOT have to be the same. X 3.0 x MULTIPLY the coefficients and then 11 12 x 10 ADD the exponents. 105 1.2 x 1012 Rewrite in proper scientific notation. Division 4.0 x 106 Exponents do NOT have ÷ 3.0 x 105 1.3 x 101 to be the same. DIVIDE the coefficients and then SUBTRACT the exponents. Section 2.2 Dimensional Analysis Pages 44-46 Dimensional Analysis Dimensional Analysis A tool often used in science for converting units within a measurement system Conversion Factor A numerical factor by which a quantity expressed in one system of units may be converted to another system Dimensional Analysis The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out g cm g 3 cm 3 Dimensional Analysis Steps to solving problems: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: Factors: 1 in. = 2.54 cm 1 in. 2.54 cm and 2.54 cm 1 in. How many minutes are in 2.5 hours? conversion factor 2.5 hr x 60 min 1 hr 1 cancel = 150 min By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers! Convert 400 mL to Liters 400 mL 1 L 1000 mL = .400 L = 0.4 L = 4x10-1 L Convert 0.02 kilometers to m 0.02 km 1 000 m 1 km = 20 m = 2x101 m Squared and Cubed Conversions Convert 455.5 cm3 to dm3. 1dm=10cm 4 5 5 . 5 c 3m 1 d m 1 d m 1dm X X X 0 . 4 5 5 5 d 3m 1 10c m 10c m 10c m Multiple Unit Conversions Convert 568 mg/dL to g/L. 1 g = 1000 mg 1L = 10 dL 568mg 1g 10dL g X X 5.68 L dL 1000mg 1L Section 2.3 Uncertainty in Data Pages 47-49 Types of Observations and Measurements We make QUALITATIVE observations of reactions — changes in color and physical state. We also make QUANTITATIVE MEASUREMENTS, which involve numbers. Nature of Measurement Measurement – quantitative observation consisting of two parts: Number Scale (unit) Examples: 20 grams 6.63 × 10-34 joule·seconds 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 Accuracy vs. Precision Precision and Accuracy in Measurements In the real world, we never know whether the measurement we make is accurate We make repeated measurements, and strive for precision We hope (not always correctly) that good precision implies good accuracy Percent Error Indicates accuracy of a measurement experim ent al accepted % error 100 accepted your value given value Percent Error 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 1.40 g/m L 1.36 g/m L 1.36 g/m L 0 .0 4 1 0 0 3 % 1 .3 6 100 (correct sig figs) Section 2.3 Significant Figures or Digits Pages 50-54 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. Why Is there Uncertainty? Measurements are performed with instruments No instrument can read to an infinite number of decimal places Significant Figures Indicate precision of a measurement. Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.31 cm Significant Figures What is the length of the cylinder? Significant figures The cylinder is 6.3 cm…plus a little more The next digit is uncertain; 6.36? 6.37? We use three significant figures to express the length of the cylinder. When you are given a measurement to work with in a chemistry problem you may not know the type of instrument that was used to make the measurement so you must apply a set of rules in order to determine the number of significant digits that are in the measurement. Rules for Counting Significant Figures Nonzero integers always count as significant figures. 3456 has 4 significant figures Rules for Counting Significant Figures Zeros - Leading zeros do not count as significant figures. 0.0486 has 3 significant figures Rules for Counting Significant Figures Zeros - Captive zeros always count as significant figures. 16.07 has 4 significant figures Rules for Counting Significant Figures Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 has 4 significant figures 9,300 has 2 significant figures Rules for Counting Significant Figures Exact Numbers do not limit the # of sig figs in the answer. They have an infinite number of sig figs. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs 3.29 x 103 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 2 sig figs Significant Numbers in Calculations • A calculated answer cannot be more precise than the measuring tool. • A calculated answer must match the least precise measurement. • Significant figures are needed for final answers from 1) multiplying or dividing 2) adding or subtracting Rules for Significant Figures in Mathematical Operations Multiplication and Division Use the same number of significant figures in the result as the data with the fewest significant figures. 1.827 m x 0.762 m = 1.392174 m2 (calculator) = 1.39 m2 (three sig. fig.) 453.6 g / 21 people = 21.6 g/person (calculator) = 21.60 g/person (four sig. fig.) (Question: why didn’t we round to 22 g/person?) Rounding Numbers in Chemistry • If the digit to the right of the last sig fig is less than 5, do not change the last sig fig. 2.532 2.53 • If the digit to the right of the last sig fig is greater than 5, round up the last sig fig. 2.536 2.54 • If the digit to the right of the last sig fig is a 5 followed by a nonzero digit, round up the last sig fig. 2.5351 2.54 • If the digit to the right of the last sig fig is a 5 followed by zero or no other number, look at the last sig fig. If it is odd round it up; if it is even do not round up. 2.5350 2.54 2.5250 2.52 Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 m2 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 23 m2 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. Use the same number of decimal places in the result as the data with the fewest decimal places. 49.146 m + 72.13 m – 9.1434 m = ? = 112.1326 m (calculator) = 112.13 m (2 decimal places) Adding and Subtracting with Trailing Zeros The answer has the same number of trailing zeros as the measurement with the greatest number of trailing zeros. 110 one trailing zero 2500 two trailing zeros + 230.3 2840.3 answer 2800 two trailing zeros Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 g + 3.37 g 1821.57 g 1821.6 g 2.030 mL - 1.870 mL 0.16 mL 0.160 mL Learning Check A. Which answers contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105 Learning Check In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000 Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 1) 256.75 B. 58.925 1) 40.725 19.6 + 2.1 = 2) 256.8 3) 257 - 18.2 = 2) 40.73 3) 40.7 Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 B. 4.311 ÷ 0.07 1) 61.58 = C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 2) 62 3) 9.198 3) 60 3) 0.041