Chapter 1B. Measurement CHAPTER OUTLINE

Transcription

1 Chapter 1B Measurement 1 CHAPTER OUTLINE SI Units Scientific Notation Error in Measurements Significant Figures Rounding Off Numbers Conversion of Factors Conversion of Units Volume & Density 2 1

2 SI UNITS q Measurements are made by scientists to determine size, length and other properties of matter. q For measurements to be useful, a measurement standard must be used. q A standard is an exact quantity that people agree to use for comparison. q SI is the standard system of measurement used worldwide by scientists. 3 SI BASE UNITS Quantity Measured Units Symbol Length Meter m Mass Kilogram kg Time Seconds s Temperature Kelvin K Amount of substance Mole mol Electric current Ampere A Intensity of light Candela cd 4 2

3 DERIVED UNITS q In addition to the base units, several derived units are commonly used in SI system. Quantity Measured Units Symbol Volume Liter L Density grams/cc g/cm 3 5 SCIENCTIFIC NOTATION q Scientific Notation is a convenient way to express very large or very small quantities. q Its general form is A x 10 n coefficient n = integer 1 A <

4 SCIENTIFIC NOTATION To convert from decimal to scientific notation: q Follow Move the decimal new number point by in the a multiplication original number sign so and that 10 it is with located an exponent after the (power). first nonzero digit. q The exponent is equal to the number of places that the decimal point was shifted x SCIENTIFIC NOTATION q For numbers smaller than 1, the decimal moves to the left and the power becomes negative x

5 Examples: 1. Write 6419 in scientific notation. decimal after first nonzero digit power of x x x Examples: 2. Write in scientific notation. decimal after first nonzero digit power of x

6 CALCULATIONS WITH SCIENTIFIC NOTATION q To perform multiplication or division with scientific notation: 1. Change numbers to exponential form. 2. Multiply or divide coefficients. 3. Add exponents if multiplying, or subtract exponents if dividing. 4. If needed, reconstruct answer in standard exponential form. 11 Example 1: Multiply 30,000 by 600,000 Convert Multiply Reconstruct Add to exponential exponents coefficients answerform (3 x 10 4 ) (6 x 10 5 ) = 18 x x

7 Example 2: Divided 30,000 by Convert Reconstruct Subtract Divide to exponential coefficients exponents answerform (3 x 10 4 ) (6 x 10-3 ) = 0.5 x 10 5 x (-3) 13 Follow-up Problems: (5.5x10 3 )(3.1x10 5 ) = 17.05x10 8 = 1.7x10 9 (9.7x10 14 )(4.3x10 20 ) = 41.71x10 6 = 4.2x x10 2 = x10 4 = 4.5x x10 1.7x x10 8 = x10 3 = 2.1x10 2 (3.7x10 6 )(4.0x10 8 ) = 14.8x10 2 = 1.5x

8 Follow-up Problems: (8.75x10 14 )(3.6x10 8 ) = 31.5x10 22 = 3.2x x10 28 = x x10 41 = 2.04x ERROR IN MEASUREMENTS q Two kinds of numbers are used in science: Counted or defined: Measured: exact numbers; have no uncertainty are subject to error; have uncertainty q Every measurement has uncertainty because of instrument limitations and human error. 16 8

9 ERROR IN MEASUREMENTS certain 8.65 uncertain certain 8.6 uncertain q What The is last this digit measurement? in any What measurement is this measurement? is the estimated one. 17 SIGNIFICANT FIGURES RULES q 1. Significant All non-zero figures digits rules are are the significant. are certain used to and determine uncertain which digits in digits a measurement. are significant and which are not. 2. All sandwiched zeros are significant. 3. Leading zeros (before or after a decimal) are NOT significant. 4. Trailing zeros (after a decimal) are significant

10 Examples: Determine the number of significant figures in each of the following measurements. 461 cm 3 sig figs g 5 sig figs 1025 g 4 sig figs m 1 sig fig ml 3 sig figs 5500 km 2 sig figs 19 ROUNDING OFF NUMBERS q If rounded digit is less than 5, the digit is dropped Round to 3 sig figs Less than 5 Round to 4 sig figs Less than

11 ROUNDING OFF NUMBERS q If rounded digit is equal to or more than 5, the digit is increased by Round to 3 sig figs More than 5 Equal to 5 Round to 4 sig figs 21 SIGNIFICANT FIGURES & CALCULATIONS q The results of a calculation cannot be more precise than the least precise measurement. q In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures. q For addition and subtraction, the answer must have the same number of decimal places as there are in the measurement with the fewest decimal places

12 3 sig figs MULTIPLICATION & DIVISION 4 sig figs Calculator answer 2 sig figs (9.2)(6.80)(0.3744) = The answer should have two significant figures because 9.2 is the number with the fewest significant figures. The correct answer is ADDITION & SUBTRACTION Add 83.5 and Least precise number Correct answer Calculator answer

13 Example 1: = Least precise number Round to 25 Example 2: 3 sig figs 3.15 x 1.53 = sig figs Round to 26 13

14 SI PREFIXES q The Common SI system prefixes of units are SI Prefixes used is easy with to the use base because units to is based indicate on the multiples of of ten. ten that the unit represents. Prefixes Symbol Multiplying factor mega- M 1,000,000 kilo- k 1000 centi- c 0.01 milli- m micro- µ 0.000, SI PREFIXES How many mm cm are in in a km? cm? 10x10x10x10x or

15 CONVERSION FACTORS q Many problems in chemistry and related fields require a change of units. q Any unit can be converted into another by use of the appropriate conversion factor. q Any equality in units can be written in Metric-Metric the form of a fraction called a conversion factor. For example: Factor Equality 1 m = 100 cm Conversion Factors 1 m 100 cm or 100 cm 1 m 29 Equality Conversion Factors Percent quantity: CONVERSION FACTORS 1 kg = 2.20 lb 1 kg 2.20 lb or Metric-English Factor 2.20 lb 1 kg q Sometimes a conversion factor is given Percentage as a percentage. For example: Factor Conversion Factors 18% body fat by mass 18 kg body fat 100 kg body mass or 100 kg body mass 18 kg body fat 30 15

16 CONVERSION OF UNITS q Problems involving conversion of units and other chemistry problems can be solved using the following step-wise method: Determine Plan Write Set up a the sequence conversion the problem intial of steps by unit factor arranging given convert for and each cancelling the units final initial change units needed. in to the final your numerator unit. plan. and denominator of the steps involved. beginning unit x final unit beginning unit = final unit Conversion factor 31 Example 1: Convert 164 lb to kg (1 kg = 2.20 lb) Step 1: Given: 164 lb Need: kg Step 2: lb English-Metric factor kg Step 3: Step 4: 1 kg 2.20 lb or 2.20 lb 1 kg 1 kg 164 lb x = 74.5 kg 2.20 lb 32 16

17 Example 2: The thickness of a book is 2.5 cm. What is this measurement in mm? Step 1: Given: 2.5 cm Need: mm Step 2: cm Metric-Metric factor mm Step 3: Step 4: 1 cm 10 mm or 10 mm 1 cm 10 mm 2.5 cm x = 25 mm 1 cm 33 Example 3: How many centimeters are in 2.0 ft? (1 in=2.54 cm) Step 1: Given: 2.0 ft Need: cm Step 2: ft English-English factor in English-Metric factor cm Step 3: Step 4: 1 ft 12 in and 1 in 2.54 cm 12 in 2.54 cm 2.0 ft x x = 1 ft 1 in cm cm 34 17

18 Example 4: Bronze is 80.0% by mass copper and 20.0% by mass tin. A sculptor is preparing to case a figure that requires 1.75 lb of bronze. How many grams of copper are needed for the brass figure? Step 1: Given: 1.75 lb bronze Need: g of copper Step 2: lb brz English-Metric factor g brz Percentage factor g Cu 35 Example 4: Step 3: 1 lb 454 g and 80.0 g Cu 100 g brz Step 4: 1.75 lb brz x 454 g 1 lb x 80.0 g Cu 100 g brz = = g 36 18

19 VOLUME q Volume is the amount of space an object occupies. q Common units are cm 3 or liter (L) and milliliter (ml). 1 L = 1000 ml 1 ml = 1 cm 3 37 DENSITY q Density is mass per unit volume of a material. q Common units are g/cm 3 (solids) or g/ml (liquids). Density is is indirectly proportional to to the the volume mass of an object. Which has greatest density? 38 19

20 Example 1: A copper sample has a mass of g and a volume of 5.0 cm 3. What is the density of copper? m = g V = 5.0 cm 3 d = m V = g 5.0 ml = 8.93 g/cm 3 3 d =??? 39 Example 2: A silver bar with a volume of 28.0 cm 3 has a mass of 294 g. What is the density of this bar? m = 294 g V = 28.0 cm 3 d = m V = 294 g 28.0 ml = 10.5 g/cm 3 d =??? 40 20

21 Example 3: If the density of gold is 19.3 g/cm 3, how many grams does a 5.00 cm 3 nugget weigh? Step 1: Given: 5.00 cm 3 Need: g Step 2: cm 3 density g Step 3: Step 4: 19.3 g 1 cm 3 or 1 cm g 19.3 g 1 cm cm x = 96.5 g 3 41 Example 4: If the density of milk is 1.04 g/ml, what is the mass of 0.50 qt of milk? (1L = 1.06 qt) Step 1: Given: 0.5 gt Need: g Step 2: qt English-metric Factor ml 1000 Step 3: 1L ml and 1.04 g 1.06 qt 1 ml Step 4: density 1000 ml 1.04 g 0.50 qt x x = g g 1.06 qt 1 ml g 42 21

22 Example 5: What volume of mercury has a mass of 60.0 g if its density is 13.6 g/ml? x 1 ml 60.0 g g = ml inverse of density 43 DENSITY & FLOATING q Objects float in liquids when their density is lower relative to the density of the liquid. q The density column shown was prepared by layering liquids of various densities. q See demo less dense more dense Isopropyl alcohol Vegetable oil Water Soap Syrup Honey 44 22

23 IS UNIT CONVERSION IMPORTANT? q o Further In 1999 Mars investigation Climate showed that orbiter engineers was lost at in Lockheed space Martin, because which engineers built failed the to aircraft, make a simple calculated conversion navigational from English measurements units to in English metric, an units. embarrassing When NASA s JPL lapse engineers that sent received the $125 the data, million they craft assumed fatally the close to information the Martian was surface. in metric units, causing the confusion. 45 THE END 46 23