Chemistry 1180 Ebbing and Gammon Chapter 1 The Numbers and Units of Science Chemistry is both a qualitative science and a quantitative science Quantitative observations require both a numerical part and a units part Examples The mass of the sample 16 23 grams The speed of light 3 00 x 108 meters sec The SI Base Units Most sciences have adopted a basic set of international units commonly referred to as the SI Base units From this basic set all other acceptable units can be derived See table 1 2 for complete set of Base units The SI Base units used in Chemistry Mass Kilogram kg Length Meter m Time Second s Temp Kelvin K Amount of substance Mole mol Derived SI Units speed area volume density A common exception to the SI units is found in the use of liters L for volume 1 SI Prefixes The SI system of units also employs a set of prefixes which can be used to indicate decimal fractions or decimal multiples of the SI unit The prefixes used are commonly referred to as metric prefixes and at least some of them will already be familiar to you See table 1 4 in your textbook Giga Mega Kilo Deci Centi Milli Micro Nano Pico Femto 109 106 103 10 1 10 2 10 3 10 6 10 9 10 12 10 15 G M k d c m n p f Examples time 3 56 ns length 0 234 pm volume 38 6 m3 mass 345 g Remember 1 Liter 1L 1000 mL 1000 cm3 The Numbers of Science The numbers that we use generally come from just two sources They are either the result of a measurement or they come from a definition Numbers that are the result of a measurement either directly or indirectly will always contain some amount of estimation also referred to as uncertainty or error Numbers that are the result of a measurement are referred to as inexact numbers 2 Measurements Precision Significant Figures and Errors It is the responsibility of the scientist to report any inexact number with only one estimated digit 3 If measured numbers are correctly reported then you should be able to correctly determine the quality of the measurements For example The number 3 567 g indicates that any uncertainty must exist only in the 7 and that the 3 5 and 6 are known without uncertainty error Conversely if I tell you a number is good to 4 sf then you know that there are three digits known without uncertainty and 1 digit contains some uncertainty SIGNIFICANT FIGURES The following rules will be used to determine the number of significant figures in a measured or 4 calculated number 1 All nonzero digits are always significant examples 1 23 3 s f 1567 4 s f 2 Zeros between nonzero digits are always significant examples 17009 5 s f 6 008 4 s f 3405 4 s f 3 Leading zeros zeros to the left of the first nonzero digit are never significant examples 00987 3 s f 0 00001234 4 s f 4 Trailing zeros zeros to the right of the last nonzero digit in a number with a decimal point will always be counted as significant examples 345 980 6 s f 12300 5 s f 0 0009800 4 s f 5 1 Trailing zeros in a number without a decimal point generally will not be significant examples 2000 1 s f 101200 4 s f 5 2 If one or more of the trailing zeroes are significant then it is best to convert the number to scientific notation and include only the significant zeroes Remember every digit included number written in scientific notation is considered to be significant Consider the following possibilities for the number 109000 a None of the trailing zeroes are significant 3 s f 109000 written with 3 s f 1 09 x 105 b Only the first trailing zero is significant 4 s f 109000 written with 4 s f 1 090 x 105 c The first two trailing zeroes are significant 5 s f 109000 written with 5 s f 1 0900 x 105 d All three trailing zeroes are significant 6 s f 109000 written with 6 s f 109000 notice the decimal point or using scientific notation it would be 1 09000 x 105 5 in a Significant Figures Counting significant figures would be very easy if it was not for zeros Please take out your handout on significant figures How many sf do each of the following numbers contain 123 786 123 000783 0002349 1 0002349 123 12300 123 000 120000 120000 120000 0 Round off the following numbers to 4 sf 123 786 123 746 123 750 123 751 123 850 123 851 0001213786 1 000236 10000 123000 00001200067 There are additional practice exercises on my website Defined Numbers Numbers that contained no measurements and are entirely the result of a definition or a count contain no uncertainty and are called exact numbers Exact numbers are considered to have an infinite number of significant figures For example By definition there are exactly 60 seconds in 1 minute By definition there are exactly 12 things in 1 dozen I can count exactly the number of seats in this room I cannot count exactly tje number of seats in this building 6 Determining the number of significant figures in the result of a calculation Rule 1 The result of a multiplication or division should contain the same number of significant figures as was present in the number with the fewest significant figures 2 0044 5 s f x 12 54 4 s f 25 13517 25 14 4 s f 00342 3 s f x 1 230 4 s f 56 78072484 000074085 Rule 2 The result of an addition or subtraction should contain the same number of decimal places d p as the number with the fewest decimal places 3 123 3 d p 123 23 2 d p 126 353 126 35 2 d p 456 1 1 d p 476 25 2 d p 20 15 20 2 1 d p Notice how the number of significant figures and decimal places change in the following calculation as the different rules come into play 3 123 3 d p 123 23 2 d p 126 353 126 35 2 d p 5 s f Round off the following calculation to the correct number of significant figures 1385 x12 61 80 25 873170845 17 90 90 21 7 Introduction to Chemical Calculations a Calculations based on dimensional analysis b Calculations based on mathematical equations Dimensional Analysis Calculate the number of milliseconds in 139 days Calculate the number of s in 175ps A car is traveling 35 0 miles per hour How long in seconds will it take the car to travel 75 meters A solution contains 0125 mols of a substance 129 7 g mol in 371 mL How many grams of this substance will be in 50 0 mL of this solution A room 15 0 feet by 12 0 feet by 8 00 feet contains 2 35x10 5 kg of mercury …