1.3 Significant Figures and Scientific Notation Types of Uncertainty • Error - the difference between the true value and our estimation – Random – Systematic • Accuracy - the degree of agreement between the true value and the measured value • Precision - a measure of the agreement of replicate measurements 1.3 Significant Figures and Scientific Notation Significant Figures in Calculation of Results Rules for Addition and Subtraction • The result in a calculation cannot have greater significance than any of the quantities that produced the result • Consider: 37.68 6.71862 108.428 152.82662 liters liters liters liters correct answer 152.83 liters 1.3 Significant Figures and Scientific Notation Rules for Multiplication and Division • The answer can be no more precise than the least precise number from which the answer is derived • The least precise number is the one with the fewest significant figures 4.2 103 (15.94) 8 2 . 9688692 10 (on calculator) 4 2.255 10 Which number has the fewest significant figures? 4.2 x 103 has only 2 The answer is therefore, 3.0 x 10-8 1.3 Significant Figures and Scientific Notation Rules for Multiplication and Division Use in unit conversion 1.3 Significant Figures and Scientific Notation Exact and Inexact Numbers • Inexact numbers have uncertainty by definition • Exact numbers are a consequence of counting • A set of counted items (beakers on a shelf) has no uncertainty • Exact numbers by definition have an infinite number of significant figures 1.3 Significant Figures and Scientific Notation Rules for Rounding Off Numbers • When the number to be dropped is less than 5 the preceding number is not changed • When the number to be dropped is 6 or larger, the preceding number is increased by one unit • When the number to be dropped is 5 and is followed by non-zero numbers, the last figure kept should be unchanging if the last figure is even, and increased by one if the last figure is odd. • Round to 3 significant figures: 3.34966 x 104 =3.35 x 104 1.3 Significant Figures and Scientific Notation Rules for Rounding Off Numbers • When the number to be dropped is less than 5 the preceding number is not changed • When the number to be dropped is 6 or larger, the preceding number is increased by one unit • When the number to be dropped is 5 and is followed by non-zero numbers, the last figure kept should be unchanging if the last figure is even, and increased by one if the last figure is odd. 6.65 to 2 figures ….6.6 6.55 to 2 figures ….6.6 6.45 to 2 figures ….6.4 but 6.4501 to to figures …6.5 1.3 Significant Figures and Scientific Notation How Many Significant Figures? Round off each number to 3 significant figures: 1. 61.40 2. 6.171 3. 0.066494 1.3 Significant Figures and Scientific Notation How Many Significant Figures? Round off each number to 3 significant figures: 1. 61.40 61.4 2. 6.171 6.17 3. 0.066494 0.0665 1.4 Units and Unit Conversion Data, Results, and Units • Data - each piece is an individual result of a single measurement or observation – mass of a sample – temperature of a solution • Results - the outcome of the experiment • Data and results may be identical, however usually related data are combined to generate a result • Units - the basic quantity of mass, volume or whatever quantity is being measured – A measurement is useless without its units 1.4 Units and Unit Conversion English and Metric Units • English system - a collection of functionally unrelated units – Difficult to convert from one unit to another – 1 foot = 12 inches = 0.33 yard = 1/5280 miles • Metric System - composed of a set of units that are related to each other decimally, systematic – Units relate by powers of tens – 1 meter = 10 decimeters = 100 centimeters = 1000 millimeters 1.4 Units and Unit Conversion Basic Units of the Metric System Mass Length Volume gram meter liter g m l • Basic units are the units of a quantity without any metric prefix 1.4 Units and Unit Conversion 1.4 Units and Unit Conversion UNIT CONVERSION • You must be able to convert between units - within the metric system - between the English system and metric system • The method used for conversion is called the factor-label method or dimensional analysis !!!!!!!!!!! VERY IMPORTANT !!!!!!!!!!! 1.4 Units and Unit Conversion • Let your units do the work for you by simply memorizing connections between units. – For example: How many donuts are in one dozen? – We say: “Twelve donuts are in a dozen.” – Or: 12 donuts = 1 dozen donuts • What does any number divided by itself equal? • ONE! 12 donuts 1 1 dozen 1.4 Units and Unit Conversion 12 donuts 1 1 dozen • This fraction is called a unit factor • What does any number times one equal? • That number • Multiplication by a unit factor does not change the amount – only the unit 1.4 Units and Unit Conversion • We use these two mathematical facts to use the factor label method – a number divided by itself = 1 – any number times one is the same number • Example: How many donuts are in 3.5 dozen? • You can probably do this in your head but try it using the factor-label method. 1.4 Units and Unit Conversion Start with the given information... 12 donuts 3.5 dozen 1 dozen = 42 donuts Then set up your unit factor... See that the units cancel... Then multiply and divide all numbers... 1.4 Units and Unit Conversion If you screw up, and some of you will, and use the reciprocal conversion factor 1dozen instead of 12 donuts 12 donuts you get 1dozen dozen 2 1dozen 0.29 3.5 dozen donuts 12 donuts 1.5 Experimental Quantities • Mass - the quantity of matter in an object – not synonymous with weight – standard unit is the gram • Weight = mass x acceleration due to gravity • Mass must be measured on a balance (not a scale) 1.5 Experimental Quantities • Units should be chosen to suit the quantity described – A dump truck is measured in tons or tons – A person is measured in kg or pounds – A paperclip is measured in g or ounces – An atom? • For atoms, we use the atomic mass unit (amu) – 1 amu = 1.661 x 10-24 g 1.5 Experimental Quantities • Length - the distance between two points – standard unit is the meter – long distances are measured in km – distances between atoms are measured in nm, 1 nm = 10-9 m • Volume - the space occupied by an object – standard unit is the liter – the liter is (closely) the volume occupied by 1000 grams of water at 4 oC – 1 ml = 1/1000 l = 1 cm3 1.5 Experimental Quantities The milliliter (ml) and the cubic centimeter (cm3) are equivalent 1.5 Experimental Quantities • Time - metric unit is the second • Temperature - the degree of “hotness” of an object 1.5 Experimental Quantities Kelvin Temperature Scale • The Kelvin scale is another temperature scale. • It is of particular importance because it is directly related to molecular motion. • As molecular speed increases, the Kelvin temperature proportionately increases. K = oC + 273 1.5 Experimental Quantities Energy • Energy - the ability to do work • kinetic energy - the energy of motion • potential energy - the energy of position (stored energy) • Energy is also categorized by form: • • • • • light heat electrical mechanical chemical 1.5 Experimental Quantities Characteristics of Energy • Energy cannot be created or destroyed • Energy may be converted from one form to another • Energy conversion always occurs with less than 100% efficiency • All chemical reactions involve either a “gain” or “loss” of energy 1.5 Experimental Quantities Units of Energy • Basic Units: • joule or calorie • 1 calorie (cal) = 4.184 joules (J) • A kilocalorie (kcal) also known as the large Calorie. This is the same Calorie as food Calories. • 1 kcal = 1 Calorie = 1000 calories • 1 calorie = the amount of heat energy required to increase the temperature of 1 gram of water 1oC. 1.5 Experimental Quantities Concentration Concentration: – the number of particles of a substance – the mass of those particles – that are contained in a specified volume Often used to represent the mixtures of different substances – Concentration of oxygen in the air – Pollen counts – Proper dose of an antibiotic 1.5 Experimental Quantities Density and Specific Gravity • Density – the ratio of mass to volume – an extensive property – use to characterize a substance as each substance has a unique density – Units for density include: • g/ml • g/cm3 • g/cc (cc - cubic centimeter, do not use) mass m d volume V 1.5 Experimental Quantities cork water brass nut liquid mercury Brass 8.4 - 8.73 Cork 0.24 1.5 Experimental Quantities Calculating the Density of a Solid • 2.00 cm3 of aluminum are found to weigh 5.40 g. Calculate the density of aluminum in units of g/cm3. – Use the formula – Substitute our values 5.40 g 2.00 cm3 = 2.70 g/cm3 mass m d volume V 1.5 Experimental Quantities Air has a density of 0.0013 g/ml. What is the mass of 6.0-l sample of air? Calculate the mass in grams of 10.0 ml if mercury (Hg) if the density of Hg is 13.6 g/ml. Calculate the volume in milliliters, of a liquid that has a density of 1.20 g/ml and a mass of 5.00 grams. 1.5 Experimental Quantities Specific Gravity • Values of density are often related to a standard • Specific gravity - the ratio of the density of the object in question to the density of pure water at 4oC • Specific gravity is a unitless term because the 2 units cancel [measurement without unit!] • Often the health industry uses specific gravity to test urine and blood samples density of object (g/ml) specific gravity density of water (g/ml) Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 2 The Structure of the Atom and the Periodic Table Denniston Topping Caret 6th Edition 2.1 Composition of the Atom • Atom - the basic structural unit of an element • The smallest unit of an element that retains the chemical properties of that element 2.1 Composition of the Atom Electrons, Protons and Neutrons • Atoms consist of three primary particles • electrons • protons • neutrons • Nucleus - small, dense, positively charged region in the center of the atom - protons - positively charged particles - neutrons - uncharged particles 2.1 Composition of the Atom Characteristics of Atomic Particles • Electrons are negatively charged particles located outside of the nucleus of an atom • Protons and electrons have charges that are equal in magnitude but opposite in sign • A neutral atom that has no electrical charge has the same number of protons and electrons • Electrons move very rapidly in a relatively large volume of space while the nucleus is small a dense 2.1 Composition of the Atom Symbolic Representation of an Element Charge of particle Mass Number Atomic Number A Z X C Symbol of the atom • Atomic number (Z) - the number of protons in the atom • Mass number (A) - sum of the number of protons and neutrons