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Chapter 1 Introduction to Chemistry What is Chemistry? Matter – anything that has mass and occupies space. Chemistry – study of the composition of matter and the changes that matter undergoes. Because living and nonliving things are made of matter, chemistry affects all aspects of life Areas of Chemistry Organic – study of all chemicals containing carbon Inorganic – study of chemicals that, in general, do not contain carbon. (found mainly in nonliving things) Biochemistry – study of processes that take place in organisms. (digestion, muscle contraction) Analytical – focuses on the composition of matter. (measuring lead in drinking water) Physical – area of study that deals with the mechanism, the rate, and the energy transfer that occurs when matter undergoes a change. See page 8 for examples Pure & Applied Chemistry Pure Chemistry – pursuit of chemical knowledge for its own sake • Chemists does not expect there to be any immediate practical use for the knowledge Applied – research that is directed toward a practical goal or application In practice, pure chemistry & applied chemistry are linked. The Scientific Method Logical, systematic approach to the solution of a scientific problem. 1. Making Observations – using your senses to obtain information. An observation can lead to a question. 2. Making a Hypothesis – a proposed explanation for an observation. A hypothesis is only useful if it accounts for what is actually observed. 3. Experiment – a procedure that is used to test a hypothesis. a) Independent variable – a variable that you change during an experiment The Scientific Method b) Dependent variable – a variable that is observed during the experiment. c) For the results of an experiment to be accepted, the experiment must produce the same result no matter how many times it is repeated or by whom. 4. Developing a Theory – a well-tested explanation for a broad set of observations. 5. Scientific Law – concise statement that summarized the results of many observations and experiments. Ex. Gas Laws The Scientific Method Observations Hypothesis Experiments A hypothesis may be revised based on experimental data A theory is tested by more experiments & modified if necessary Scientific Law Steps do not have to occur in the order shown Theory Summarizes the results of many observations and experiments Solving Numeric Problems 1. Analyze – identify what is known and what is unknown. 2. Calculate – make the calculations. You may need to convert a measurement or rearrange an equation before you can solve. 3. Evaluate – after you calculate, evaluate your answer. Is the answer reasonable? Does it make sense? Chapter 2 Matter Matter – anything that has mass and takes up space Mass – measure of the amount of matter that an object contains Volume – measure of the space occupied by the object Extensive & Intensive Properties What you observe when you examine a sample of matter is its properties. 1. Extensive Property – a property that depends on the amount of matter in a sample Ex. Mass, volume, weight, length 2. Intensive Property – a property that depends on the type of matter in a sample (prefix–in means within) Ex. Hardness, color, odor, luster, conductivity, malleability, ductility, freezing point, boiling point, melting point, density Substances Substance – Matter that has a uniform and definite composition • Either an element or a compound • Also called pure substance • Rarely found in nature • Fixed proportions to each other Examples Diamond Water Gold Copper Sugar Nitrogen Mixtures Mixture – a physical blend of two or more substances that are not chemically combined • Do not exist in fixed proportions to each other • Most natural substances are mixtures • Can usually be separated back into its original components Examples Concrete Soil Salt water Milk Coke Gasoline Fruit salad Atmosphere Two Types of Mixtures Homogeneous Mixture (solution) – a mixture in which the composition is uniform throughout. • Consists of a single phase • Can’t see them separately or separate them physically Examples stainless steel air olive oil vinegar Two Types of Mixtures Heterogeneous Mixture – a mixture in which the composition is not uniform throughout. • Consists of a two or more phases Examples chicken soup oil & vinegar mixed milk rice crispy treats Separating Mixtures Differences in physical properties can be used to separate mixtures Filtration – process that separates a solid from a liquid Examples coffee filters draining pasta Separating Mixtures Distillation – process of boiling a liquid to produce a vapor and then condensing the vapor into a liquid Example separating water from other substances in the water States of Matter 1. Solid 3. Gas 2. Liquid States of Matter Solid Definite shape Definite volume Not easily compressed • • • • Characteristics Does not take the shape of the container Particles packed tightly together, and often in orderly arrangement Almost incompressible Expands only slightly when heated States of Matter Liquid Indefinite shape Definite volume Not easily compressed • • • • Characteristics Take the shape of the container in which it is placed Particles in close contact, but arrangement of particles is not orderly (can flow past each other) Almost incompressible Expands slightly when heated States of Matter Gas Indefinite shape indefinite volume Easily compressed • • • • Characteristics Take the shape of the container in which it is placed Can expand to fill any volume Particles are much farther apart Easily compressed into a smaller volume Physical Change Physical Change Some properties of a material change, but the composition of the material does not change Examples Changes of state such as boiling water, condensation (boil, freeze, melt, condense) Physical deformation such as cutting, denting, stretching, breaking, crushing Chemical Change Chemical Change A change that produces matter with a different composition than the original matter Examples Silver spoon tarnishes Metal rusts Methane burns Methane burns Sugar ferments Burn, rot, rust, decompose, ferment, explode, corrode usually mean a chemical change Elements Element – simplest form of matter that has a unique set of properties. • cannot be broken down into simpler substances Examples Hydrogen Nitrogen Oxygen Compounds Compound – substance that contains two or more elements chemically combined in a fixed proportion. • Compounds can be broken down into simpler substances by chemical means Examples Sugar (C12H22O11) Salt (NaCl) Water (H2O) Classifying Matter Any sample of matter is either an element, a compound, or a mixture Matter Can be separated physically Substance Definite composition Mixture Variable composition Can be separated chemically Element Simplest form Silver Compound Salt Homogeneous Mixture Heterogeneous Mixture Uniform; also called a solution Nonuniform; Distinct phases Stainless Steel Cement Symbols Derived From Latin Sodium Na Potassium Antimony Copper Gold Silver Iron Lead Tin K Sb Cu Au Ag Fe Pb Sn Physical Properties Physical Property – a quality or condition of a substance that can be observed or measured without changing the substance’s composition Examples Appearance Density Texture Malleability Color Boiling Point Odor Melting Point Conductivity Hardness Chemical Property Chemical Property Ability of a substance to undergo a specific chemical change • Chemical properties can be observed only when a substance undergoes a chemical change. Examples Gasoline -- burns in air Iron -- rusts Baking Soda -- reacts with vinegar Copper -- rusts in water Table salt -- does not react with vinegar Recognizing Chemical Changes Words such as burn, rot, rust, decompose, ferment, explode, and corrode usually signify a chemical change. During a chemical change, the composition of matter always changes. Examples Gasoline -- burns in air Iron -- rusts Baking Soda -- reacts with vinegar Copper -- rusts in water Table salt -- does not react with vinegar Recognizing Chemical Changes Possible Clues • Transfer of energy • A change in color • The production of gas • The formation of a precipitate Precipitate – solid that forms and settles out of a liquid mixture Ex. – ring of soap scum in your bathtub The only way to be sure a chemical change has occurred is to test the composition of a sample before and after the change Law of Conservation of Mass During any chemical reaction, the mass of the products is always equal to the mass of the reactants. Example 2H2 + O2 2g 2g reactants 2H20 = = 4g product Chapter 3 Observation, Measurement and Calculations Precision and Accuracy Accuracy – measure of how close a measurement comes to the actual or true value of whatever is being measured. Precision – measure of how close a series of measurements are to one another. Neither accurate nor precise Precise but not accurate Precise AND accurate Determining Error Accepted Value – the correct value based on reliable references Experimental Value – the value measured in the lab Error(can be +or-)=experimental value – accepted value Percent error = absolute value of error x 100% accepted value Rules for Counting Significant Figures Nonzero integers always count as significant figures. 3456 has 4 sig figs. Rules for Counting Significant Figures Leading zeros do not count as significant figures. 0.0486 has 3 sig figs. Rules for Counting Significant Figures Zeros at the end of a number and to the right of a decimal point are always significant. 9.000 has 4 sig figs 1.010 has 4 sig figs Rules for Counting Significant Figures Captive zeros always count as significant figures. 16.07 has 4 sig figs. Rules for Counting Significant Figures Zeros at the rightmost end that lie at the left of an understood decimal point are not significant. 7000 has 1 sig fig 27210 has 4 sig figs Rules for Counting Significant Figures Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76 13 (2 sig figs) 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. 6.8 + 11.934 = 18.734 18.7 (3 sig figs) 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 International Systems of Units There are seven SI base units Quantity SI Base Units SI base unit Symbol Length Mass Temperature Time Amount Luminous intensity Electric current Meter kilogram kelvin second mole candela ampere m kg K s mol cd A Metric Prefixes Mega (M) Kilo (k) 103 Hecto (hm) 102 Deka(da) 101 Meter (m) left Deci (d) 10-1 Centi (c) 10-2 Milli (m) 10-3 right Micro (µ) 10-6 Nano (nm) 10-9 Pico (pm) 10-12 Other Common Conversions 1 cm3 = 1ml 1dm3 = 1L 1 inch = 2.54 cm 1kg = 2.21 lb 454 g = 1 lb 4.18 J = 1 cal 1 mol = 6.02 x 1023 pieces 1 GA = 3.79 L Units of Length meter – the basic SI unit of length or linear measure Common metric units of length include the centimeter (cm), meter (m), and kilometer (km) Units of Volume Volume -the space occupied by any sample of matter Volume (cube or rectangle) = length x width x height The SI unit of volume is the amount of space occupied by a cube that is 1m along each edge. (m3) Liter (L) – non SI unit – the volume of a cube that is 10cm along each edge (1000cm3) The units milliliter and cubic centimeter are used interchangeably. 1 cm3 = 1ml 1dm3 = 1L Units of Mass Common metric units of mass include the kilogram, gram, milligram and microgram. Weight – is a force that measures the pull on a given mass by gravity. Weight is a measure of force and is different than mass. Mass – measure of the quantity of matter. Although, the weight of an object can change with its location, its mass remains constant regardless of its location. Objects can become weightless, but not massless Units of Temperature Temperature – measure of how hot or cold an object is. The objects temperature determines the direction of heat transfer. When two objects at different temperatures are in contact, heat moves from the object at the higher temperature to the object at the lower temperature. Scientist use two equivalent units of temperature, the degree Celsius and the Kelvin. Units of Temperature A change of 1 º on the Celsius scale is equivalent to one kelvin on the Kelvin scale. The zero point on the Kelvin scale, 0K, or absolute zero, is equal to -273.15º C. K = ºC + 273 ºC = K - 273 . Units of Energy Energy – the capacity to do work or to produce heat. The joule and the calorie are common units of energy. The joule (J) is the SI unit of energy named after the English physicist James Prescott Joule. 1 calorie (cal) - is the quanity of heat that raises the temperature of 1 g of pure water by 1ºC. 1 J = 0.2390 cal 1 cal = 4.184 J Dimensional Analysis Dimensional analysis – a way to analyze and solve problems using the units, or dimensions, of the measurements. How many minutes are there in exactly one week? 60 minutes = 1 hour 24 hours = 1 day 7 days = 1 week 1 week 7 days 24 hours 60 minutes = 10,080 min 1 week 1 day 1 hour 1.0080 x 104 min Dimensional Analysis How many seconds are in exactly a 40-hr work week? 60 minutes = 1 hour 7 days = 1 week 24 hours = 1 day 60 seconds = 1 minute 40 hr 60 min 60 sec = 144,000 s 1 hr 1 min 1.44000 x 105 s Dimensional Analysis Gold has a density of 19.3 g/cm3. What is the density in kg/m3 19.3 g 1 kg 1 x 106 cm3 = 1.93 x 104 kg / m3 1000 g m3 cm3 There are 7.0 x 106 red blood cell (RBC) in 1.0 mm3 of blood. How many red blood cells are in 1.0 L of blood? 7.0 x 106 RBC 1 x 106 mm3 1 dm3 = 7.0 x 1012 1.0 mm3 dm3 1L Density If a piece of led and a feather of the same volume are weighted, the lead would have a greater mass than the feather. It would take a much larger volume of feather to equal the mass of a given volume of lead. Density = mass / volume D=m/v Mass is a extensive property (a property that depends on the size of the sample) Density is an intensive property (depends on the composition of a substance, not on the size of the sample) Questions A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245cm3 and a mass of 612g. Was is the density? Is it aluminum? D = 612g / 245cm3 = 2.50g/cm3 D of aluminum is 2.70 g/cm3; no it is not aluminum A bar of silver has a mass of 68.0 g and a volume of 6.48 cm3. What is the density? D = 68.0g / 6.48 cm3 = 10.5 g/cm3 Chapter 4 Atomic Structure The Atom You cannot see the tiny fundamental particles that make up matter. Yet, all matter is composed of such particles, called atoms Atom – the smallest particles of an element that retains its identity in a chemical reaction Several early philosophers and scientists could not observe individual atoms, but still were able to propose ideas on the structure of atoms. Democritus’s Atomic Philosophy Greek philospher Democritus (460B.C – 370 B.C.) was among the first to suggest the existence of atoms. Democritus believed that matter consisted of tiny, indivisible and indestructible. • Democritus’s ideas did not explain chemical behavior. • Lacked experimental support, because his approach was not based on scientific method. Dalton’s Atomic Theory According to Dalton’s atomic theory, and element is composed of only one kind of atom, and a compound is composed of particles that are chemical combinations of different kinds of atoms. 1. All elements are composed of tiny indivisible particles called atoms 2. Atoms of the same element are identical. The atoms of any one element are different from those of any other element. Dalton’s Atomic Theory 3. Atoms of different elements can physically mix together or can chemically combine in simple whole-number ratios to form compounds. 4. Chemical reactions occur when atoms are separated, joined, or rearranged. Atoms of one element, however, are never changed into atoms of another element as a result of a chemical reaction. Subatomic Particles Most of Dalton’s atomic theory is accepted today. Except, we now know atoms to be divisible. Atoms can be broken down into smaller particles, called subatomic particles. There are 3 kinds of subatomic particles. 1. electrons 2. Protons 3. neutrons Electrons In 1897, English physicist J.J. Thomson discovered the electron. Electrons – negatively charged subatomic particles. Dalton performed experiments that involved passing electric current through gases at low pressure. Protons and Neutrons After a hydrogen atom loses an electron, what is left? A particle with one unit of positive charge should remain when a typical hydrogen atom loses an electron. In 1886, Eugene Goldstein observed a cathode-ray tube and found rays traveling in the direction opposite to that of the cathode rays. He concluded they were positive particles. Protons – positively charged subatomic particles. Protons and Neutrons English physicist James Chadwick confirmed the existence of another subatomic particle. Neutron – subatomic particles with no charge but with a mass nearly equal to that of a proton. Particle Symbol Relative Relative Charge Mass electron e11/1840 Actual mass (g) 9.11 x 10-28 proton p+ 1+ 1 1.67 x 10-24 neutron n0 0 1 1.67 x 10-24 Rutherford’s Gold-foil Experiment However, the great majority of alpha particles passed straight through the gold atoms, without deflection. Also, a small fraction of the alpha particles bounced off the gold foil at very large angles. Rutherford’s Gold-foil Experiment Based on his experimental results, Rutherford suggested a new theory of the atom. He proposed that the atom is mostly empty space, thus explaining the lack of deflections of most of the alpha particles. He concluded that all the positive charge and almost all the mass are concentrated in a small region that has enough positive charge to account for the great deflection . Nucleus – the tiny central core of an atom and is composed of protons and neutrons. Questions Describe Thomson’s and Millikan’s contributions to atomic theory. Thomson – Cathode ray experiments which concluded that electrons must be parts of the atoms of all elements. Millikan determined the charge and mass of the electron. What experimental evidence led Rutherford to conclude that an atom is mostly empty space? The great majority of the alpha particles passed straight through the gold foil Questions Compare Rutherford’s expected outcome of the gold-foil experiment with the actual outcome. Expected all alpha particles to pass straight through with little deflection. Found that most passed straight through, but some particles were deflected at large angles and some bounced back. Distinguishing Among Atoms How are atoms of hydrogen different from atoms of oxygen? Elements are different because they contain different number of protons. Atomic number – of an element is the number of protons in the nucleus of an atom of that element. Example – all hydrogen atoms have 1 proton and the atomic number of hydrogen is 1. The atomic number identifies an element. Distinguishing Among Atoms Most of the mass of an atom is concentrated in its nucleus and depends on the number of protons and neutrons. Mass number – the total number of protons and neutrons in an atom Example: Helium atom contains 2 protons and two neutrons, so its mass number is 4 If you know the atomic number and mass number of an atom of any element, you can determine the atom’s composition. Distinguishing Among Atoms Example: Oxygen Atomic number is 8 = number of p+ = e- (So oxygen has 8 electron s and 8 protons.) Mass number is 16 = number of p+ plus the number of n0. (So oxygen has 8 neutrons) Number of neutron = mass number – atomic number Mass number Atomic number 197 79 Au Isotopes There are some elements that have different kinds of atoms of the same element Example – there are three different kinds of Neon atoms Isotopes – are atoms that have the same number of protons, but different numbers of neutrons. Because isotopes of an element have different numbers of neutrons, they also have different mass numbers. Isotopes are chemically alike because they have identical numbers of protons and electrons, which are the subatomic particles responsible for chemical behavior. Chemical Symbols of Isotopes Write the chemical symbols for three isotopes of oxygen. Oxygen 16, oxygen 17, and oxygen 18. Mass Number (# protons + # neutrons) 16 17 O 8 18 O 8 O 8 Atomic number (# proton = # electrons) Atomic Mass The slight difference takes into account the larger masses, but smaller amounts of the other two isotopes of hydrogen. Atomic mass – of an element is a weighted average mass of the atoms in a naturally occurring sample of the element. The atomic mass of copper is 63.546 amu. Which of copper’s two isotopes is more abundant: copper -63 or copper-65? Atomic mass of 63.546 is closer to 63 than 65, thus copper-63 must be more abundant. Atomic Mass Atomic mass = multiply the mass of each isotope by its natural abundance, expresses as a decimal, and then add the products. Element X has two natural isotopes. The isotope with a mass of 10.012 amu has a relative abundance of 19.91%. The isotope with a mass of 11.009 amu has a relative abundance of 80.09%. Calculate the atomic mass of this element. (10.012 amu x 0.1991) + (11.009 amu x 0.8009) (1.993 amu) + (8.817 amu) Atomic mass = 10.810 Question Copper – 63 has a mass of 62.93 amu and 69.2% abundance. Copper-65 has a mass of 64.93 amu and 30.8% abundance. What is copper’s average atomic mass? (62.93 amu x 0.692) + (64.93 amu x 0.308) (43.548 amu) + (19.998 amu) Atomic mass = 63.55 Periodic Table Each element is identified by its symbol place in a square. The atomic number of the element is shown centered above the symbol. Elements are listed in order of increasing atomic number, from left to right and from top to bottom. Period - each horizontal row of the periodic table. Within a given period, the properties of the elements vary as you move across it from element to element. Group – each vertical column of the periodic table. Elements within a group have similar chemical and physical properties. Each group is identified by a number and the letter A or B. Chapter 5 Models of the Atom Atomic Models Rutherford used existing ideas bout the atom and proposed an atomic model in which the electrons move around the nucleus. However, Rutherford’s atomic model could not explain the chemical properties of element. Niels Bohr, a student of Rutherford’s, changed Rutherford’s model to include how the energy of an atom changes when it absorbs or emits light. The Bohr Model – he proposed that an electron is found only in specific circular paths, or orbits, around the nucleus. The Bohr Model Each possible electron orbit in Bohr’s model has a fixed energy. The fixed energies an electron can have are called energy levels. The fixed energy levels of electrons are somewhat like the rungs of the ladder in which the lowest rung of the ladder corresponds to the lowest energy level. An electron can jump from one energy level to another. Electrons in an atom cannot be between energy levels. The Bohr Model To move from one energy level to another, an electron must gain or lose jus the right amount of energy. In general, the higher an electron is on the energy ladder, the farther it is from the nucleus. A quantum of energy is the amount of energy required to move and electron from one energy level to another energy level. The energy of an electron is said to be quantized. The term quantum leap originates from the ideas found in the Bohr model of the atom. The Quantum Mechanical Model The Quantum Mechanical Model is the modern description of the electrons in atoms comes from the mathematical solution to the Schrodinger equation. Like the Bohr model, the quantum mechanical model restricts the energy of electrons to certain values. Unlike the Bohr model, the quantum mechanical model does not involve an exact path the electron takes around the nucleus. The quantum mechanical model determines the allowed energies an electron can have an how likely it is to find the electron in various locations around the nucleus The Quantum Mechanical Model How likely it is to find the electron in a particular location is described by probability. The quantum mechanical model describes of how the electron moving around the nucleus is similar to the motion of a rotating propeller blade. The propeller blade has the same probability of being anywhere in the blurry regions it produces, but you cannot tells its precise location at any instant. The Quantum Mechanical Model The probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud. The cloud is more dense where the probability of finding the electron is high. The cloud is less dense where the probability of finding the electron is low. It is unclear where the cloud ends, there is at least a slight chance of finding the electron at a considerable distance form the nucleus. Number Number Energy of of Number Energy Sublevel Orbitals Orbitals of e- per Level ( # = n) per per Sublevel Type Level n=1 1s 1 n=2 2s 2p 1 3 n=3 3s 3p 3d 1 3 5 n=4 4s 4p 4d 4f 1 3 5 7 Max e- in Sublevel Maximum e- in Energy Level (2n2) 1 2e- 2e- 2 e- 4 2e2e- 2e6e- 8 e- 9 2e2e2e- 2e6e10e- 18 e- 16 2e2e2e2e- 2e6e10e14e- 32 e- Electron Configuration In most natural phenomena, change proceeds toward the lowest possible energy. In the atom, electrons and the nucleus interact to make the most stable arrangement possible. The way in which electrons are arranged into various orbitals around the nuclei of atoms are called electron configuration. Three rules tell you how to find the electron configurations of atoms. •The aufbau principle •The Pauli exclusion principle •Hund’s rule Electron Configuration Rules aufbau Principle Electrons occupy the orbitals of lowest energy first. Pauli Exclusion Principle • An orbital can hold a maximum of 2 electrons. • 2 electrons in the same orbital must have opposite spins. • An electron is "paired" if it is sharing an orbital with another electron with an opposite spin. • An electron is "unpaired" if it is alone in an orbital Paired unpaired Electron Configuration Rules Hund’s Rule •Electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible. •One electron enters each orbital until all the orbitals contain one electron with the same spin direction •For example, three electron would occupy three orbitals of equal energy as follows: •Second electrons then occupy each orbital so that their spins are paired with the first electron in the orbital. Thus each orbital can eventually have two electrons with paired spins. Electron Configuration Practice Write the electron configuration for each atom. How many unpaired electrons does each atom have? Carbon (atomic number 6 so 6 protons = 6 electrons) 1s22s22p2 2 unpaired electrons Argon 1s22s22p63s23p6 no unpaired electrons Silicon 1s22s22p63s23p2 2 unpaired electrons Exceptional Electron Configurations Some actual electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels. You can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the aufbau diagram for orbital filling. Cr 1s22s22p63s23p64s23d4 using aufbau Cr 1s22s22p63s23p64s13d5 correct Exceptional Electron Configurations Transition elements are some exceptions to the filling rules. These exceptions can be explained by the atom’s tendency to keep its energy as low as possible. These exceptions help explain the unexpected chemical behavior of transition elements. Shorthand Electron Configurations Electron configurations are often abbreviated by naming the last element with a filled shell (halogens) in brackets and listing only the orbitals after the filled shell. Na: 1s22s22p63s1 shorthand Al: Na: [Ne] 3s1 1s22s22p63s23p1 shorthand Al: [Ne] 3s23p1 V: 1s22s22p63s23p6 4s23d3 shorthand V: [Ar] 4s23d3 Waves Each complete wave cycle starts at zero, increases to its highest value, passes through zero to reach its lowest value, and returns to zero again. Amplitude of a wave is the wave’s height from zero to the crest. Wavelength (λ) is the distance between the crests. Waves Frequency (ν) is the number of wave cycles to pass a given point per unit of time. The units of frequency are usually cycles per second. The SI unit of cycles per second is called a hertz (Hz) A hertz can also be expressed as a reciprocal seconds (s-1) Hz = s-1 Light The product of frequency and wavelength always equal a constant (c) = the speed of light c = λν The wavelength and frequency of light are inversely proportional to each other. As the wavelength increases, the frequency decreases. According to the wave model, light consists of electromagnetic waves. Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays. Light All electromagnetic waves travel in a vacuum at a speed of 2.998 x 108 m/s c = 2.998 x 108 m/s Sunlight consists of light with a continuous range of wavelengths and frequencies. The color of light depends on its frequency. When sunlight passes through a prism, the different frequencies separate into a spectrum of color. A rainbow is an example of this phenomenon. Electromagnetic Spectrum Each color of the spectrum blends into the next in the order red, orange, yellow green, blue and violet. In the visible spectrum, red light has the longest wavelength and the lowest frequency. Sample Problems What is the wavelength of radiation with a frequency of 1.50 x 1013 Hz? Does this radiation have a longer or shorter wavelength than red light? c = λν or λ=c/ν λ = (2.998 x 108 m/s) / (1.50 x 1013 s-1) λ = 2.00 x 10-5 m (longer wavelength than red light) What frequency is radiation with a wavelength of 5.00 x 10-8m? In what regions of th e electromagnetic spectrum is this radiation? c = λν or ν=c/λ ν = (2.998 x 108 m/s) / (5.00 x 10-8 m) ν = 6.00 x 1015 s-1 (ultraviolet) When light passes through a prism, the frequencies of light emitted by an element separate into discrete lines to give the atomic emission spectrum of the element. Explanation of Atomic Spectra Atomic line spectra were known before Bohr proposed his model of the H atom. However, Bohr’s model explained why the emission spectrum of H consists of specific frequencies of light. In the Bohr model, the lone electron in the H atom can have only certain specific energies. The lowest possible energy of the electron is its ground state. In the ground state, the electron’s principal quantum number is 1 (n=1) Excitation of the electron by absorbing energy raises it from the ground state to an excited state with n = 2,3,4,5… Explanation of Atomic Spectra A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level. The emission occurs in a single abrupt step, called an electronic transition. Bohr knew from earlier work that the quantum of energy (E) is related to the frequency (ν) of the emitted light by the equation E=hxν h is the fundamental constant of nature, the “Planck constant” and is equal to 6.626 x 10-34 J·s Explanation of Atomic Spectra (Transition to n = 3 energy level, infrared range of spectra) (Transition to n = 2 energy level Visible end of the spectra) (Transition to the n = 1 energy level electron moving from a higher Ultraviolet part of the spectra) The light emitted by an to a lower energy level has a frequency directly proportional to the energy change of the electrons. Each transition produces a line of a specific frequency in the spectrum. Quantum Mechanics Albert Einstein successfully explained experimental data by proposing that light could be described as quanta of energy. The quanta behave as if they were particles. Light quanta are called photons. Although the wave nature of light was well known, the dual waveparticle behavior of light was difficult for scientists to accept. Louis de Broglie a French graduate student, asked an important question: Given that light behaves as waves and particles, can particles of matter behave as waves? The proposal that matter moves in a wavelike way would not be accepted unless experiments confirmed its validity. Quantum Mechanics German physicist Werner Heisenberg examined another feature of quantum mechanics that is absent is classical mechanics. The Heisenberg uncertainly principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time. This limitation is critical in dealing with small particles such as electrons. The Heisenberg uncertainty principle does not matter, however, for ordinary-sized objects such as cars or airplanes. Recap The frequency and wavelength of light waves are inversely related. As the wavelength increases, the frequency decreases. (c = λν) The electromagnetic spectrum consists of radiation over a broad band of wavelengths. The visible light portion is very small. It is in the 10-7 m wavelength rand 1015 Hz (s-1) frequency range. When atoms absorb energy, electrons move into higher energy levels, and these electrons lose energy by emitting light when they return to lower energy levels. Recap A prism separates light into the colors it contains. For white light this produces a rainbow of colors. Light from a helium lamp produces discrete lines. An electron microscope can produce sharp images of a very small object, because of the small wavelength of a moving electron compared with that of light. The Heisenberg uncertainty principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time. Chapter 6 The Periodic Table The Periodic Law Mendeleev developed his table before scientists knew about the structure of atoms. He did not know that the atoms of each element contain a unique number of protons. A British physicist, Henry Moseley, determined an atomic number for each known element. In the modern periodic table, elements are arranged in order of increasing atomic number. The Periodic Law There are seven rows, or periods in the table. Period 1 has 2 elements, Period 2 has 8 elements, Period 4 has 18 elements & Period 6 has 32 elements. Each period corresponds to a principal energy level. There are more elements in higher numbered periods because there are more orbitals in higher energy levels. The Periodic Law The elements within a column or group in the periodic table have similar properties. The properties of the elements within a period change as you move across a period from left to right. The pattern of properties within a period repeats as you move from one period to the next. The Periodic Law Periodic Law – when elements are arranged in order of increasing atomic number, there is a periodic repetition of their physical and chemical properties. Group 1 – (alkali metals) are all highly reactive and are rarely found in elemental form in nature Group 2 – (alkaline earth metals) are silvery colored, soft metals Group 17- (halogens) the only group which contains elements in all three familiar states of matter at standard temperature and pressure. Metal, Nonmetals, and Metalloids The International Union of Pure and Applied Chemistry (IUPAC) set the standard for labeling groups in the periodic table. They numbered the groups from left to right 1 – 18, The elements can be grouped into three broad classes based on their general properties. • Metals • Nonmetals • Metalloids Across the period, the properties of elements become less metallic and more nonmetallic. Metals About 80 % of the elements are metals. Properties of Metals • Good conductors of heat and electric current. • Have a high luster or sheen caused by the ability to reflect light • Solids at room temperature (except Hg) • Many metals are ductile (can be drawn into wires) • Most metals are malleable (they can be hammered into thin sheets without breaking) Nonmetals Nonmetals are in the upper-right corner of the periodic table. There is a greater variation in physical properties among nonmetal than among metals. Properties of Nonmetals • Most are gases at room temperature. S and P are solids, Br is a liquid. • Nonmetals tend to have properties that are opposite to those of metals. • In general, nonmetals are poor conductors of heat and electric current. Solid nonmetals tend to be brittle. Metalloids There is a heavy stair-step lines that separates the metals from the nonmetals. Most of the elements that border this line are metalloids. Properties of Metalloids • Generally has properties that are similar to metals and nonmetals. • Under some conditions they behave like a metal. Under other conditions they behave like a nonmetal. Questions How did chemists begin the process of organizing elements? Used the properties of elements to sort them into groups. What property did Mendeleev use to organize his periodic table? In order of increasing atomic mass How are elements arranged in the modern periodic table? In order of increasing atomic number Name the three broad classes of elements. Metals, nonmetals, and metalloids Squares in the Periodic Table The periodic table displays the symbols and names of the elements along with information about the structure of their atoms. The symbol for the element is located in the center of the square. The atomic number is above the symbol. The element name and average atomic mass are below the symbol. Squares in the Periodic Table The background colors in the squares are used to distinguish groups of elements. (Ex:2 shades of gold are used for the metals in Groups IA and 2A) Group IA elements are called alkali metals. Group 2A elements are called alkaline earth metals. The nonmetals of Group 7A are called halogens. Group 8A elements are called Noble Gases Groups 1B – 8B are called transition metals The two periods usually located at the bottom of the periodic table separate from the main table are called inner transition elements. Period 8 is called the Lanthanide Series and Period 9 is called the Actinide Series Electron Configuration in Groups Electrons play a key role in determining the properties of elements. So there is a connection between an element’s electron configuration and its location in the periodic table. Elements can be sorted into noble gases, representative elements, transition metals, or inner transition metals based on their electron configurations. The Noble Gases are in Group 8A and are sometimes called inert gases because they rarely take part in a reaction. Electron Configuration in Groups Helium (He) 1s2 Neon (Ne) Argon (Ar) Krypton (Kr) 1s22s22p6 1s22s22p63s23p6 1s22s22p63s23p63d104s24p6 The highest occupied energy level for each element, (the s & p sublevels) are completely filled with electrons. s sublevel p sublevel The Representative Elements Elements in groups 1A through 7A are often referred to as representative elements because they display a wide range of physical and chemical properties. In atoms of representative elements, the s and p sublevels of the highest occupied energy level are not filled. Lithium(L) 1s22s1 Sodium (Na) 1s22s22p63s1 Potassium (K) 1s22s22p63s23p64s1 s sublevel The Representative Elements Carbon (C) 1s22s22p2 Silicon (Si) 1s22s22p63s23p2 Germanium (Ge) 1s22s22p63s23p64s23d104p2 In atoms of carbon, silicon, and germanium, in Group 4A, there are four electrons in the highest occupied energy level For any representative elements, its group number equals the number of electrons in the highest occupied energy level. s sublevel p sublevel Transition Metals Elements in the B groups are referred to as transition elements. There are two types of transitions elements: transition metals and inner transition metals In atoms of a transition metal, the highest occupied s sublevel and a nearby d sublevel contain electrons. These elements are characterized by the presence of electrons in d orbitals. Ions Some compounds are composed of particles called ions. An ion is an atoms or group of atoms that has a positive or negative charge. An atom is electrically neutral because it has equal numbers of protons and electrons. Positive and negative ions from when electrons are transferred between atoms. Atoms of metallic elements tend to form ions by losing one or more electrons from their highest occupied energy levels. A sodium atom tend to lose one electron. Cations In the sodium ion, the number of electrons (10) is no longer equal to the number of protons (11). Because there is more positively charged protons than negatively charged electrons, the sodium ion has a net positive charge. An ion with a positive charge is called a cation. The charge for a cation is written as a number followed by a plus sign. (Example: 1+ ) If the charge is 1+, the number 1 is usually omitted from the complete symbol for the ions. (Na+) Anions Atoms of nonmetallic elements, such as chlorine, tend to form ions by gaining one or more electrons. A chlorine atom tend to gain one electron. In a chlorine ion, the number of electrons (18) is no longer equal to the number of protons (17). Because there are more negatively charged electrons than positively charged protons, the chloride ion has a net negative charge. An ion with a negative charge is called an anion. Examples: Cl-, S2- Trends in Ionization Energy Recall that electrons can move to higher energy levels when atoms absorb energy. Sometimes there is enough energy to overcome the attraction of the protons in the nucleus. The energy required to remove an electron from an atom is called ionization energy. The energy to remove the first electron from an atom is called the first ionization energy. The cation produced has a 1+ charge. Ionization Energy The energy to remove the first electron from an atom is called the first ionization energy. The cation produced has a 1+ charge. The second ionization energy is the energy required to remove an electron from an ion with a 1+ charge. The ion produced has a 2+ charge. The third ionization energy is the energy required to remove an electron from an ion with a 2+ charge. The ion produced has a 3+ charge. Trends in Electronegativity There is a property that can be used to predict the type of bond that will form during a reaction. This property is electronegativity, which is the ability of an atom of an element to attract electrons when the atom is in a compound. In general, electronegativity values decrease from top to bottom within a group. For representative elements, the values tend to increase from left to right across a period. Trends for Groups 1A Atomic size decreases Through 8A • Can be explained by variations Ionization energy increases in atomic structure • Increase in nuclear charge Electronegativity increases within groups & across periods, also shielding within Nuclear charge increases groups Shielding increases Nuclear charge increases Electronegativity decreases Ionic size increases Atomic size increases Ionization Energy decreases Shielding is constant Size of cation decreases Size of anions decreases Chapter 7 Ionic and Metallic Bonding valence Electrons Scientists learned that all of the elements within each group of the periodic table behave similarly because they have the same number of valence electrons. valence electrons are the electrons in the highest occupied energy level of an element’s atom. The number of valence electrons largely determines the chemical properties of an element. To find the number of valence electrons in an atom of a representative elements, simply look at its group number Elements of Group IA have one valence electron. Elements in Group 4A have four valence electrons, and so forth valence Electrons The noble gases, Group 8A, are the only exceptions to the group-number rule. Helium has two valence electrons, and all of the other noble gases have eight. valence electrons are usually the only electrons used in chemical bonds. As a general rule, only the valence electrons are shown in electron dot structures. Electron dot structures are diagrams that show valence electrons as dots. Electron Dot Structures The Octet Rule Noble gases, such as neon and argon, are unreactive in chemical reactions. (They are stable) Gilbert Lewis explained why atoms form certain kinds of ions and molecules in the octet rule The Octet Rule - in forming compounds, atoms tend to achieve the electron configuration of a noble gas. An octet is a set of eight. (each noble gas except helium has eight electrons in its highest energy level) Atoms of the metallic elements tend to lose their valence electrons, leaving a complete octet in the next-lowest energy level. Atoms of some nonmetallic elements tend to gain electron or to share electrons with another nonmetallic element to achieve a complete octet. Formation of Cations Using electron dot structures, you can show the ionization of some elements more simply. Na· Na+ Sodium atom Sodium ion neutral 1 unit of + charge ·Mg· Mg2+ + e- electron 1 unit of - charge + 2e- Magnesium atom Magnesium ion electron neutral 2 unit of + charge 2 units of - charge Transition Metals For transition metals, the charges of cations may vary. An atom of iron (Fe) may lose two, or three electrons forming either Fe2+ or Fe3+ ions. Some ions formed by transition metals do not have noble gas electron configurations and are therefore exceptions to the octet rule. Ag is an example - 1s22s22p63s23p63d104s24p64d105s1 To achieve the structure of krypton, which is the preceding noble gas, a silver atom would have to lose eleven electrons. Transition Metals Ions with charges of three or greater are uncommon, and losing eleven electrons is highly unlikely. If Ag loses its 5s1 electron, the configuration that results, (4s24p64d10) with 18 electrons in the outer energy level and all of the orbitals filled, is relatively favorable in compounds. Such a configuration is known as pseudo noble-gas electron configuration. Ag forms a positive ion (Ag+) in this way. Formation of Anions The gain of negatively charge electrons by a neutral atom produces an anion. The name of an anion of a nonmetallic element is not the same as the element name. The name of the ion typically ends in -ide. Chlorine atom (Cl) forms a chloride ion (Cl-) Oxygen atom (O) forms an oxide ion (O2-) Because they have relatively full valence shells, atoms of nonmetallic elements attain noble-gas electron configurations more easily by gaining electrons than by losing them. Formation of Anions Chlorine belongs to Group 7A and has seven valence electrons. A gain of one electron gives chlorine an octet and converts a chlorine atom into a chloride ion. Atoms of nonmetallic elements form anions by gaining enough valence electrons so as to attain the electron configuration of the nearest noble gas. The chloride ion has the same electron configuration as the noble gas argon. Chloride ion (Cl-) 1s22s22p63s23p6 Argon (Ar) 1s22s22p63s23p6 Formation of Ionic Compounds Compounds composed of cations and anions are called ionic compounds. Ionic compounds are usually composed of metal cations and nonmetal anions. Ex: NaCl is formed from Na+ + ClAlthough they are composed of ions, ionic compounds are electrically neutral. The total + charge of the cations equals the total – charge of the anions. Anions and cations have opposite charges and attract one another by means of electrostatic forces. The electrostatic forces that hold ions together in ionic compounds are called ionic bonds. Formation of Ionic Compounds Look at the reaction of a Na atom and a chlorine atom. Na has 1 valence electron that it can easily lose. (Na is in group 1A of the representative elements, thus has 1 valence electron) Cl has seven valence electrons and can easily gain one electron. (Cl is in group 7A of the representative elements, thus has 7 valence electrons) If Na loses its valence electron it achieves the stable electron configuration of neon. If Cl gains a valence electron, it achieves the stable electron configuration of argon. (Remember the Octet Rule) Formation of Ionic Compounds When Na and Cl react, the Na atom gives its one valence electron to a Cl atom. They react in a 1:1 ratio and both ions have stable octets. + Na+ Cl- 1s22s22p6 1s22s22p63s23p6 Formula Units Chemists represent the composition of substances by writing chemical formulas. A chemical formula shows the kinds and numbers of atoms in the smallest representative unit of a substance. NaCl is the chemical formula for sodium chloride. A Formula unit is the lowest whole-number ratio of ions in an ionic compound. One Na+ to each Cl-, thus the formula unit for sodium chloride is NaCl. Even though ionic charges are used to derive the correct formulas, they are not shown when you write the formula unit of the compound Formula Units The ionic compound Magnesium chloride (MgCl2) contains magnesium cations (Mg2+) and chloride anions (Cl-) In MgCl2, the ratios of Mg2+ to Cl- is 1:2 (One Mg2+ to two Cl). Its formula unit is MgCl2 Because there are twice as many Cl- (each with a 1- charge) as Mg2+ (each with a 2+ charge), the compound is electrically neutral. Another example: Al3+ + Br- combine to form AlBr3. Metallic Bonds & Properties Metals are made up of closely packed cations rather than neutral atoms. The valence electrons of metal atoms can be modeled as a sea of electrons. (they are mobile and can drift freely from one part of the metal to another). Metallic bonds consists of the attraction of the free-floating valence electrons from the positively charged metal ion. The sea-of-electrons model explains many physical properties of metals. – Good conductors of electrical current because electrons can flow freely. – Ductile – they can be drawn into wires. – Malleable – they can be hammered or forced into shapes. Crystalline Structure of Metals There are several closely packed arrangements that are possible. • body-centered cubic arrangement • face-centered cubic arrangement • hexagonal close-packed arrangement Body-centered cubic Every atom (except those on the Surface) has eight neighbors. Crystalline Structure of Metals Face-centered cubic arrangement • every atom has twelve neighbors. Crystalline Structure of Metals Hexagonal close-packed arrangement • every atom also have twelve neighbors. Because of the hexagonal shape, the pattern is different from the facecentered. Alloys Very few of the metallic items that you use every day are pure metals. Ex: spoons. Most of the metals you encounter are alloys. Alloys are mixtures composed of two or more elements., at least on of which is a metal. Ex: Brass (Cu & Zn) Alloys properties are often superior to those of their component elements. Sterling silver (92.5% silver & 7.5% copper) is harder and more durable than pure silver, but still soft enough to be made into jewelry and tableware. Laws Governing Formulas & Names Law of Definite Proportions A chemical formula tells you (by subscripts) the ratio of atoms of each element in the compound. Ratios of atoms can also be expressed as ratios of masses. 100 g of MgS breaks down into 43.12g Mg and 56.88g of sulfur. 100g MgS 1 mol MgS 1 mol Mg 24.305g Mg = 43.12g Mg 56.4g MgS 1 mol MgS 1 mol Mg 100g MgS 1 mol MgS 1 mol S 32.06g S = 56.88g S 56.4g MgS 1 mol MgS 1 mol S Chapter 10 Chemical Quantities Measuring Matter Avogadro’s number is the number of representative particles in a mole, 6.02 x 1023. The term representative particles refers to the species present in a substance: usually atoms, molecules or formula units. Representative particles for ionic compounds is the formula unit : CaCl2 , NaCl Representative particles for molecular compounds is the molecule: H2O , H2 Representative particles for most elements is the atom: Fe, Li Measuring Matter A mole of any substance contains Avogadro’s number of representative particles or 6.02 x 1023 representative particles. The relationship, 1 mole = 6.02 x 1023 representative particles, is the basis for a conversion factor to convert numbers of representative particles to moles. How many moles of Mg is 1.25 x 1023 atoms of Mg? 1.25 x 1023 atoms Mg (1 mol Mg / 6.02 x 1023 atoms Mg) Measuring Matter How many atoms are in 2.12 mol of propane (C6H8)? In the formula of a molecule of C3H8 , the subscripts show that propane is composed of 14 atoms: 3 atoms of C and 8 atoms of H. 2.12 mol C6H8 6.02 x 1023 molecules C6H8 11 atoms 1 mol C6H8 1 molecule of C6H8 1.40 x 1025 atoms Mass of a Mole The atomic mass of an element (mass of a single atom) is expressed in atomic mass units (amu) The atomic masses are relative values based on the mass of the most common isotope of carbon 12. The atomic mass of an element expressed in grams is the mass of a mole of the element. The mass of a mole of an element is its molar mass. Molar mass of C is 12.0 g. H – 1.0 g, S – 32.1g Molar mass is the atomic mass of an element rounded off to the first decimal place. Molar Mass If you were to compare 12.0g of C atoms with 16.0g of O atoms, you would find they contain the same number of atoms. The molar mass of any element contains 1 mole or 6.02 x 1023 atoms of that element. 12.0g of C is 1 mol of C atoms 1.0 g of H is 1 mol of H atoms Molar mass is the mass of 1 mole of atoms of any element. Mass of a Mole of a Compound To find the mass of a mole of a compound, you must know the formula of the compound. A molecule sulfur trioxide, SO3, is composed of one atom of sulfur and three atoms of oxygen. Calculate the mass of a molecule of SO3 by adding the atomic masses of the atoms making up the molecule. The atomic mass of Sulfur is 32.1g and the mass of three Oxygen atoms is 48.0g (3 x 16.0), so the molecular mass of SO3 is 80.1g (32.1 + 48.0) The molar mass of any compound is the mass of 1 mole of that compound. Mass of a Mole of a Compound 1 mole of SO3 has a mass of 80.1g and is the mass of 6.02 x 1023 molecules of SO3 To calculate the molar mass of a compound, find the number of grams of each element in one mole of the compound and then add the masses of the elements. The method for calculating molar mass applies to any compound, molecular or ionic. Mole/Mass Relationship You need 3.00 mol of NaCl. How do you measure this amount? What mass in grams is 3.00 mol of NaCl? 3.00 mol NaCl 58.5 g NaCl = 176g NaCl 1 mol NaCl (use the molar mass) When you measure 176g of NaCl on a balance, you are measuring 3.00 mol of NaCl. What is the mass of 9.45 mol of aluminum oxide? (Al2O3) 9.45 mol Al2O3 102.0g Al2O3 = 964 g Al2O3 1 mol Al2O3 Mole/Mass Relationship How many moles of sodium sulfate (Na2SO4) is in 10 g of Na2SO4? 10.0 g Na2SO4 1 mol Na2SO4 = 7.04 x 10-2 mol Na2SO4 142.1 g Na2SO4 How many moles of iron(III) oxide are contained in 92.2 g of pure Fe2O3? 92.2 g Fe2O3 1 mol Fe2O3 = 0.578 mol Fe2O3 159.6 g Fe2O3 Mole/Volume Relationship The volume of one mole of different solid and liquid substances are not the same. However, the volumes of moles of gases measured under standard condition are much more predictable. Avogadro’s hypothesis states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. If you buy a party balloon filled with helium and take it home on a cold day, you might notice that the balloon shrinks while it is outside. The volume of a gas varies with a change in temperature. Mole/Volume Relationship The volume of a gas also varies with a change in pressure. An increase in pressure causes the volume of the gas to decrease. Because of these variation due to temperature and pressure, the volume of a gas is usually measured at standard temperature and pressure. Standard temperature and pressure (STP) means a temperature of 0ºC and a pressure of 101.3 kPa (1atm) At STP, 1 mole or 6.02 x 1023 representative particles of any gas occupies 22.4L. 22.4 L is called the molar volume of gas. Mole/Volume Relationship If you have 0.375 mol of O2 gas, what volume at STP will this gas occupy? 0.375 mol O2 22.4L O2 = 8.40 L O2 1 mol O2 Determine the volume in liters of 0.60 mole of SO2 gas at STP. 0.60 mol SO2 22.4L SO2 1 mol SO2 = 13 L SO2 How many moles of H2 are in 0.200 L at STP? 0.200 L H2 1 mol H2 22.4 L H2 = 8.93 x 10-3 mol H2 Molar Mass From Density Different gases have different densities. Usually the density of a gas is measured in grams per liter (g/L) The density of a gas at STP and the molar volume at STP can be used to calculate the molar mass of the gas. The density of a gaseous compound containing C and O is 1.964 g/L at STP. What is the molar mass of the compound? 1.964 g L 22.4 L 1 mol = 44.0 g/mol Percent Composition The relative amounts of the elements in a compound are expressed as the percent composition or the percent by mass of each element in the compound. The percent composition of a compound consists of a percent value for each different element in the compound. The percent composition of K2CrO4 is K = 40.3%, Cr = 26.8%, O = 32.9%. (They must total 100%) The percent by mass of an element in a compound is the number of grams of the element divided by the mass in grams of the compound, multiplied by 100%. Percent Composition % mass of element = mass of element mass of compound x 100% When a 13.60 g sample of a compound containing only Mg and O is decomposed, 5.40g of O is obtained. What is the percent composition of this compound? % O = 5.40 g / 13.60g x 100% = 39.7% % Mg = 13.60 g – 5.40 g / 13.60g x 100% = 60.3% Percent Composition by Formula % mass = mass of element in 1 mol compound x 100% molar mass of compound Calculate the percent composition of propane C3H8 % C = 36.0 g / 44.0 g x 100% = 81.8% % H = 8.0 g / 44.0 g x 100% = 18.0% Percent Composition as a Conversion Factor How much C and H are contained in 82.0 g of propane? (C3H8) Calculate the percent composition of propane C3H8 % C = 36.0 g / 44.0 g x 100% = 81.8% % H = 8.0 g / 44.0 g x 100% = 18.0% In a 100 g sample of propane you would have 81.8 g of C and 18 g of O. (82.0 g propane)(81.8 g C / 100 g propane) = 67.1 g C (82.0 g propane)(18 g O / 100 g propane) = 15 g H