Chem Exam 1 PDF - Chemistry Study Guide

6/25/2024 Chapter 1: Essential Ideas 1 1 The Study of Chemistry Chemistry is the study of matter and the changes that matter undergoes. Matter is anything that has mass and occupies spac...

6/25/2024 Chapter 1: Essential Ideas 1 1 The Study of Chemistry Chemistry is the study of matter and the changes that matter undergoes. Matter is anything that has mass and occupies space. Scientists follow a set of guidelines known as the scientific method: Make observations Formulate a hypothesis Experiment to test hypothesis may evolve into a theory 2 Further experimentation to test predictions based on theory theory could become a law (if others see same thing) 2 1  6/25/2024 Classification of Matter Solid, liquid and gas are the three states of matter commonly found on earth. A substance can convert from one state to another without changing the identity of the substance. Solids Rigid and do NOT conform to the shape of their container. Liquids conform to the shape of their container. Gases assume both the shape and volume of their container. 3 3 Atoms Atom: smallest indivisible unit for an element Molecule: consists of two or more atoms joined by chemical bonds. Law of Conservation of Mass: No detectable change in mass during an ordinary chemical reaction. Law of Definite proportions: A chemical compound always contains the same elements in the same proportions by mass Example: Aspirin will always have 9 Carbon, 8 Hydrogen and 4 Oxygen Atoms (C9H8O4) A mixture can be separated by physical means into its components without changing the identities of the components. 4 4 2  6/25/2024 Classification of Matter Chemists classify matter as either a substance or a mixture of substances. Pure Substance is a form of matter that has definite composition and distinct properties. Examples: salt (sodium chloride), iron, water, mercury, carbon dioxide, and oxygen Pure substances may be divided into two classes: elements and compounds. Pure substances that cannot be broken down into simpler substances by chemical changes are called elements. Pure substances that are comprised of two or more elements are called compounds. Compounds may be broken down by chemical changes to yield either elements or other compounds, or both. Mixture is a physical combination of two or more substances. A homogeneous mixture is uniform throughout. Also called a solution. (Examples: seawater, apple juice) A heterogeneous mixture is not uniform throughout. (Examples: trail mix, chicken noodle soup) 5 5 Types of Matter Matter (may be solid, liquid, or gas): anything that occupies space and has mass Physically Heterogeneous matter: separable into Homogeneous matter: nonuniform composition uniform composition throughout Physically Pure Substances: fixed separable into Solutions: homogeneous composition; cannot mixtures; uniform compositions be further purified that may vary widely Chemically separable into Compounds: elements Elements: cannot be subdivided united in fixed ratios by chemical or physical changes Combine chemically to form 6 6 3  6/25/2024 The Properties of Matter There are two general types of properties of matter: Quantitative properties are measured and expressed with a number. (Quantity = An Amount) Qualitative properties do not require measurement and are usually based on observation. Examples: Extracts from Pacific-yew bark kill cancer cells. Compound “13a” is twenty times more effective than paclitaxel in killing ovarian cancer cells. 7 7 The Properties of Matter A physical property is one that can be observed and measured without changing the identity of the substance. Examples: color, melting point, boiling point, density A physical change is one in which the state of matter changes, but the identity of the matter does not change. Examples: changes of state (melting, freezing, condensation) Examples of physical processes, mixtures are separated , but the identities 8 of the matter does not change 8 4  6/25/2024 The Properties of Matter A chemical property is one a substance exhibits as it interacts with another substance. Examples: flammability, corrosiveness A chemical change is one that results in a change of composition; the original substances no longer exist. Examples: digestion, combustion, oxidation An extensive property depends on the amount of matter. Examples: mass, volume An intensive property does not depend on the amount of matter. Examples: temperature, density Properties that can be measured are called quantitative properties. A measured quantity must always include a unit. The English system has units such as the foot, gallon, pound, etc. The metric system includes units such as the meter, liter, kilogram, etc. 9 9 SI Base Units The revised metric system is called the International System of Units (abbreviated SI Units) and was designed for universal use by scientists. SI Base Units Base Quantity Name of Unit Symbol Length meter m Mass kilogram kg Time second s Electric Current ampere A Temperature kelvin K Amount of Substance mole mol Luminous Intensity candela cd 10 10 5  6/25/2024 SI Base Units The magnitude of a unit may be tailored to an application using prefixes. Prefix Symbol Meaning Example (base unit grams) Tera– T 1 x 1012 1 Tg = 1 x 1012 g Giga– G 1x 109 1 Gg = 1 x 109 g Mega– M 1 x 106 1 Mg = 1 x 106 g Kilo– k 1x 103 1 kg = 1 x 103 g Hecto– h 1 x 102 1 hg = 1 x 102 g Deka– da 1 x 101 1 dag = 1 x 101 g Unit (g, L, etc.) 1 1g=1g Deci– d 1x 10–1 1 dg = 1 x 10–1 g Centi– c 1 x 10–2 1 cg = 1 x 10–2 g Milli– m 1x 10–3 1 mg = 1 x 10–3 g Micro– μ 1 x 10–6 1 μg = 1 x 10–6 g Nano– n 1 x 10–9 1 ng = 1 x 10–9 g Pico– p 1x 10–12 1 pg = 1 x 10–12 g 11 The great mighty king hector died unexpectedly drinking chocolate milk many nights past. 11 Using the conversion chart 1 T(base unit) = 1 x 1012 (base unit) 1 G(base unit) = 1 x 109 (base unit) 1 M(base unit) = 1 x 106 (base unit) 1 k(base unit) = 1 x 103 (base unit) 1 h(base unit) = 1 x 102 (base unit) 1 da(base unit) = 1 x 101 (base unit) How do we use this chart? So let's say our base units are liters? How could 1 (base unit) = 1 (base unit) we find our conversion factor? 1 d(base unit) = 1 x 10–1 (base unit) 1 c(base unit) = 1 x 10–2 (base unit) 1 m(base unit) = 1 x 10–3 (base unit) 1 μ(base unit) = 1 x 10–6 (base unit) 1 n(base unit) = 1 x 10–9 (base unit) 1 p(base unit) = 1 x 10–12 (base unit) 12 12 6  6/25/2024 Using the chart 1 T(unit) = 1 x 1012 (unit) 1 TL = 1 x 1012 L 1 G(unit) = 1 x 109 (unit) 1 GL = 1 x 109 L 1 M(unit) = 1 x 106 (unit) 1 ML = 1 x 106 L 1 k(unit) = 1 x 103 (unit) 1 kL = 1 x 103 L 1 h(unit) = 1 x 102 (unit) Replace the word base unit 1 hL = 1 x 102 L with the symbol for liter (L) 1 da(unit) = 1 x 101 (unit) 1 daL = 1 x 101 L (gives an equality statement). 1 (base unit) = 1 (base unit) 1L=1L 1 d(unit) = 1 x 10–1 (unit) 1 dL = 1 x 10–1 L 1 c(unit) = 1 x 10–2 (unit) 1 cL = 1 x 10–2 L 1 m(unit) = 1 x 10–3 (unit) 1 mL = 1 x 10–3 L 1 μ(unit) = 1 x 10–6 (unit) 1 μL = 1 x 10–6 L 1 n(unit) = 1 x 10–9 (unit) 1 nL = 1 x 10–9 L 1 p(unit) = 1 x 10–12 (unit) 1 pL = 1 x 10–12 L This can be done with all standard units of measurement (grams, meter, second, kelvin, etc.). You need to know these conversions! 13 13 Conversion Factors A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. Created from an equality statement (shows the relationship between two units. When we multiply by a conversion factor, we are only multiplying by 1, so nothing is changed! Equality Statement 1 hour = 60 minutes Divide one side of the equality statement by the other side of the equality statement and you have one of the two conversion factors…. They mean the same thing!! Both are saying there is 1 hour in 60 minutes, meaning either fraction is correct because both came from the equality statement. We are going to use this concept of conversion factors to convert 14 (or move) between SI base units… 14 7  6/25/2024 How many kg are in 3.6 g? 1 kg = 103g 1 T(base unit) = 1 x 1012 (base unit) 1 G(base unit) = 1 x 109 (base unit) Equality Statement….We can make conversion factors. Think of conversion factors as the roads to the next unit…. 1 M(base unit) = 1 x 106 (base unit) 1 k(base unit) = 1 x 103 (base unit) What are the two possible conversion factors from 1 h(base unit) = 1 x 102 (base unit) the equality statement? 1 da(base unit) = 1 x 101 (base unit) 1 kg 103 g 3 and 1 (base unit) = 1 (base unit) 10 g 1 kg 1 d(base unit) = 1 x 10–1 (base unit) Which is the correct one to use? We let the units tell us. Write down what is given in the problem and 1 c(base unit) = 1 x 10–2 (base unit) those units will need to be crossed out…. 1 m(base unit) = 1 x 10–3 (base unit) 1 μ(base unit) = 1 x 10–6 (base unit) We were given 3.6 g and asked to convert it to kg. So the first thing we write down is 3.6 g. Then we will use the 1 n(base unit) = 1 x 10–9 (base unit) conversion factor that allows us to cancel the grams so that 1 p(base unit) = 1 x 10–12 (base unit) we are left with kg. 15 15 Conversion Practice Calculate the number of kg that are found in 1.3 g? How many Mg are in 43.7 mg? 16 16 8  6/25/2024 Mass Mass is a measure of the amount of matter in an object or sample. Because gravity varies from location to location, the weight of an object varies depending on where it is measured. But mass doesn’t change. The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram (g) is often used. 1 kg = 1000 g = 1×103 g Atomic mass unit (amu) is used to express the masses of atoms and other similar sized objects. 1 amu = 1.6605378×10–24 g Temperature There are two temperature scales used in chemistry: The Celsius scale (°C): Freezing point (pure water): 0°C; Boiling point (pure water):100°C The Kelvin scale (K): The “absolute” scale; Lowest possible temperature: 0 K (absolute zero) K = °C + 273.15 17 17 Practice Normal human body temperature can range over the course of a day from about 36°C in the early morning to about 37°C in the afternoon. Express these two temperatures and the range that they span using the kelvin scale. The Fahrenheit scale is common in the United States. Freezing Point (pure water) 32°F Boiling Point (pure water) 212°F There are 180 degrees between freezing and boiling in Fahrenheit (212°F–32°F) but only 100 degrees in Celsius (100°C–0°C). 9 The size of a degree on the Fahrenheit scale is only of a degree on the Celsius scale. 5 9℉ Temp in °F = 5℃ temp in ℃ + 32 ℉ 18 18 9  6/25/2024 Practice A body temperature above 39°C constitutes a high fever. Convert this temperature to the Fahrenheit scale. Gold Boils at 5173ºF. What is the Boiling Point of Gold in Celsius? Chlorine melts at –100.95 ºC what is that in ºF? 19 19 Practice Perform the following conversions: 41°F to °C 68 °C to Kelvin 426 K to °C 681 K to °F Normal body temperature is 37oC. What is this in Kelvin? 20 20 10  6/25/2024 Derived Units:Volume and Density The density of a substance is the ratio of mass to volume. 𝐦 d = density 𝐝= m = mass 𝐕 V = volume There are many units (such as volume) that require units not included in the base SI units. The derived SI unit for volume is the meter cubed (m3). A more practical unit for volume is the liter (L). 1 dm3 = 1 L 1 cm3 = 1 mL SI-derived unit: kilogram per cubic meter (kg/m3) Common units based on state of matter: g (solids) g cm–3 (solids) cm3 g (liquids) Same As: g mL–1 (liquids) mL 21 g (gases) g L–1 (gases) L 21 Density at 20 ℃ Practice Substance Magnesium D ( g mL–1) 1.74 Aluminum 2.70 A piece of metal has mass = 215.8 g. When placed into a measuring Titanium 4.50 cylinder it displaces 19.1 mL of water. Identify the metal. Copper 8.93 Lead 11.34 Mercury 13.55 Gold 19.32 What is the density of CO gas if 0.196 g occupies a volume of 100 mL? An irregularly-shaped sample of aluminum (Al) is put on a balance and found to have a mass of 43.6 g. The student decides to use the water-displacement method to find the volume. The initial volume reading is 25.5 mL and, after the Al sample is added, the water level has risen to 41.7 mL. Find the density of the Al sample in g cm–3. (Remember: 1 mL = 1 cm3.) 22 22 11  6/25/2024 Practice Gasoline is a non-polar liquid that will float on water. 450 grams of gasoline is spilled into a puddle of water. If the density of gasoline is 0.665 g mL–1, what volume of gasoline is spilled? A cup of gold colored metal beads was measured to have a mass 425 grams. By water displacement, the volume of the beads was calculated to be 48.0 cm 3. Given the following densities, identify the metal. (Gold: 19.3 g mL–1; Copper: 8.86 g mL–1; Bronze: 9.87 g mL–1) Calculate the mass of a liquid with a density of 3.2 g mL–1 and a volume of 25 mL. Find the volume that 35.2 g of carbon tetrachloride (CCl 4) will occupy if it has a density of 1.60 g mL–1. 23 23 Uncertainty in Measurement There are two types of numbers used in chemistry: 1) Exact numbers: a) are those that have defined values 1 kg = 1000 g 1 dozen = 12 objects b) are those determined by counting 28 students in a class 2) Inexact numbers: a) measured by any method other than counting length, mass, volume, time, speed, etc. An inexact number must be reported to indicate its uncertainty. 24 24 12  6/25/2024 Uncertainty in Measurement Significant figures (or digits) are the meaningful digits in a reported number. 2.5 cm When using the top ruler to measure the memory card, we could estimate 2.5 cm. We are certain about the 2, but we are not certain about the 5. When using the bottom ruler to measure the memory card, we might record 2.45 cm. Again, we estimate one more digit than we are certain of. As a rule, estimate between the markings and the estimated digit is the uncertain digit. 2.45 + 0.01 cm 25 25 Significant Figures The number of significant figures (S.F.) can be determined using the following guidelines: 1) Any nonzero digit is significant. 112.1 4 significant figures 2) Zeros between nonzero digits are significant. 305 3 significant figures 50.08 4 significant figures 3) Zeros to the left of the first nonzero digit are not significant. 0.0023 2 significant figures 0.000001 1 significant figure 4) Zeros to the right of the last nonzero digit are significant if a decimal is present. 1.200 4 significant figures 5) Zeros to the right of the last nonzero digit in a number that does not contain a decimal point may or may not be significant. 100 1, 2, or 3 – ambiguous To avoid ambiguity, use scientific notation… 1 S.F. = 1 x 102 26 2 S.F. = 1.0 x 102 3 S.F. = 1.00 x 102 26 13  6/25/2024 Practice Determine the number of significant figures in the following measurements: (a) 123 cm (b) 25.03 g (c) 0.0857 kg (d) 1.106×10–7 L (e) 50.0 mL (f) 0.1600 m Number Sig. Figs. Comment on Zeros 2.12 4.500 0.002541 0.00100 500 500. 5.0 x 102 1.05 g Dozen Eggs 27 0.90 x 1045 L 27 Calculations with Measured Numbers In addition, and subtraction, the answer cannot have more digits to the right of the decimal point than any of the original numbers. 102.50 ← two digits after the decimal point + 0.230 ← three digits after the decimal point 102.730 ← round to two digits after the decimal point, 143.29 ← two digits after the decimal point – 20.1 ← one digit after the decimal point 123.19 ← round to one digit after the decimal point, In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures. (1.4)(8.011) = 11.2154 ← fewest significant figures is 2, so round to 2 S.F. 4 S.F. 4 S.F. 11.57 = 0.0378252 ← fewest significant figures is 4, 5 S.F. 305.88 so round to 28 28 14  6/25/2024 Calculations with Measured Numbers Exact numbers can be considered to have an infinite number of significant figures and do not limit the number of significant figures in a result. Example Three pennies each have a mass of 2.5 g. What is the total mass? Exact Inexact (counting number) (measurement) In calculations with multiple steps, round at the end of the calculation to reduce any rounding errors. If the 1st digit to be dropped is < 5, round down If the 1st digit to be dropped is > 5, round up If the dropped digit is 5, we round up or down to yield a value for the retained digit that is even. Do not round after each step! Compare the following: Rounding after each step Rounding at end 1) 3.66 × 8.45 = 30.9 1) 3.66 × 8.45 = 30.93 2) 30.9 × 2.11 = 65.2 2) 30.93 × 2.11 = 65.3 29 In general, keep at least one extra digit until the end of a multistep calculation. 29 Summary– Significant Figures Functions Rule Addition and Subtraction Least number of decimals Multiplication and Division Least number of digits (1.278 + 0.3480) 3 places after the decimal (4 sig figs) 𝑥= = 1.08881 1.08881 (6 sig figs) (8.278 + 2.34) 2 places after the decimal and 2 places before (4 sig figs) 𝑥= = 1.08 1.08 (3 sig figs) 583.00 ÷ 83 172.8 (57.6 * 3) ÷ (34 * 3.00 * 87.507) = 8925.714 30 30 15  6/25/2024 Accuracy and Precision Accuracy tells us how close a measurement is to the true value. Precision tells us how close a series of replicate measurements are to one another. Good accuracy/ Poor accuracy / Poor accuracy / good precision good precision poor precision Three students were asked to find the mass of an aspirin tablet. The true mass of the tablet is 0.370 g. Student A: Precise but not accurate 0.38 Student B: Neither precise nor accurate 0.375 Student C: Both precise and accurate 0.37 0.365 Mass (g) 0.36 True Value 0.355 Student A Measured 0.35 Student B Measured Student C Measured 0.345 0.34 0.335 31 0 A1 2B 3 C Student 31 Dimensional Analysis – Tracking Units A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. 1 in 2.54 cm For example, 1 in = 2.54 cm, may be written: or 2.54 cm 1 in The use of conversion factors in problem solving is called dimensional analysis or the factor– label method. Example 12.00 in Convert 12.00 inches to meters. What conversion factor will cancel inches and give us centimeters? 12.00 in 2.54 cm 12.00 in 1 in or 1 in 2.54 cm 32 = 30.5 cm 32 16  6/25/2024 Common Conversion Factors Length Volume Mass 1 m = 1.0936 yd 1 L = 1.0567 qt 1 kg = 2.2046 lb 1 in. = 2.54 cm (exact) 1 qt = 0.94635 L 1 lb = 453.59 g 1 km = 0.62137 mi 1 ft3 = 28.317 L 1 (avoirdupois) oz = 28.349 g 1 mi = 1609.3 m 1tbsp = 14.787 mL 1 (troy) oz = 31.103 g 33 Example Convert 20.0 milligrams of gold into pounds. Start with what you are given. Look for a pathway: compare the units. What units are shared between the conversion factors? To find the path you must find the necessary conversion factors derived from the equality statements. From the textbook we know: 1 g = 1000 mg and 1 lb = 453.6 g. milligrams grams pounds 1g 1000 mg 1 lb 453.6 g or or 1000 mg 1g 453.6 g 1 lb 34 34 17  6/25/2024 Example An average adult has 5.2 L of blood. What is the volume of blood in pints? If someone weighs 175 lbs. What is that in kilograms. (1 lb = 453.6 g) A child requires a 5 ml dose of medicine each day. How many days would a gallon of this medicine last? Note that each gallon has 3.7854 L. The moon is 384,403 km from the earth. Estimate how many quarters laid end to end will it take to reach the moon if a quarter has a diameter of 2.3 cm. 35 35 Example Convert 14.62 in3 to cubic centimeters, given that there are 2.54 centimeters for every inch. A chair lift at the Divide ski resort in Cold Springs,WY is 4806 feet long and takes 9 minutes. A.)What is the average speed in miles per hour (There are 5280 ft per every mile)? B.)How many feet per second does the lift travel? An average human heart beats 60 times per minute. If an average person lives to the age of 75, how many times does the average heartbeat in a lifetime? A car travels 14 miles in 15 minutes. A.)How fast is it going in miles per hour? How fast is it going in meters per second (1.60933 km = 1 mile)? 36 36 18  6/25/2024 Example How many ng are there in 5.27x10−13 kg? A. 5.27 x 10–16 ng B. 5.27 x 10–7 ng C. 5.27 x 10–4 ng D. 5.27 x 10–1 ng If the density of an object is 2.87 x 10−4 lbs per cubic inch, what is its density in g mL–1? There are 453.592 grams in each pound and 2.54 centimeters in every inch. A. 2.49 x 10–7 g/mL B. 1.13 x 10-4 g/mL C. 7.95 x 10–3 g/mL D. 5.13 x 10–2 g/mL 37 37 19  6/25/2024 Chapter 2: Atoms, Molecules, and Ions Start Learning the Elemental Names and Symbols: Table 2.3 in Textbook (Table 2.3 Link Here) 1 1 Early Ideas in Atomic Theory An element is a substance that cannot be broken down into two or more simpler substances by any means. These are shown on the periodic table, with their symbols. John Dalton (1803-1807) Dalton’s Atomic Theory 1) All matter is composed of tiny particles called atoms. An atom is the smallest unit of an element that can participate in a chemical change. 2) All atoms of a given element have identical chemical properties that are characteristic of that element. 3) Atoms of one element differ in properties from atoms of all other elements. 4) A compound consists of atoms of 2 or more elements combined in a small, whole-number ratio. 5) Atoms can change how they are combined, but they are neither created nor destroyed in chemical reactions. Law of Constant Composition/Law of Definite Proportion All samples of a pure compound contain the same elements in the same 3 proportion by mass (experiments of French chemist Joseph Proust) 3 1  6/25/2024 The Atomic Theory Dalton used the data from Proust (who developed the Law of definite proportions) to formulate the Law of Multiple Proportions. Law of Multiple Proportions (Dalton’s Law): When two elements react, the mass of one element will react with masses of a second element so compounds always equals a ratio of small, whole number. Compound A g O 32 1.33 g O 32 grams O reacts with 24 grams C ⟶ ratio = g C = 24 = 1 g C Compound B g O 64 2.66 g O 64 grams O reacts with 24 grams C ⟶ ratio = g C = 24 = 1gC 2.66 grams O 2 grams O Compound B 1 gram C 1 gram C 2 = 1.33 grams O = 1 gram O =1 Compound A 1 gram C 1 gram C Therefore, compound B has 2 grams O for every 1-gram carbon; compound 4 A has 1-gram oxygen for every 1-gram carbon. This means compound B has twice the amount of oxygen per carbon. 4 Subatomic Particles and Atomic Structure In the late 1800’s, many scientists were doing research involving radiation, the emission and transmission of energy in the form of waves. They commonly used a cathode ray tube, which consists of two metal plates sealed inside a glass tube from which most of the air has been evacuated. fluorescent screen – high voltage + cathode ray 5 5 2  6/25/2024 Subatomic Particles and Atomic Structure Researchers discovered that like charges repel each other, and opposite charges attract one another. J. J. Thomson (1856–1940) noted the rays were repelled by a plate bearing a negative charge and attracted to a plate bearing a positive charge. Cathode Ray Tube Experiment Video J.J. Thomson Talking about an electron Thomson’s contributions: He proposed the rays were a stream of negatively charged particles and these are called electrons. He determined the charge–to–mass ratio of electrons to be 1.76×108 C/g. Thomson proposed the “plum pudding” model of an atom (“+” and “–” charges are squished together like a chocolate chip cookie). Electric and magnetic fields deflect the beam. Gives charge/mass of e– = 1.76×108 C/g Coulomb (C) = SI unit of charge 6 1 C = (A∙s) 6 Subatomic Particles and Atomic Structure Millikan (1911) studied electrically–charged oil drops. R. A. Millikan (1868–1953) determined the charge on an electron by examining the motion of tiny oil drops. The charge of an electron was determined to be –1.6022×10–19 C. Oil Drop Experiment Video 7 7 3  6/25/2024 Subatomic Particles and Atomic Structure Ernest Rutherford used α particles to find the structure of atoms. Most particles penetrated the gold foil undeflected, but some were deflected at a large angle, while others bounced back in the direction from which they had come. Gold Foil Experiment Video1 Gold Foil Experiment Video 2 Gold Foil Textbook Link Rutherford proposed the nuclear model where the positive charge is concentrated in the nucleus. The nucleus accounts for most of an atom’s mass (extremely dense central core in the atom). A typical atomic radius is about 100 pm A typical nucleus has a radius of about 5 ×10–3 pm 8 1 pm = 1×10–12 m 8 Subatomic Particles and Atomic Structure Protons are positively charged particles found in the nucleus. Neutrons are electronically neutral particles found in the nucleus. Neutrons are slightly larger than protons. Electrons are negatively charged particles distributed around the nucleus. Particle Mass (g) Mass (amu) Charge (C) Charge Unit Electron* 9.10938 x 10–28 5.534 x 10–4 –1.6022 x 10–19 –1 Proton 1.67262 x 10–24 1.0073 +1.6022 x 10–19 +1 Neutron 1.67493 x 10–24 1.0086 0 0 9 9 4  6/25/2024 Subatomic Particles and Atomic Structure Which of the following is true about protons and neutrons? A. They both have a charge. B. They have approximately the same mass. C. They are unstable with respect to radioactive decay. D. They are found in the same region of space around the nucleus as the electron. Which experiment can be linked to Millikan? A. Photographic plate fogged with Uranium – discovering radioactivity B. Oil drop experiment – charge of an electron C. Shooting alpha particles at gold foil – structure of the atom D. Cathode ray tube – mass of an electron 10 10 Atomic Number, Mass Number, and Isotopes All atoms can be identified by the number of protons and neutrons they contain. The atomic number (Z) is the number of protons in the nucleus. ▪ Atoms are neutral, so it’s also the number of electrons. ▪ Protons determine the identity of an element. ▪ For example, nitrogen’s atomic number is 7, so every nitrogen has 7 protons. The mass number (A) is the total number of protons and neutrons. ▪ Protons and neutrons are collectively referred to as nucleons. Mass number (number of protons + neutrons) A ZX Chemical symbol Atomic number (number of protons: Constant for a given element) or AX e.g. 12C or X–A e.g. carbon–12 For atoms: we use small units of measurement 1 amu = 1 atomic mass unit = 1/12 the mass of 1 carbon 12 atom 11 1 amu = 1.6605 x 10–24 g 11 5  6/25/2024 Examples Determine the numbers of protons, neutrons, and electrons in each of the following species: (a) 28Si, (b) 19F, (c) 57Fe, and (d) carbon–13. Identify the # of protons, neutrons and electrons given the following information: 197Au 48Ti 55Mn Which neutral element are the following? 26 protons, 56 neutrons 20 neutrons, 18 electrons, no charge 76 neutrons, 52 protons Pick the correct description for 59Co. 12 A. 59 protons, 27 neutrons B. 27 protons, 59 neutrons C. 32 protons, 27 neutrons D. 27 protons, 32 neutrons 12 Atomic Number, Mass Number, and Isotopes Most elements have two or more isotopes, atoms that have the same atomic number (Z) but different mass numbers (A). This is due to each isotope having a different number of neutrons. Isotopes are atoms of the same element with different A (mass). equal numbers of p+ different numbers of n0 Hydrogen isotopes: 1 proton 1 proton 1 proton 0 neutrons 1 neutron 2 neutrons The mass of H is The mass is increased: The mass is increased: 1: 1 proton and 1 neutron/1 proton 2 neutrons/1 proton zero neutrons giving a mass of 2 giving a mass of 2 13 Isotopes of the same element typically exhibit very similar chemical properties same types of compounds and similar reactivities. 13 6  6/25/2024 Isotopes and Atomic Weight Most elements occur as a mixture of isotopes. Magnesium is a mixture of: 24Mg 25Mg 26Mg Number of p+ 12 12 12 Number of n° 12 13 14 Mass/amu 23.985 24.986 25.982 Atomic mass is the mass of an atom in atomic mass units (amu). The average atomic mass on the periodic table represents the average mass of the naturally occurring mixture of isotopes. Isotope Isotopic Mass (amu) Natural abundance (%) 12C 12.00000 98.93 13C 13.003355 1.07 14 14 Average Atomic Mass Measuring Atomic Mass: The most direct and most accurate method for determining atomic and molecular masses is mass spectrometry, using a mass spectrometer. Mass Spectrometry Video Isotopes and Mass Spectrometry Description Chlorine has two stable isotopes, 35Cl (75.78 percent) and 37Cl (24.22 percent) which have masses of 34.9689 and 36.9659 amu, respectively. Calculate the average atomic mass of chlorine. Strategy: Multiplying the mass of each isotope by its fractional abundance (percent value divided by 100) will give its contribution to the average atomic mass. 15 15 7  6/25/2024 Example Natural lithium is: 7.59% 6Li (6.015 amu) and 92.41% 7Li (7.016 amu), what is the average atomic mass of lithium? Argon has three naturally occurring isotopes: 0.337% Ar-36 (35.968 amu), 0.063% Ar-38 (37.963 amu) and 99.60% Ar-40 (39.962 amu). What is the atomic weight of natural Argon? The average atomic mass of nitrogen is 14.0067. The atomic masses of the two stable isotopes of nitrogen, 14N and 15N are 14.003074002 and 15.00010897 amu, respectively. Determine the percent abundance of each nitrogen isotope. 16 16 Example Silver has two stable isotopes; Ag-107 (106.90509 amu) and Ag-109 (108.90476 amu). Determine the percentage abundance of these two isotopes of silver. Rubidium has two naturally occurring isotopes, 85Rb (relative mass 84.9118 amu) and 87Rb (relative mass 86.9092 amu). If rubidium has an average atomic mass of 85.47 amu, what is the percent abundance of each isotope? A. 52.45% 85Rb, 47.55% 87Rb B. 26.81% 85Rb, 73.19% 87Rb C. 85Rb :72.05%, 87Rb: 27.95% D. Aaaggh! 17 17 8  6/25/2024 Covalent Bonding and Molecules A molecule is a combination of at least two atoms in a specific arrangement held together by chemical forces (chemical bonds). A molecule may be an element or a compound. Some elements that naturally exist as molecules include: Br2, I2, N2, Cl2, H2, O2, F2, and C60 and S8 BrINClHOF (The super 7) Different samples of a given compound always contain the same elements in the same ratio. This is known as the law of definite proportions. Sample Mass of O (g) Mass of C (g) Ratio (O(g):C(g) 123 g carbon dioxide 89.4 33.6 2.66:1 50.5 g carbon dioxide 36.7 13.8 2.66:1 88.6 g carbon dioxide 64.4 24.2 2.66:1 18 18 Covalent Bonding and Molecules If two elements can form a series of different compounds, the law of multiple proportions tells us that the ratio of masses of one element that combine with a fixed mass of the other element can be expressed in small whole numbers. Sample Mass of O (g) Mass of C (g) Ratio (O(g):C(g)) 123 g CO2 89.4 33.6 2.66:1 50.5 g CO2 36.7 13.8 2.66:1 88.6 g CO2 64.4 24.2 2.66:1 In addition to carbon dioxide, carbon also combines with oxygen to form carbon monoxide. Sample Mass of O (g) Mass of C (g) Ratio (O(g):C(g) 16.3 g CO 9.31 6.99 1.33:1 25.9 g CO 14.8 11.1 1.33:1 88.4 g CO 50.5 37.9 1.33:1 2.66 O 2 O in CO2 = 1.33 O 1 O in CO 19 law of multiple proportions tells us 2O in CO2:1O in CO 19 9  6/25/2024 Molecular Formulas Diatomic molecules contain two atoms and may be either heteronuclear or homonuclear (BrINClHOF). Polyatomic molecules contain more than two atoms. Homonuclear diatomic: H2 Heteronuclear diatomic: CO Polyatomic: PO43– A chemical formula denotes the composition of the substance through element symbols and numbers, as well as parentheses, dashes, brackets, commas, plus, and minus signs. A molecular formula shows the exact number of atoms of each element in a molecule. Some elements have two or more distinct forms known as allotropes. For example, oxygen (O2) and ozone (O3) are allotropes of oxygen. C, S, and P also have allotropic forms A structural formula shows not only the elemental composition, but also the general arrangements. 20 20 Empirical Formulas Molecular substances can also be represented using empirical formulas, the whole–number ratio of elements. While the molecular formulas tell us the actual number of atoms in the molecule (the true formula), the empirical formula gives the lowest whole–number ratio of elements (the simplest formula). Molecular formula: N2H4 Empirical formula: NH2 The molecular and empirical formulas are often the same. Compound Molecular Formula Empirical Formula Water H2O H2O Hydrogen peroxide H2O2 HO Ethane C2H6 CH3 Propane C3H8 C3H8 Acetylene C2H2 CH Benzene C6H6 CH 21 21 10  6/25/2024 Examples Write the empirical formulas for the following molecules: (a) glucose (C6H12O6), a substance known as blood sugar; (b) adenine (C5H5N5), also known as vitamin B4; and (c) nitrous oxide (N2O), a gas that is used as an anesthetic (“laughing gas”) and as an aerosol propellant for whipped cream. Strategy To write the empirical formula, the subscripts in the molecular formula must be reduced to the smallest possible whole numbers True or False: If any coefficient (subscript) in the molecular formula is 1, then the molecular formula and empirical formula are the same. A. True B. False 22 22 Molecular and Formula Mass The molecular mass is the mass in atomic mass units (amu) of an individual molecule. To calculate molecular mass, multiply the atomic mass of each element in a molecule by the number of atoms of that element and then total the masses Molecular mass of H2O: 2(atomic mass units of H) +(1)(atomic mass units of O) 2(1.008 amu) + (1)(16.00 amu) = 18.02 amu Because the atomic masses on the periodic table are average atomic masses, the result of such a determination is an average molecular mass, sometimes referred to as the molecular weight. Although an ionic compound does not have a molecular mass, we can use its empirical formula to determine its formula mass (the mass of a “formula unit”), sometimes called the formula weight. The process is the same: To calculate formula mass, multiply the atomic mass for each element 2 in a formula unit by the number of atoms of that element and 3 then total the masses 23 11  6/25/2024 Example Problem Calculate the molecular mass or the formula mass, as appropriate, for each of the following: (a) ethane, C2H6, (b) lithium hydroxide, (c) CaCl2 (a) C2H6 : This says 2 carbon atoms and 6 hydrogen atoms. The molecular mass of ethane is: (b) LiOH : This says 1 lithium atom and 1 oxygen atom and 1 hydrogen atom. The formula mass is: (c) CaCl2: This says 1 calcium atom and 2 chlorine atoms. The formula mass is: 24 24 Practice Problem Determine the Formula/Molecular weight for the following compounds: Li2NO3 KCN Al2O3 Fe2(SO4)3 CO2 25 25 12  6/25/2024 The Mole and Molar Mass The mole is defined as the amount of a substance that contains as many elementary entities as there are atoms in exactly 12 g of carbon–12.This experimentally determined number is called Avogadro’s number (NA) 1 mole = 6.022 x 1023 Molar Mass is the mass (grams) in 1 mole of a compound or element given in units of g mol–1. Example Problem 3: What is the molar mass of nitrogen dioxide (NO2)? Hint: Use a similar strategy you would use to calculate the molecular mass of NO 2. Molecular mass of NO2 = atomic mass of N + 2(atomic mass of O) =14.01 amu +(2)(16.00 amu) = 46.01 amu Molar Mass of NO2 = molar mass of N + 2(molar mass of O) 14.01 g 16.00 g 46.01 g = + (2)( ) = mol mol mol 2 6 26 The Mole He (inside balloon) One mole of some familiar substances: 4.0 g of He ~ 18.0 g of H2O ~ 26.98 g Al ~ 63.55 g Cu H2O Sucrose ~ 58.44 g salt (NaCl) Cu ~ 180.16 g sugar (C6H12O6) NaCl Al Mole Video Mole Textbook Link 1 mole of marshmallows would be enough marshmallows to make a 19 km (12 mi) thick layer of marshmallows covering the entire face of the Earth. (Marshmallows would be in the clouds) 1 mole of cells would be approximately equivalent to the number of cells found 2 composing every human on earth. 7 (100 trillion cells per person x 7.4 billion people = 7.4 x 10 23 cells) 27 13  6/25/2024 Example Problems Determine (a) the number of C atoms in 12.00 moles of carbon and (b) the number of moles of sodium in a sample containing 3.23×1010 Na atoms. 2 8 28 Molar Mass The molar mass of a substance is the mass in grams of one mole of the substance. The mass of 1 mole of carbon–12 is exactly 12 g. The mass of 1 carbon–12 atom is exactly 12 amu We usually express molar masses in units of grams per mole (g mol–1) to facilitate cancellation of units in calculations. Molar masses can be found on the periodic table. For example, in1 mole of carbon–12, we have: 12 g carbon 1 mole carbon OR 1 mole carbon 12 g carbon How many moles are in 62.8 grams of Fe? 2 9 29 14  6/25/2024 Molecular Mass and Molar Mass Molecular mass (or molecular weight) is the sum of the atomic masses (in amu) in a molecule. 1 Sulfur 32.07 amu 2 Oxygen + (2 x 16.00 amu) SO2 64.07 amu For any molecule 1 molecule SO2 = 64.07 amu molecular mass (amu) = molar mass (grams) 1 mole SO2 = 64.07 g SO2 How many moles of Ca3(PO4)2 are in 10.0 g of the compound? 3 0 30 Conversion between Mass, Moles, Number of Atoms Molar mass is the conversion factor from mass to moles, and vice versa. Avogadro’s constant converts from moles to atoms. Divide by Molar Mass Multiply by NA #g 1 mol # mol 6.022 x 1023 particles = mol = particles Particles #g 1 mol Atoms Grams Moles Molecules Formula Units Multiply by Molar Mass Divide by NA # mol #g # particles 1 mol =g = mol 1 mol 6.022 x 1023 particles Determine (a) the number of Ca atoms in 0.515 g of Ca, and (b) the mass of H that contains 6.89×1018 H atoms. 31 31 15  6/25/2024 Practice (a) Determine the number of water molecules and the numbers of H and O atoms in 3.26 g of water. (b) Determine the mass of 7.92×1019 carbon dioxide molecules. 32 32 Molar Mass The molar mass (M) of a substance is the mass in grams of one mole of the substance.The molar mass of a compound is the sum of molar masses of the elements it contains. 1 mol H2O = 2 ×1.008 g + 16.00 g = 18.02 g (a) How many moles are in 73.7 g of calcium nitrite? (b) How many atoms are in 0.551 g of potassium (K) ? (c) What is the number of moles of CO2 in 10.00 g of carbon dioxide? (d) How many H atoms are in 72.5 g of C3H8O ? 33 33 16  6/25/2024 Molar Mass How many moles of Na are in 50.4 g of sodium? How many atoms are in 0.0034 g Platinum? The moles in 143.5 g of Zn(NO3)2 What is the mass in grams of 7.70 x 1020 molecules of caffeine, C8H10N4O2? What is the molar mass of cholesterol if 0.00105 mol has a mass of 0.406 g? The most important beryllium-containing compound is beryl, which occurs mostly as blue-green crystals with the formula Be3Al2(SiO3)6. How many moles of beryl are there in a 0.25 g crystal? How many molecules? How many Be atoms? 34 34 17  6/25/2024 Chapter 3: Electronic Structure and Periodic Properties of Elements 1 1 Energy and Energy Changes Energy is the capacity to do work or transfer heat. All forms of energy are either kinetic or potential. Kinetic energy (Ek) is the energy of motion. 1 m is the mass of the object 𝐸k = 𝑚𝑢2 2 u is its velocity One form of kinetic energy of interest to chemists is thermal energy, which is the energy associated with the random motion of atoms and molecules. Potential energy is the energy possessed by an object by virtue of its position. There are two forms of potential energy of great interest to chemists: Chemical energy is energy stored within the structural units of chemical substances. Electrostatic energy is potential energy that results from the interaction of charged particles. 𝑄1 𝑄2 Q1 and Q2 represent two charges 𝐸el = 2 𝑑 separated by the distance, d. 2 1  6/25/2024 Energy and Energy Changes Kinetic and potential energy are interchangeable – one can be converted to the other. Although energy can assume many forms, the total energy of the universe is constant. Energy can neither be created nor destroyed. When energy of one form disappears, the same amount of energy reappears in another form or forms. This is known as the law of conservation of energy. A diver: Has Ep due to macroscale position. Converts Ep to macroscale Ek. Converts Ek,macroscale to Ek,nanoscale (motion of water, heat) 3 3 Practice Water in a damned-up lake : Water rushing through turbines: Moving baseball: Diver standing on a cliff: Gallon of gas: 4 4 2  6/25/2024 Units of Energy The SI unit of energy is the joule (J), named for the English physicist James Joule. A Joule is the amount of energy possessed by a 2–kg mass moving at a speed of 1 m/s. 1 1 1m 2 𝟏 𝐤𝐠 ∙𝐦𝟐 Ek = 𝑚𝑢2 = 2 kg = =𝟏𝐉 2 2 s 𝐬𝟐 The joule can also be defined as the amount of energy exerted when a force of 1 newton (N) is applied over 1 meter. 1J=1N·m Because the magnitude of a joule is so small, we often express large amounts of energy using the unit kilojoule (kJ). 1 kJ = 1000 J calorie (cal) Originally: “The energy needed to heat of 1g of water from 1°C.” Now: 1 cal = 4.184 J (exactly) Dietary Calorie (Cal) – the “big C” calorie. Used on food products. 5 1 Cal = 1000 cal = 1 kcal 5 The Nature of Light Visible light is only a small component of the continuum of radiant energy known as the electromagnetic spectrum. All forms of electromagnetic radiation travel in waves.Waves are characterized by: Wavelength (λ) – the distance between identical points on successive waves Frequency (ν) – the number of waves that pass through a point in 1 second. Amplitude – the vertical distance from the midline of a wave to the top of the peak or the bottom of the trough. An electromagnetic wave has both an electric field component and a magnetic component. The electric and magnetic components have 6 the same frequency and wavelength. 6 3  6/25/2024 The Double–Slit Experiment When light passes through two closely spaced slits, an interference pattern is produced. Constructive interference is a result of adding waves that are in phase. Destructive interference is a result of adding waves that are out of phase. This type of interference is typical of waves and demonstrates the wave nature of light. The speed of light (c) through a vacuum is a constant: c = 2.998 x108 m s–1. Speed of light, frequency and wavelength are related: 𝜆 is expressed in meters 𝒄 = 𝝀𝝂 𝜈 is expressed in reciprocal seconds (s–1) s–1 is also known as hertz (Hz) 7 7 Practice (a) What is the frequency of radiation with a wavelength of 280 nm? (b) What is the wavelength of light with a frequency of 5.65 x 1014 Hz? What is the frequency for 500. nm light? Assume a microwave oven operates at a frequency of 1.80 x 1011 s–1. What is the wavelength? 8 8 4  6/25/2024 Quantum Theory Early attempts by nineteenth-century physicists to figure out the structure of the atom met with only limited success.They were using the laws of classical physics. These laws describe the behavior of macroscopic objects. Over time, the realization and acceptance was the behavior of subatomic particles is NOT governed by the same physical laws as larger objects. This became known as Quantum Mechanics. 10 Ramp (“classical”) & stairs (quantized) 10 Quantization of Energy When a solid is heated, it emits electromagnetic radiation, known as blackbody radiation, over a wide range of wavelengths. The amount of energy given off at a certain temperature depends on the wavelength. Classical physics assumed that radiant energy was continuous; that is, could be emitted or absorbed in any amount. Max Planck suggested that radiant energy is only emitted or absorbed in discrete quantities, like small packages or bundles. A quantum of energy is the smallest quantity of energy that can be emitted (or absorbed). The energy E of a single quantum of energy is 𝑬 = 𝒉𝝂 h : Planck’s constant: 6.626 x10–34 J∙s The idea that energy is quantized rather than continuous is like walking up a staircase or playing the piano.You cannot step or play anywhere (continuous), you can only step on a stair or play on a key (quantized). Einstein proposed that the beam of light is really a stream of particles. These “particles” of light are now called photons. 𝒄 𝒉𝒄 11 𝒄 = 𝝀𝝂 𝝂= 𝑬 = 𝒉𝝂 𝑬= 𝝀 𝝀 11 5  6/25/2024 Practice Calculate the energy (in joules) of (a) a photon with a wavelength of 501 nm and (b) a photon with a wavelength of 50.1 nm. What is the energy of a photon at 379. nm? What is the energy of a photon of frequency 4.86 x 10 11 s-1? What is the frequency of light having an energy of 1.93 x 10–17 J The nitrogen laser emits light at 337.1 nm. What is the energy of this light? 12 12 Bohr’s Theory of the Hydrogen Atom The emission spectrum of a substance can be seen by energizing a sample of material with some form of energy. The “red hot” or “white hot” glow of an iron bar removed from a fire is the visible portion of its emission spectrum. The emission spectrum of both sunlight and a heated solid are continuous; all wavelengths of visible light are present. Line spectra are the emission of light only at specific wavelengths. Every element has its own unique emission spectrum. 13 13 6  6/25/2024 Atomic Line Spectra The Rydberg equation can be used to calculate the wavelengths of the four visible lines in the emission spectrum of HYDROGEN. 1 1 1 R∞ :Rydberg constant (1.09737317 x 107 m–1) = 𝑅∞ 2 − 2 𝜆 𝑛1 𝑛2 λ the wavelength of a line in the spectrum of hydrogen n1 and n2 are positive integers where n2 > n1. ni (initial state) and nf (final state) 1 1 ∆E negative (photon emitted: energy lost to ∆𝐸 = −2.18 𝑥 10−18𝐽 − surroundings); positive (photon absorbed) 𝑛f2 𝑛i2 Bohr’s theory explains the line spectrum of the hydrogen atom. Radiant energy absorbed by the atom causes the electron to move from the ground state (n = 1) to an excited state (n > 1). Conversely, radiant energy is emitted when the electron moves from a higher–energy state to a lower–energy excited state or the ground state. The quantized movement of the electron from one energy state to another 14 is analogous to a ball moving and down steps. 14 Atomic Line Spectra The quantized movement of the electron from one energy state to another is analogous to a ball moving and down steps. 15 15 7  6/25/2024 The Line Spectrum of Hydrogen Neils Bohr attributed the emission of radiation by an energized hydrogen atom to the electron dropping from a higher–energy orbit to a lower one. As the electron dropped, it gave up a quantum of energy in the form of light. Bohr showed that the energies of the electron in a hydrogen atom are given by the equation: 1 En energy 𝐸n = −2.18 𝑥 10−18 J 𝑛2 n a positive integer As an electron gets closer to the nucleus, n decreases. En becomes larger in absolute value (more negative) as n gets smaller. En is most negative when n = 1. Called the ground state, the lowest energy state of the atom For hydrogen, this is the most stable state The stability of the electron decreases as n increases. 16 Each energy state in which n > 1 is called an excited state. 16 The Line Spectrum of Hydrogen 1 1 ∆𝐸 = −2.18 𝑥 10−18 J − 𝑛f2 𝑛i2 Emission Series in the Hydrogen Spectrum Series nf ni Spectrum Region Lyman 1 2,3,4,…. Ultraviolet (UV) Balmer 2 3,4,5,…. Visible and UV Paschen 3 4,5,6,…. Infrared Brackett 4 5,6,7…. Infrared Calculate the wavelength (in nm) of the photon emitted when an electron transitions from the n = 4 state to the n = 3 state in a hydrogen atom. 17 17 8  6/25/2024 Practice Calculate the ΔE and wavelength (in nm) for an H–atom undergoing an n = 4 to n = 2 transition. Calculate the wavelength emitted with an electron changes from n = 6 to n = 2 in the H atom. What is the Energy for that photon? What is energy (in kJ) for 1 mole of those photons? 18 18 Wave Properties of Matter Louis de Broglie reasoned that if light can behave like a stream of particles (photons), then electrons could exhibit wavelike properties. According to de Broglie, electrons behave like standing waves. Only certain wavelengths are allowed. At a node, the amplitude of the wave is zero. De Broglie deduced that the particle and wave properties are related by the following expression: ℎ λ is the wavelength associated with the particle 𝜆= m is the mass (in kg) 𝑚𝑢 u is the velocity (in m/s) The wavelength calculated from this equation is known as the de Broglie wavelength. 19 19 9  6/25/2024 Electron diffraction Diffraction of Electrons pattern of aluminum foil. Experiments have shown that electrons do indeed possess wavelike properties: The Heisenberg uncertainty principle states that it is impossible to know simultaneously both the momentum p and the position x of a particle with certainty. ℎ Δx is the uncertainty in position in meters Δ𝑥 ∙ Δ𝑝 ≥ Δp is the uncertainty in momentum 4𝜋 ℎ Δu is the uncertainty in velocity in m/s Δ𝑥 ∙ 𝑚Δ𝑢 ≥ m is the mass in kg 4𝜋 An electron in a hydrogen atom is known to have a velocity of 4.99×106 m/s + 5 percent. Using the uncertainty principle, calculate the minimum uncertainty in the position of the electron. (the mass of an electron is 9.11 x 10–31 kg) 21 21 The Schrödinger Equation and The Quantum Mechanical Description of the H–Atom Erwin Schrödinger derived a complex mathematical formula to incorporate the wave and particle characteristics of electrons.Wave behaviour is described with the wave function ψ. The probability of finding an electron in a certain area of space is proportional to ψ2 and is called electron density. Probability map of an Quantum Mechanics defines the region where the electron is most electron in an H atom likely to be at a given time The Schrödinger equation specifies possible energy states an electron can occupy in a hydrogen atom. The energy states and wave functions are characterized by a set of quantum numbers. Instead of referring to orbits as in the Bohr model, quantum numbers and wave functions describe atomic orbitals. 22 22 10  6/25/2024 Quantum Numbers Quantum numbers are required to describe the distribution of electron density in an atom (location of the electron.) There are three quantum numbers necessary to describe an atomic orbital. The principal quantum number (n) – designates size Larger values of n correspond to larger orbitals (higher energy). The allowed values of n are integral numbers: 1, 2, 3 and so forth. The value of n corresponds to the value of n in Bohr’s model of the hydrogen atom. A collection of orbitals with the same value of n is frequently called a shell. The angular moment quantum number (l) – describes shape The values of l are integers that depend on the value of the principal quantum number The allowed values of l range from 0 to n – 1. Example: If n = 2, l can be 0 or 1. l 0 1 2 3 Orbital Designation (Shape) s p d f A collection of orbitals with the same value of n and l is referred to as a subshell. The magnetic quantum number (ml) – specifies orientation/direction The values of ml are integers that depend on the value of the angular moment quantum number: – l,…0,…+l 23 23 Atomic Orbitals All s orbitals are spherical: One orientation: l =0 ml =0 angular momentum quantum principal quantum 2s number (l = 0) number (n = 2) ml = 0; only 1 orientation possible p orbitals are dumbbell shaped: Three orientations: l =1 ml = –1, 0, +1 d orbitals: Five orientations: l =2 ml = –2, –1, 0, +1, or +2 24 24 11  6/25/2024 Quantum Numbers Allowed Values of the Quantum Numbers n, l, and ml n l can be When l is ml can be 1 Only 0 0 Only 0 0 Only 0 2 0 or 1 Quantum 1 –1, 0, or +1 numbers 0 Only 0 designate 3 0, 1, or 2 1 –1, 0, or +1 shells, subshells, and 2 –2, –1, 0, +1, +2 orbitals. 0 Only 0 1 –1, 0, or +1 4 0, 1, 2, or 3 2 –2, –1, 0, +1, +2 3 –3, –2, –1, 0, +1, +2, +3 25 25 Atomic Orbitals The electron spin quantum number (ms ) is used to specify an electron’s spin. There are two possible directions of spin. Allowed values of ms are +½ and –½. To summarize quantum numbers: principal (n) – size angular (l ) – shape magnetic (ml) – orientation electron spin (ms) direction of spin Angular Principal (n=2) Momentum (l =1) 2px Related to the Magnetic 26 Quantum (ml =1) 26 12  6/25/2024 Practice What are the possible values for the magnetic quantum number (m l) when the principal quantum number (n) is 2 and the angular quantum number (l) is 0? List the values of n, l, and ml for each of the orbitals in a 2p subshell. Which of the following is a legitimate set of quantum numbers for n, l, and ml respectively, which corresponds to an 5f orbital? A. 5, 4, –4 B. 3, 3, – 1 C. 5, 4, 0 D. 5, 3, 0 Which of the following is a list of allowed quantum numbers for an electron? A. n = 1, l = 1, ml = 0, ms = ½ B. n = 2, l = 0, ml = 1, ms = ½ C. n = 3, l = 0, ml = 0, ms = ½ D. n = 4, l = 3, ml = 4, ms = –½ 27 27 Electron Configurations General rules for writing electron configurations: 1. Electrons will reside in the available orbitals of the lowest possible energy. 2. Each orbital can accommodate a maximum of two electrons. Up-Side Down 3. Electrons will not pair in degenerate orbitals if an empty orbital is available. Christmas Tree 4. Orbitals will fill in the order indicated in the figure. Periodic Table Method 29 29 13  6/25/2024 Electron Configurations The electron configuration describes how the electrons are distributed in the various atomic orbitals. In a ground state hydrogen atom, the electron is found in the 1s orbital. Ground state electron 2s 2p 2p 2p Energy configuration of hydrogen principal 1s1 number of electrons in (n = 1) the orbital or subshell ↿ The use of an up arrow indicates an electron with ms = + ½ angular momentum (l = 0) 1s 30 30 Electron Configurations If hydrogen’s electron is found in a higher energy orbital, the atom is in an excited state. Possible excited state electron ↿ configuration of hydrogen. 2s 2p 2p 2p 2s1 Energy 1s The helium emission spectrum is more complex than the hydrogen spectrum.There are more possible energy transitions in a helium atom because helium has two electrons. 31 31 14  6/25/2024 Electron Configurations In a multi-electron atoms, the energies of the atomic orbitals are split. 4d 4d 4d 4d 4d 5s 4p 4p 4p 3d 3d 3d 3d 3d Splitting of energy levels refers to the 4s splitting of a shell (n=3) into subshells 3p 3p 3p of different energies (3s, 3p, 3d) 3s Energy 2p 2p 2p 2s 1s 32 32 Electron Configurations According to the Pauli exclusion principle, no two electrons in an atom can have the same four quantum numbers. The Aufbau principle states that electrons are added to the lowest energy orbitals first before moving to higher energy orbitals. The ground state electron The ground state electron configuration of He (2 e–) configuration of Li (3 e–) 1s2 1s22s1 2p 2p 2p ↿ 2p 2p 2p 2s Energy 2s Energy The 3rd e– must go in the The 2nd e– has the next available orbital with the lowest possible energy ↿⇂ same n, l, and ml but ms is opposite in sign. ↿⇂ 1s 1s 33 33 15  6/25/2024 Electron Configurations The Aufbau principle states that electrons are added to the lowest energy orbitals first before moving to higher energy orbitals. The ground state electron The ground state electron configuration of Be (4 e–) configuration of B (5 e–) 1s22s2 1s22s22p1 ↿ ↿⇂ 2p 2p 2p ↿⇂ 2p 2p 2p 2s 2s Energy Energy ↿⇂ ↿⇂ 1s 1s 34 34 Electron Configurations According to Hund’s rule, the most stable arrangement of electrons is the one in which the number of electrons with the same spin is maximized. The ground state electron The ground state electron configuration of C (6 e–) configuration of N (7 e–) 1s22s22p2 1s22s22p3 ↿ ↿ ↿ ↿ ↿ ↿⇂ 2p 2p 2p ↿⇂ 2p 2p 2p 2s 2s Energy Energy The 2p orbitals are of equal ↿⇂ energy, or degenerate. ↿⇂ 1s Put 1 electron in each 1s 35 before pairing (Hund’s rule). 35 16  6/25/2024 Electron Configurations According to Hund’s rule, the most stable arrangement of electrons is the one in which the number of electrons with the same spin is maximized. When there are one or more unpaired electrons, as in the case of oxygen and fluorine, the atom is called paramagnetic. The ground state electron The ground state electron configuration of O (8 e–) configuration of F (9 e–) 1s22s22p4 1s22s22p5 ↿⇂ ↿ ↿ ↿⇂ ↿⇂ ↿ ↿⇂ 2p 2p 2p ↿⇂ 2p 2p 2p 2s 2s Energy Energy Once all the 2p orbitals are singly occupied, ↿⇂ additional electrons will have to pair with those ↿⇂ 1s already in the orbitals. 1s 36 36 Electron Configurations When all electrons in an atom are paired, as in neon, it is called diamagnetic. The ground state electron c