Quantum Physics and Atomic Structure: Wave-Particle Duality and Atomic Spectroscopy, Summaries of Chemistry

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R. Chang, J. Overby,

General chemistry

Exam 1 material begins: 8/28 lecture notes Chemistry = studying properties of matter by particles that make them up

• 91 natural atoms Structure of atom
• nucleus has lots of dense mass with all + charge (protons and neutrons)
• most of atom is empty space
• number protons of nucleus = number of electrons in orbit
• protons and electrons have equal but opposite charge
• protons and neutrons have similar mass but electrons are much less massive Elements
• atomic number = number of protons in nucleus
• SYMBOL NO NAME ON PERIODIC TABLES ON TESTS Isotopes
• different number of neutrons = different isotope
• mass number = # of protons plus number of neutrons Ions
• has missing or extra electrons
• negative charged ions = anion (extra electrons)
• positively charged ions = cations (missing electrons)
• can only make ions by changing electrons CHANGING PROTONS CHANGES THE ELEMENT Atomic mass
• weighted value based on natural abundance of isotopes which naturally occur
• unit is ami or grams/mole (g/mol) Dimensional analysis
• ALWAYS REPORT UNITS IN ANSWERS ON HW AND EXAMS
• unit conversion: current unit= desired unit/current unit
• make the fraction equal to one (numerator must = denominator in different units) and cross of both sides
• 1ml = 1cm^
• 1in = 2.54cm 8/30 lecture notes
• 10^9 nm in meter
• Avogadro’s number: a constant which tells exactly how many molecules per mole (1 mole = 6.022 x 10^23 particles)
• this number comes from the exact number of atoms in 12 grams of pure carbon- 12

• the more transferred energy from light the more kinetic energy with electron
• classical electromagnetic theory would say light is a wave so the energy of the wave is proportional to the amplitude only (predicting the greater intensity of light the more kinetic energy in electrons)
• this was experimented and no relation was found between kinetic energy of electrons but there was a relationship between intensity and number of electrons
• they did find that after a point ( 0 or threshold frequency) there is a constant increase of kinetic energy as the frequency is increased
• after threshold frequency number of electrons stayed constant when frequency increased
• Einstein concluded that light is acting as a particle in this situation and wave in other cases
• frequency = speed/ wavelength
• energy of particles of light proportional to frequency
• number of particles of light proportional to intensity (more photons of light = more electrons released) 9/4 lecture notes Einstein: Light can be described as a collection of packets of energy (photons)
• energy of one photon = plancks constant times frequency (Ephoton=h)  since we concluded energy of light particles proportional to frequency
• energy in = energy out
• in photoelectric problem if there is leftover energy after the binding energy is used it turns into Kinetic energy
• if there is just enough for binding energy then the frequency is the threshold frequency
• since electrons are ejected with kinetic energy  binding energy is usually < Ephoton
• if binding energy > Ephoton then no electrons are released with KEe-
• if binding energy = Ephoton then electrons are released with no kinetic energy Can electrons behave as waves as well?
• Atomic spectrocity: exciting elements to cause different colored light (neon signs)
• if electrons obeyed classical physics there would be a full continuous spectrum of light but there are major gaps on the spectrum (it jumps from one color to another with no transition) The Bohr Model
• energy of atom is quantized
• electrons are at fixed distances from the nucleus
• this explains the spectrum because electrons don’t exist between the levels meaning there is no transition between colors
• the further from nucleus the higher energy
• electrons want to lose energy and move closer to nucleus
• energy released in light is energy released when electrons change energy levels Double slit experiment with electrons
• with one slit electrons show interference pattern of a particle
• with two slits electrons show interference pattern of a wave

• when observed with two slits the electrons went back to acting as a particle De Broglie relation
• all matter has wavelength but its not relevant unless the matter is tiny
• wavelenghth is inversely proportional to momentum Heisenberg’s uncertainty principal
• if we observe either position or momentum of electron we will not be certain of the other Indeterminacy
• unlike in classical mechanics when under the exact same circumstances matter does the same thing in quantum we can only statistically guess what particles will do Quantum and the atom
• Schrodinger equation: h=E Quantum numbers
• principle quantum number = n (determines size and energy of orbital)
• each orbital has a n value (energy level of electron) which can be any positive integer (1, 2, 3…)
• the smaller the n value the closer to the nucleus (lower energy level)
• angular momentum = L which can be any number from 0 (n-1)
• when L = 0  S orbital
• when L = 1  P orbital
• when L = 2  D orbital
• when L = 3  F orbital
• magnetic quantum number = mL which can range from - LL
• mL describes how many of each type of orbital there are [ex. If L=1 there are 3 P orbitals since there are 3 mL values (-1, 0, 1)]
• spin number = ms describes spin of electron (can only be ½ or - ½)
• since each orbital can only hold 2 electrons if two electrons are in the same orbital they have opposite spin numbers
• when naming orbitals the n value goes first (ex 3s orbital)
• wave function n(x)=Asin(n𝑢x/L) where n = 1, 2, 3, etc.
• helpful video I found: https://www.youtube.com/watch?v=Aoi4j8es4gQ 9/6 Chapter 8 reading notes Periodic table
• atomic mass increase left to right
• similar properties in columns
• periodic properties: atomic radius, ionization energy, electron affinity, density, metallic character
• periodic properties are predictable based on location on periodic table

Noble gases

• unreactive and stable
• 8 valence (except He has 2)
• full outer quantum levels Halogens
• one electron short of being full
• tend to form anions by gaining electron Alkali metals
• one electron more than noble gas
• tend to give away electron to become cation Alkaline earth
• have two more electrons than noble gas
• tend to give away two to become cation Atomic radius
• average radius of element
• n increases and radius increase as you move down on table
• as you move from right to left atomic radius increases Effective nuclear charge
• Zeff=Z-S
• Z = charge of nucleus (protons)
• S = number of shielding electrons (between valence and nucleus) = number of core electrons
• effective nuclear charge increase from left to right because core stays same but charge on nucleus grows
• as you move down there is effectively no change in effective nuclear charge
• because the attraction of electrons to nucleus increase with eff nuclear charge the atomic radius shrinks as effective nuclear charge grows (left to right) Ionic radii
• anions are larger in terms of atomic radius than neutral atom due to repulsion amongst valence electrons
• cations are smaller in terms of atomic radius than neutral atom due to lack of repulsion Ionization energy
• energy to remove electron from neutral atom
• increases from bottom to top
• increases from left to right
• opposite of atomic radius trend because the closer to nucleus the harder to remove Chemical bonds

• ionic: metal and nonmetal
• covalent: two or more none metals
• metallic: not important for this class Ionic bonds
• transfer electrons between two atoms
• metalscations
• nonmetalsanions
• opposite charges attract through electrostatic forces
• always charge neutral
• makes lattice (3 dimensional uniform alternating anions and cations) Covalent bonds
• sharing electrons
• empirical formula: relative number of atoms of each element in compound (accurate ratios)
• molecular formula: actual number of atoms of each element
• structural formula: sketch
• molecular model: 3d model Naming
• Ionic or covalent? binary ionic
• case 1: ide at the end
• case 2: put charge of ion in parenthesis in roman numerals ex fe3+ = iron(III) 9/18 lecture notes Acids
• arrhenius definition: substance that produces H+ ions in aqueous solution
• has H as first element Naming acids
• binary (only two elements): hydro + element name + ic + acid
• oxyacids (contain oxygen): if it ends with ate: base name of oxyanion + ic + acid, if it ends in ous: base name of oxyanion + ous + acid Molecular compounds
• covalent bonds
• multiple stable forms of combinations of elements Naming molecular compounds
• latin prefixes
• first element: if only one atom of first element drop the mono
• add suffixes as well

• 1 carbon: Ch4 = methane
• 2 carbon: H 3 C(single bond)CH3 ethane, H 2 C(double bond)CH2 ethene, HC(triple bond)CH ethyne
• more than two carbons: don’t have to know how to write names just know how to recognize names into molecules Functional groups
• R on chain is shortand for a carbon/carbon chain or hydrogen (usually carbon)
• giant list to memorize… yay Functional groups in naming
• prefixinfixsuffix
• prefix = number of carbons
• infix= carbon-carbon bond character (an, en, yn)
• suffix = functional group  ex: ketone = “…one” alcohol = “…ol” amine = “…amine”
• ex. Ethanol: eth = 2 carbon, an = single bond, ol = alcohol functional group Why do atoms bond
• lower their energy Bond polarity
• pure covalent bonds = electrons equally shared
• polar covalent bonds = electrons shared unequally (one is neg. one is pos.)
• ionic bonds = electrons not shared Electronegativity
• how much an atom wants electron density (more likely to have partial negative charge in polar bond)
• as you move left to right on the table electronegativity increases
• as you move from bottom to top the electronegativity increases
• flourine has highest electronegativity since noble gases don’t have electronegativity 9/27 lecture notes Formal charge
• formal charge= # valence electrons – # nonbonding electrons – # ½ bonding electrons
• calculated for each atom in structure
• fictitious charge
• charge atom would have if all bonding electrons shared equally rules for using formal charge to decide between competing structures
• sum of all formal charges in a neutral molecule = 0
• sum of all formal charges in an ion = charge of ion
• on individual atoms small (or 0) charge is better

• when you must have formal charge /= to zero put negative formal charge on most electronegative atom Exceptions to the Lewis diagram octet rule
• free radical: molecules/ions with odd number of electrons (not common)
• incomplete octets: less than an octet of electrons in total around a central atom (not common)
• expanded octet: more than an octet of electrons in total around central atom, only elements on the 3rd^ row of the periodic table and below can have expanded octets with up to 12- 14 electrons allowed (common)

Exam 2 material begins

10/9 lecture notes Electron group geometry

• five arrangements of electron groups around atom
• linear, trigonal planar, tetrahedral, bipyramidal, octahedral Vsper theory: effect of lone pairs
• electron geometry: geometric arrangement of electron groups
• molecular geometry: geometrical arrangement of molecules
• molecular changes shape by not considering lone pairs
• lone pair groups take more space and make bond angles smaller than expected
• the more lone pairs on central atom the smaller than expected the bond angles Derivatives of trigonal bipyramidal electron geometry
• when there are five electron groups and lone pairs the lone pairs will take the equatorial position
• bond angles between equatorial positions is less than 120 degrees
• bond angles between equatorial and axial is less than 90 degrees
• the more lone pairs in equatorial position the lower the bond angle
• when there are 5 electron groups and two are lone pairs the result is t shaped
• when there are 5 electron groups and three are lone pairs the result is linear Derivatives of octahedral electron geometry
• when there are six electron groups and some are lone pairs each even number lone pair will take position opposite the previous lone pair
• when there are 6 electron groups and one is a lone pair the result is a square pyramid(bond angles are less than 90 degrees between axial and equatorial)
• when there are 6 electron groups and two are lone pairs the result is a square planar shape(bond angles are 90 degrees between axial and equatorial) Molecular dipole moments
• chemical bonds can be polar

Which hybridization?

• look at vespr geometry first and determine logically Lecture notes 10/ Writing and balancing chemical reactions
• reactant products
• stoichiometric coefficients = coefficients representing moles in front of chemical formulas on chemical reaction formulas
• stoichiometry: balancing equations by balancing atoms
• limiting reactant: reactant that is used up first in chemical reaction leaving leftovers if the other one
• percent yield = actual yield/theoretical yield x 100 Combustion reactions
• reaction of substance with O2 producing compounds containing oxygen
• hydrocarbons always combust involving CO2 or H2O as products
• always exothermic Lecture notes 10/ Solutions
• homogeneous mixture
• solute: minor which changes state
• solvent: major which stays same Concentration
• dilute solution- less solute
• concentrated solution- more solute
• concentration unit = molarity (M)
• M = amount of solute (mol)/volume of solution (L)
• dilution equation: M1(V1)=M2(V2) Solubility
• if solute-solute interaction is more favorable it is not soluble
• if solute-solvent interaction is more favorable it is soluble Electrolytes
• if it a solute dissolves into water and conducts electricity it conducts electricity its an electrolyte
• if a solute dissolves into water and conducts electricity it doesn’t conduct electricity its not an electrolyte

Solubility of ionic compounds

• long list of rules given on exam no memorize Aqueous reactions
• spectator ions: kinda just hang out and don’t change during reaction
• a spectator ion must be present if solution would be charged otherwise
• precipitate = solid that falls out of solution after reaction
• to predict reaction results switch the anion and cation in reactants
• acid: substance that produces H+ ions in aqueous solution
• base: substance that produces OH- ions in aqueous solution
• strong acids/bases completely break into ions and are great electrolytes
• weak acids/bases only partially break into ions staying partially as the original compound and are bad electrolytes Types of aqueous reactions (can be more than one)
• precipitation reactions- one or more of the products is insoluble and fall out as solid
• acid based reactions- also called neutralization reaction
• gas-evolution reactions- one product bubbles out as gas
• oxidation-reduction (redox) reactions Lecture notes 10/ Acid base reactions
• acid + base  salt +water
• monoprotic acids: can give off only one H+ ion in aqueous reaction since they only have one H atom (ex. HCl)
• polyprotic acids: can give off more than one H+ ion in aqueous reaction since they have multiple H atom (ex. H2SO4)
• total ionic equations are written with + and – for ions
• net ionic equations get rid of the spectator ions Gas evolution reaction (on mastering chem but not exam)
• identified by product bubbling out as gas oxidation-reduction (redox) reactions (on exam)
• identified by electrons transferring between reactants
• oxidation: increases oxygen content in product (loss of electrons)
• reduction: decreases oxygen content in product (gain of electrons)
• oxidation and reduction change the “oxidation number” of the other reactant (reduction reduces and oxidation increases)
• rules for oxidation numbers is on a sheet given on the exam
• reactant being reduced is an oxidizing agent
• reactant being oxidized is a reducing agent

• standard enthalpies/heat of formation for compounds will be given on table for exam Properties of gases
• fill container uniformly
• exerts pressure on surroundings
• changes volume with temp. and pressure
• STP = standard temp and pressure (T = 0 celcius and p = one bar = 1 atmosphere)
• molar volume = volume occupied by one mole ideal gas at STP = 22.4 L
• ideal gas: volume of one molecule is insignificant compared to overall volume, they also do not interact with eachother Pressure
• pressure = force per unit area (p = f/a)
• SI unit: newton/meter^2 = 1 pascal (Pa) (newton = n = kg x m) Atmospheric pressure
• force exerted on planet by weight of atmosphere
• pressure decreases with increasing altitude
• Patm = F/A = mg/A (mg = acceleration due to gravity = 9.8 m/s^2 on earth) Ideal gas law
• boyles law: P and volume are inversely proportional
• charles law: temp and volume are directly proportional
• avogadros law: number of moles (n) and volume are directly proportional
• amontons law: temp and pressure are directly proportional
• therefore PV  nT
• by adding the universal gas constant (R = .08206) we find that PV=nRT (the ideal gas law) Deriving combined gas law from ideal gas law
• initial state  final state
• P 1 V 1 = n 1 RT 1 and P 2 V 2
• R = P 1 V 1 /N 1 T 1 and P 2 V 2 /N 2 T 2
• therefore P 1 V 1 /N 1 T 1 = P 2 V 2 /N 2 T 2 (combined gas law)
• if moled don’t change n 1 =n 2 Daltons law of partial pressures
• Ptotal = Pn
• ex. Patm = PN2 + PO2…
• Pn= partial pressure = nnRT/Vtot
• P 1 /Ptot = n 1 /ntot (n 1 /ntot defined as mole fraction (x 1 ))
• therefore P 1 = X 1 (Ptot) Lecture notes 10/

Real gases

• when STP is plugged into ideal gas law the constant of 241 L
• this is inaccurate in reality since ideal gases assume molecules don’t react with each other or take up space which they do

Exam three material begins

Lecture notes 11/ Intermolecular forces

• exist between all molecules and atoms
• hold liquids and solids together
• responsible for existence of condensed states
• state of matter depends on magnitude of the intermolecular forces
• when thermal energy is high relative to intermolecular forces it will be gas
• when thermal energy is low relative to intermolecular forces it will be solid or liquid Phase changes
• input or output of energy
• condensing = exothermic (gasliquidsolid)
• expanding = endothermic (solidliquidgas) Attraction forces
• room temp strong attractive force means liquid or solid
• stronger attractive forces means higher boiling and freezing point
• forces created by charges (positive to negative)
• larger charge = stronger attraction
• longer distance = weaker attraction
• intermolecular forces are weaker than intramolecular forces (between atoms) because they have smaller charges and larger distances
• stronger the attraction the more separation energy required
• boiling requires adding enough energy to overcome attractions but not breaking covalent bonds Types of intermolecular forces
• dispersion force: temporary polarity in molecules due to unequal electron distribution
• dipole-dipole: permanent polarity in molecule due to structure of molecule
• hydrogen bonds: an especially strong dipole-dipole attraction between hydrogen and a very electronegative atom (only oxygen, nitrogen, and fluorine)
• ion-dipole: mixing ionic compound and polar compound Dispersion forces
• weakest forces

• physical states: homogeneous reactions occur fastest heterogeneous reactions can only occur where phases meet
• concentration: the closer they are the higher chance they react
• temperature: as temp increases kinetic energy causes the molecules to collide and react unimolecular reaction: A  B
• brackets around compound or element means concentration
• time = t
• rate of formation of B = [B]/t
• rate of disappearance of A = [A]/t
• these equations show how fast reaction is occurring Rates of reaction
• to find average rate ([B]/t) take two points on rate of formation of B graph and use formula: [B]/t=[B] 2 - [B] 1 /t 2 - t 1
• average rate is in units Molar per second (M/s)
• Rate = [B]/t = - [A]/t
• in multimolecular equations you must include the stoichiometric coefficients
• so for reaction: aA + bB  cC + dD the rate = (-1/a)([A]/t) = (-1/b)([B]/t) = (1/c)([C]/t) = (1/d)([D]/t) Instantaneous rates
• rate at a specific point in time
• on graph it’s the tangential slope at the point (derivative) Rate law
• rate is directly proportional to the concentrations of the reactants
• rate = k [A]m[B]n
• rate constant k: units vary (rate must be M/s though) it is a constant though, so it is independent of [A] and [B] but can change with temperature or catalyst
• m and n: partial reaction orders
• if m = 1 the reaction is referred to as “reaction is first order in A” and rate is directly proportional to [A]^1
• if n = 2 the reaction is referred to as “reaction is second order in B” and rate is directly proportional to [B]^2
• m + n = overall reaction order
• reaction orders must be determined experimentally (method of initial rates)
• method of initial rate: know that rate = k [A]m[B]n^ and use the data collected in experiments showing how many M of molecule there is and logically calculate Lecture notes 11/ Integrated rate laws
• gets us to concentration time relationship

• helpful since its super hard to find rate of reaction the instant it starts First order reaction
• rate = k[A]^1
• rate is directly proportional to [A]
• rate slows as reaction proceeds
• k is in units s-^1 Integrated first order rate law
• derivative = d
• rate = - d[A]/dt = k[A]^1
• so - d[A]/dt = k[A]^1
• we can then derive the integrated first order rate law: ln[A]t = - kt + ln[A]q
• the integrated first order rate law is in y = mx + b form so it can be plotted linearly
• when plotted the slope will be - k
• another form of the first order integrated rate law is [A]t = [A] 0 e-kt Half-life in the first order (t1/2) derivation [A]t1/2 = ½[A] 0 [A]t/[A] 0 = ½ ln([A]t/[A] 0 ) = - kt (when inserted into linear form of the integrated first order law) ln(1/2) = - kt1/
  • 0.693 = - kt1/ t1/2 = 0.693/K Second order reaction
• rate = k[A]^2
• rate is proportional to [A]^2
• rate is more sensitive to [A] Integrated second order rate law
• rate = k[A]^2 = - d[A]/dt
• the second order integrated rate law can then be derived: 1/[A]t = kt +1/[A] 0
• this is linear and has slope k when plotted
• half-life in second order: since [A]t = ½[A] 0 t1/2 = 1/k[A] 0
• the half-life in the second order is different since the concentration plays a role in the half-life calculation
• this law only applies when one of the reactants is in the second order not necessarily when the reaction is in the second order overall Integrated rate law of the zero order
• rate = k[A]^0
• the integrated rate law: [A] = - kt + [A] 0
• half-life: t1/2 = [A] 0 /2k