Chem. 14A Scerri
* What numbers are associated with periodicity? *
* 2,8,8,18,18,32,32 * 2n^2
* What is stoichiometry based on? *
* Calculations based on the nucleus (protons and neutrons), because electrons are so light * Depend on law of conservation of matter
* What is a pair reversal? Give an example.
* Certain elements get sorted into the wrong periodic group (column) * Happens because atomic weights are averages of the isotopes * This is solved when rearranging elements by Z, or atomic number * Example is Argon and Potassium, or Tellurium and Iodine
* Define periodic law.
* Chemical properties of elements are a periodic function of their atomic numbers
* What are the main types of periodic tables? *
* Left-step uses orbital filling, not valence filling * f-block, d, p, s * Long form has the Lanthanides and Actinides included in the main body of the table, organized by valence shell filling * Medium-long form is long form with the Lanthanides and Actinides separated and placed below * Short form has 8 columns
* What was Mendeleev's Periodic Table like?
* Originally ordered by atomic weight, because atomic numbers were not discovered yet * Mendeleev actually made several predictions on the properties of undiscovered elements (Gallium, Germanium, Cesium) * Had gaps in the table * No noble gases * Now known as the "short-form" table, with eight columns
* What ideas lead to the periodic table?
* Prout discovered that many elements had whole number multiples of the weight of Hydrogen * Prout's Hypothesis: other elements made up of H-atoms * True in the sense of protons * Astrophysically, all elements literally formed from H and He
Explain what a triad is, its characteristics, and give an example.
* Triad groups were observed before the periodic table * Way or organizing elements into sets of threes * In the same vertical column in periodic table * Middle element has characteristics approximately average of the top and bottom * Atomic weight, reactivity, density, atomic number * Reactivity increases down the triad * EX: Lithium, Sodium, Potassium (Li, Na, K) * EX2: Potassium, Rubidium, Cesium (K, Rb, Cs) * These triads never start at the top of the block
* What are transuranium elements? *
* Uranium is the last naturally occurring element, so anything after that * Currently from 93 to 118, inclusive * Few have practical applications * Plutonium: nukes, Americium: smoke detectors * Higher atomic numbers are more unstable * Help test theories of nuclear stability * Relativistic velocities of inner electrons make it difficult to study super-heavy elements * Do not behave as expected based on periodicity * First was neptunium in 1940 * Possible up to 137, or 172, or 173
Orbital Numbers (must memorize)
* n = 1, 2, 3; for ex., 3p = 3 is n * ℓ = (n-1), (n-2).... 0 * mℓ = -ℓ .... 0 ..... ℓ s orbital: ℓ = 0 p orbital: ℓ = 1 d orbital: ℓ = 2 f orbital: ℓ = 3 g orbital: ℓ = 4
Empirical Formula to Molecular Formula
If Ascorbic acid has a formula weight of 176 amu, what is the molecular formula? - Get the empirical formula = C3H4O3 - Substitute for atomic weights of C, H & O to determined the formula weight of the empirical weight ~ 88 - Molecular Formula = Formula Mass/Empirical Formula Mass (176/88) = 2 - 2 (C3H4O3) = C6H8O6
Chemical Periodicity
If the elements are ordered according to Atomic Number (Z), there is an approximate repetition in chemical and physical properties after certain varying intervals (2, 8, 8, 18, 18, 32, 32)
h (planck's constant)
In going from work function of an element to the minimum frequency required to eject an electron, divide work function by ____________. psi/h = mu
4s
Ions of transition metals involve loss of _____ electrons first. This orbitals also fills last.
pre-scientific, paradigm, anomalies, crisis, revolution
Kuhnian scheme dictate that for any science, there was a: 1. ________ stage (vague, colliding ideas, chaotic, no body of knowledge) 2. _________ (science takes shape, begins to become solid, has some evidence) 3. __________ (doesn't follow the pattern) 4. __________ (number of anomalies increase) 5. ___________ (overthrow of original scientific theories once anomalies increase)
Empirical Formula from Analysis Data
Mass % x 1 mol/amu = mol --> Do this for all Molecules --> Divide by smallest mole to get ratios = Empirical Formula
What are pair reversals? Why do they occur in terms of protons and neutrons?
Occurred when the periodic table was ordered by atomic weight. Even though the second element had fewer protons the neutrons made the atomic weight higher. This caused confusion because both elements were placed in columns that did not share their chemical or physical properties. This is why the periodic table is now lined up by atomic # and not weight.
Aufbau Principle
Orbitals are filled in order of increasing energy.
quantized
Planck's solution to the UV catastrophe (curve of intensity against wavelength shows that there is maximum intensity at a lower wavelength or higher frequency, as seen in classical mechanics) was that he assumed that energy could be __________. Thus energy could be any multiple of hv, but nothing in between. E=hv
quantization
Shrodinger believed that if an electron is like a wave, its motion should be expressible by a wave equation. Thus ________ emerges as a natural consequence of confinement or boundary conditions.
Bohr
The ________ Model attempted to solve the problems of the Rutherford model by assuming that: 1. Electrons in orbit do not radiate. They only emit energy when they change orbits. 2. Discrete atomic spectra exist because when electrons move from one energy level (orbit) to another, a particular energy is emitted which corresponds to a specific frequency in atomic spectra.
Energy, hydrogenic
The ___________ of any orbit En = -R(Z²/n²), where R is the Rydberg constant 2.18 x 10⁻¹⁸ J. However, this equation only works for ____________ atoms.
f,d, p, s, periodicity, He
The blocks of the left-step periodic table are arranged as follows: __________________ One possible advantage to using the left-step periodic table is that the ____________ of the elements is more consistent (2,2,8,8,18,18,32). One possible disadvantage to using this periodic table is that ______ doesn't belong with the alkaline earth metals, because those elements are highly reactive, yet He is a gas and is un-reactive (its properties don't match up with the elements below it.
s, f, d, p, atomic number
The blocks of the long-form periodic table are arranged as follows: __________________ One possible advantage to using the long-form periodic table is that the elements are arranged based on ____________ in an orderly fashion without any jumps or skips. It also relates the position of an element in the table with its electronic configuration. One possible disadvantage to this is that it's inconvenient or too long to reproduce in a textbook or other text.
3d⁵ 4s¹
The electron configuration of Cr is: [Ar] ___________ Note that 3d fills first, because 3d has a lower energy than 4s.
photoelectric effect
The equation explaining the __________ is as follows: E = psi + KE (Light energy absorbed by metal) = Work Function + (Kinetic Energy of Electron) hv = hv₀ + KE. The replacement of E and psi with hv showed the relationship between frequency and kinetic energy, and also implied that a threshold energy is needed to eject electrons from metal.
electron
The kinetic energy of an _______ being ejected from the absorption of electromagnetic radiation onto a metal plate is KE = 1/2(mass of electron)(velocity)²
quantized
The most significant conclusion to be drawn from the observations of the photoelectric effect is that light is contained in discrete packages called photons, which means that light energy is _________. It showed the particle nature of light.
repulsion
The presence of electron-electron ___________ in many electron systems removes the degeneracy in H atom, where all orbitals which share the same n value have the same energy.
B, O
The two anomalies within the overall trend in increasing IE across the 2nd period are ____ and ____. The first anomaly occurs because removing the one electron from the 2p orbital would return the atom to a lower energy state, which is more stable and desirable. The second anomaly occurs because putting two electrons into one suborbital increases electron-electron repulsion, which makes the element unstable, thus removing that extra electron decreases E-E repulsion.
Radial and Planar Nodes
Total nodes = n-1 Radial nodes = [n - ℓ -1] Planar nodes = ℓ ex. 2p; total nodes = 1; radial nodes = 0; planar nodes = 1
Pauli's Exclusion Principle
Two electrons can occupy a single orbital, but they must have opposite spin. Each electron in an atom also has a unique set of four quantum numbers describing it.
Rutherford
Two problems with the ______________ model include: 1. Electrons would emit electromagnetic radiation and collapse into the center of the nucleus. 2. Model didn't explain discrete atomic spectra; The spectra is not continuous; there are gaps in the wavelength that are absorbed or emitted.
Bohr
Two problems with the ______________ model include: 1. Why do electrons occur in specific energy levels in the first place? 2. The model only applies to the hydrogen atom or hydrogenic (one-electron) systems
modes, nodes
Vibrations occur in a number of ______ or n half cycles (half of a wavelength), and each mode contains n-1 _______.
kinetic energy
When asked to find the ____________ required to eject electrons, use the equation h∨ - h∨₀ Input the frequency found in the previous part and multiply by planck's constant. Then subtract by the given work function.
velocity
When asked to find the maximum ____________ of which the electrons are traveling at, use the equation √[(2KE)/mass of electron] Input the kinetic energy found in the previous part and divide by mass of an electron, which is 9.1 x 10⁻³¹ kg.
Hund's Rule
When electrons occupy orbitals with the same energy, they are put in one by one in separate sub-orbitals first so that repulsion between the electrons are lessened.
The periodic law
When elements are ordered according to Z or the atomic number of atoms, there is an approximate repetition in chemical and physical property after certain varying intervals.
Hund's Rule
When filling a set of orbitals with equal energies as many different orbitals as possible are occupied and spins are parallel.
up, let it be
When rounding sig figs: If the number before the 5 is odd, round ___. If the number before the 5 is even, ______.
Karl Popper
___________'s philosophy of science state that a theory or branch of knowledge is scientific if it can be refuted by evidence. Also, laws are beneath theories, and theories can't be proven.
transition
____________ energy problems: ∆E = -R∞(z)²[1/(nfinal)²-1/(ninitial)²] set this equal to h∨, and solve for frequency; then input ∆E into the equation λ = hc/E and solve for wavelength.
Pair reversals
_______________ occur because of the isotopes used to calculate the average mass of an element. The number of protons corresponding to atomic number is the same for all isotopes, but the number of neutrons varies. One element may have a higher atomic number, but lighter weighing isotopes, and thus its atomic mass is lower than an element with a lower atomic number, and arranging the elements by atomic mass would put it in front of the other element when it should really be behind it.
Theory
a highly supported body of knowledge or framework such as quantum theory or Einstein's theory of relativity.
Calculate De Broglie λ of
a) A 0.500 kg object moving at 20.00 m/s b) An electron moving at 1000 m/s Assume h=6.626x10^-34kg m^2/s m(e)= 9.109x10^-31kg - λ=h/m(mass)v(velocity a) λ=h/.500kg x 20.00m/s = 6.63x10^-35 b) λ=h/9.109x10^-31kg x 1000m/s = 7.274x10^-7m
Limiting Reagent
*Calculations must be based on the limiting reagent. Ex. If 1.5 mol of Al are allowed to react with 3.0 mol of Cl2. 1) What is the limiting reagent? 2) How many moles of AlCl3 are formed? --------------------------------------------- 1) Balance Equation 2Al+3Cl2->2AlCl3; - Limiting Reagent; mol-mol ratio (1.5 molAl x 3 mol Cl2/2mol Al = 2.25 moles Cl2 (needed Cl2) 2) Since there are 3 mol Cl2 and we need 2.25, Cl2 is in excess - Use limiting reagent; 1.5 mol Al x 2 mol AlCl3/2 mol Al = 1.5 mol AlCl3
Explain the photoelectric effect briefly.
- A beam of light shine onto a metal, momentum and energy is transferred to the metal, some e-'s bound in the metal are released and acquire kinetic energy - It shows how light energy is converted into electrical energy. - Intensity=brightness, it makes no difference to the activity of the electrons
Karl Popper
- A theory or branch of knowledge is scientific if it can be refuted by evidence. - If it cannot be refuted it is not scientific. - Science proceeds via 'Conjecture and Refutation' - All theories are eventually refuted
What was the problem with the photoelectric effect and how did Einstein solve it?
- According to the classical wave theory of light, the intensity of the light determines the amplitude of the wave, and so a greater light intensity should cause the electrons on the metal to oscillate more violently and to be ejected with a greater kinetic energy. - In contrast, the experiment showed that the kinetic energy of the ejected electrons depends on the frequency of the light. - Instead of assuming that the electronic oscillators had energies given by Planck's formula, Einstein assumed that the radiation itself consisted of packets of energy
Properties of Waves
- Amplitude: height - λ: from crest to crest (360 deg.) - Frequency: how many times per second the wave reaches its crest (measured in Hz) - Period: number of complete cycles/sec. - frequency>wavelength; frequency<wavelength
Louis De Broglie
- Assumed that particles behave as waves - When electrons are fired at an obstacle waves are formed - De Broglie's equation for wavelength of particles
What are the atomic radii trends?
- Atomic Radii is the size of the atom - Increases as you go down the table because filling larger orbitals - Decreases as you go to the right of the table because proton (+) charge in the nucleus increases, pulling electrons closer to the center
Interconversions of mass
- Calculate the # of moles of glucose, C6H12O6, present in 5.380g of the substance - 1 mole of glucose = 180.0g - 5.380g x 1 mol/180.0g = 0.0298 mol (4 sig figs)
Problem on Induction
- Consider the statement: All swans are white. - Impossible to prove
Diffraction and Interference
- Constructive Interference: when two waves follow each other, they combine and become a big wave and thus brighter [nλ] - Destructive Interference: when two waves have a path length distance of 1/2, when they combine they become a line and thus darkness [(n+1/2)λ]
What is wrong with Rutherford's model of the atom?
- Electrons orbit randomly - does not say anything about the arrangement of the electrons
Different Models of the Atom
- J.J. Thomson discovered the electron (the first sub-atomic particle) - J.J. Thomson: Plum pudding model; atom is positive and there are electrons embedded in the atom - R.A. Millikan determined the charge of an electron - Mass could now be calculated - E. Rutherford examined the scattering of alpha radiation by atoms of gold (fired alpha particles on a thin gold sheet, some went through and some bounced off) Nuclear atom was born
Pauli Exclusion Principle
- No two electrons in an atom can have the same 4 quantum numbers (can share 3 but not 4) - Applies to electrons, protons and neutrons, but NOT photons - Exclusion Principle: only two electrons can occupy the same orbital and they must have opposite spins
Kuhnian Scheme
- Pre-scientific stage is chaotic and vague - Then the paradigm is formed - Anomalies (things that went wrong) -ex. Newton's mechanics couldn't explain the eclipse where something orbits the sun changes (pg. 7) - Crisis (too much anomalies, too much to ignore) - Revolution (Happens suddenly, Quantum mechanics was next) and the cycle will continue.
Transuranium Elements
- elements after 93 are synthetic (don't exist in nature) - very unstable as the atomic # goes up - they are of great importance because they provide a means of testing theories of nuclear stability in extreme conditions - the study of these elements requires a combination of quantum mechanics and special relativity - first to be synthesized was 93Np - most recently synthesized is element 117
Quantization
- emerges as a natural consequence of confinement or boundary conditions - This is how the Schrödinger equation goes beyond the Bohr model. - Bohr assumed electron energy was quantized, Schrödinger derived it - Standing wave solutions of the Schrödinger equation are called ORBITALS (name is deceptive, there is no path or literal orbit)
Quantum Mechanics
- for very small objects Newtonian, or classical, mechanics break it down - for very fast moving objects and/or very large masses relativity theory is required - for middle sized objects and small velocities Quantum Mechanics and relativity merge into classical mechanics
How did Bohr attempt to resolve the problems with Rutherford's model of the atom?
- his model better explains the physical presentation of the atom - offered precise orbitals for electrons - preserved the stability of atoms and matter - assumed existence of a ground state (lower energy state) - quantization of angular momentum
Percent Yield
Consider the reaction, 2H2 + CO --> CH3OH Suppose 68.5kg of CO is reacted with 8.60kg of H2. Calculate the % yield of methanol if 3.57 x 10^4g of CH3OH is actually produced. 1) Find moles of H2 and CO; convert kg to g (1000g/1kg) 2) Determine limiting reagent - mol-to-mol ratio => in this case, H2 is limiting reagent 3) Base calculations on moles of H2 present 4) Theoretical Yield; - mol-to-mol ratio of 1 mol CH3OH/2 mol H2 - turn to grams (get the mass) =>6.86 x 10^4g 5) % yield = actual yield/theoretical yield ; (3.57/6.86)x100
nλ, 1/2nλ
Constructive interference is ______, whereas destructive interference is _______.
increase, decrease
Across any period, an overall __________ in ionization energy occurs due to increasing Z effective. Down any group, an overall ____________ in ionization energy occurs due to an increase in atomic radius, which makes it easier to ionize electrons.
fits
Asked to figure out whether an element _____ in with a certain group. Consider: Triad, Types of ions it forms, and What type of element it is (gas, nonmetal, metal)
19, 21
At z=_____, the 4s orbital fills first because the 4s orbital has a lower energy than the 3d orbital. However, at z=_____, the original ordering occurs (3d lower energy than 4s).
Combustion Reaction
CHO compound + O2 --> CO2 + H2O
What is the standard atom for the mass of the a.m.u.?
Carbon 12
Empirical Formula from Combustion Data
CxHyNz + O2 --> CO2 + H2O - When 0.1156g of a compound (C, H, & N only) reacted with O2, 0.1638g of CO2 and 0.1676g of H2O were collected. Determine empirical formula. 1) Calculate masses of C and H; - 0.1638g CO2 x 12.01g (C)/44.01g (CO2) =0.04470g C - 0.167g H2O x 2.0168g (2H)/18.02g (H2O) =0.01875g H 2) Calculate mass of N; - 0.1156g - (0.04470+0.01875) = 0.05215g of N 3) Calculate moles of each element 4) Divide by smallest result to get mol ratios = E.F.
Orbitals of Hydrogen Atom
Degeneracy: for a given n value, all the orbitals have the same energy *only occurs if you have one electron - Degeneracy movement: when they are not the same for a given n (two or more electron systems)
Calculations of Transition Energies
E = -R (Z^2)/(n^2)
n, n², 2n²
Each shell with principle quantum number = n has ______ subshells and ______ orbitals. Thus the maximum number of electrons in each shell is _____.
3d¹⁰4s¹
Electron configuration for Copper: [Ar] ____________ Note that 3d fills first, because 3d has a lower energy than 4s.
Calculation of Transition Energies
En = -R (Z^2/n^2) Calculate ΔE for the transition between levels n=1 to n=3 in a He+ ion for which Z=2. - ΔE= E3-E1 = -R(2^2) [1/(3^2) - 1/(1^2)] = 7.75x10^-18
Examples of Sig. Figs.
Example -- # of Sig. Figs. -- Scientific Notation 0.00682 -- 3 -- 6.82 x 10^-3 1.072 -- 4 -- 1.072 (x 10^0) 300 -- 1 -- 3 x 10^2 300. -- 3 -- 3.00 x 10^2 300.0 -- 4 -- 3.00 x 10^2
Gases
For any one gas: PV=nRT - At s.t.p. temp. and pressure 0 C; 1.00 atm; 22.4 dm^3/1 mol - At n.t.p. temp and pressure 20 C; 1.00 atm; 24.0 dm^3/1 mol 25 C; 1.00 atm; 24.4 dm^3 To convert C to Kelvin= C+273=K
Percentage Composition
For example, % comp. for C, H, and O in C12H22O11 is... % C = (12 x 12.0 amu x 100)/342 amu = 41.2% % H = 22 x 1.0 amu x 100)/342 amu = 6.4% % O = 11 x 16.0 amu x 100)/342 amu = 51.5%
frequency, wavelength, velocity
Given ∆E and asked to find the ____________ corresponding to this change in energy, use the equation ∆E/h, where h is Planck's constant. Given the frequency and asked to find the relative ____________, use the equation c/mu, where c is the speed of light in m/s. Given the wavelength and asked to find the ____________ the electron travels at, use h/(mv), also known as De Broglie's Equation.
increases, decreases
Going down the periodic table, there are more filled energy levels between the nucleus and the outer electrons therefore the outer electrons are more shielded from the attraction of the nucleus, so the electrons in the outer energy levels are further from the nucleus and the atomic radius______________. Going across the periodic table from left to right, Z effective increases, so the pull on the outer electrons increase as well, therefore the radius___________.
Calculations from Balanced Equations
How many grams of H2O are produced in the combustion of 1.00g of glucose? C6H12O6 (formula mass=180.0g) - Step #1 Balance Equation= C6H12O6 + 6O2 ---> 6CO2 + 6H2O - Step #2 (A=glucose, B=water); Grams of A to Moles of A -> Moles of B (mol-to-mol ratio) -> Grams of B
Quantum Numbers
n - principle quantum number ℓ - azimuthal or angular momentum quantum number mℓ - magnetic quantum number
light
p = h/λ, where p is the momentum of _______
orbitals
standing wave solutions of the Shrodinger equation
n-1, l, n-l-1
total number of nodes in orbitals = ________ total number of angular nodes/planes = _________ total number of radial nodes = __________
meter, frequency
wavelength has a unit of one ______________. planck's constant has the unit of kg m²/s. ___________ has the unit of 1/s or Hz.
Main Forms of 2-D Periodic Table (Pg. 21 Vol. 1)
- Short Form (8-columns); highlighted the importance of the octant rule; groups elements that form 4 bonds; Dimitiri Mendeleev's Periodic Table; had blank spaces for elements not yet discovered - Medium-Long Form (18-columns); the model we use today - Long form (32-columns); s, f, d, p format; disadvantage too wide; every element follows every other one in the correct sequence - Left-step table; f, d, p, s format; He is in the right place electronically but wrong because chemically it is a noble gas and not an Alkaline Earth Metal
What is wave-particle duality?
- The concept that every elementary particle or quantic entity exhibits the properties of not only particles, but also waves
Atomic and Molecular Mass
- The modern standard mass is the 12^C isotope. - One atomic mass unit = 1.66054 x 10^-27kg (VERY SMALL) - One a.m.u. = 1/12 the mass of the 12^C isotope - The a.m.u. is lighter than either the p or the n because a little bit of mass turns into energy (it is lost). - The values of relative atomic masses that appear on periodic tables are weighted averages taken over all the known isotopes of any particular element.
Formula Mass
- The sum of the masses of all the atoms in a molecule, or a formula unit, for ionic compounds. - Ex. Formula Mass of C6H12O6 = 180.0 amu - Rounding values on a periodic table to one decimal
The Mole
- The unit of amount of substance in chemistry - Exactly 12g of 12C contains a mole of atoms or 6.02214 x 10^23 (aka Avogadro's number) - A mole of Sulfur weighs 32.07g - A mole of C6H12O6 has a mass of approximately 180.0g
How does light behave like particles and waves? And what is the experimental evidence for both?
- To have momentum is to be a particle - To diffract and to interfere is to be a wave - Therefore, light is a particle and a wave - The Double-Slit Experiment showed how particles can act as waves, just as how waves act like waves - The Photoelectric Effect showed how waves behave as particles
Stoichiometric Calculation
- does not require quantum theory or quantum mechanics - it is classical chemistry - modern study of what products are formed as opposed to how much products does require quantum mechanics
Triad Importance
- the result of the repetition of 2, 8, 8, 18, 18, 32, 32 - it connects 3 elements that are similar - every other 3 elements are a triad - used to construct the periodic table - the middle element has similar chemical & physical properties as the top and bottom elements - top amu + bottom amu/2 = middle amu
Heisenberg's Uncertainty Principle
- ΔxΔp ≥ h/4 π - there will be a large amount on uncertainty - if you know position it's hard to know momentum and vice versa - indeterminacy rules
Electronic Configurations
1) Aufbau Principle: electrons in increasing energy in accordance to Hund's Rule; add 1p and 1e, following order of increasing energies 2) Pauli's Exclusion Principle 3) Hund Principle (Hund's Rule) All three are based on experiment and not on theory
Significant Figures Rules
1. Leading 0's are insignificant! Imbedded 0's always significant. Trailing 0's only significant if decimal point is specified 2. 3. Multiplication or Division: the answer contains no more significant figures than the least accurately known number
De Broglie's equation
λ = h/(mv), where m is mass, and v is velocity. In using this equation, make sure that mass is in *kg* and velocity is in *meters/sec*. You should be left with wavelength in meters.
