Chemistry Test 2 Review PDF

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Chemistry Test 2 Review Module 2: Quantum Theory and H atom 2.2 Nature of Light ● ●

Light is an electromagnetic radiation that transmits energy through space or some other medium Electromagnetic radiation is produced when electrical charges undergo acceleration

Wavelength (λ in meters) - distance between successive maxima Period (T in seconds) - time it takes for the electric field to return to its maximum strength Frequency - ( v = T1 in Hertz) - # of times per second the electric field reaches it maximum value λv = c c - speed of light (2.998 x 108 m/s) Electromagnetic Spectrum

Visible light is from 400nm - 750nm. (1 nm = 10-9 m) 2.3 Blackbody Radiation

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A heated solid produces electromagnetic radiation of many λ. These λ are passes through a prism to split the light into its component wavelengths In 1900, Max Plank resolved discrepancy between theory and experiment and made 2 primary assumptions: 1. The emitted radiation of frequency v = cλ was produced by a group of atoms in the solid that oscillate with the same frequency 2. The energy of oscillation for a particular group of atoms was restricted to certain special values given by E osc = nhv n - integer (0, 1, 2, 3, etc) h - Planck's constant (6.626 x 10-34  J)

2.4 Photoelectric Effect ●

In the photoelectric effect, light is used to separate electrons from a surface or metal.

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The energy of the light is directly proportional to its frequency. Energy of light must be highly localized in space. If the energy of the light was spread out over the entire light wave, it would take longer for an electron to break free from the surface for less intense light.

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Einstein stated that the energy of light cannot be spread out but must be concentrated into small, particle like bundles, photons. The energy of the photon must be directly proportional to the frequency of light.

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E photon = hv

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The energy of an incoming photon is transferred to an electron on the surface then that energy is used to separate the electron from the surface. That energy is then transferred into kinetic energy for the electron. We can use Einstein’s equation to make an expression for the kinetic energy of the electrons that left the surface KE electron = hv − w = hv − hvo

2.5 Line Spectra of Atoms ●

White light can be dispersed into a rainbow of colours using a prism. If you place a sample of atomic gas (i.e. H) between the light source and the prism, dark lines appear.

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The photoelectric effect said that the energy of the photon was determined by the colour of light. The line spectra of atoms provided proof that the energy of an atom is quantized.

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Bohr’s Model of the H Atom ●

Neils Bohr hypothesized that electrons moved around the nucleus with speed v  in a circular orbit of radius r. h mvr = n( 2pi )

mvr - angular momentum (l) ● ●

In other words, Bohr assumed angular momentum of the electron was “quantized”. ○ L was restricted to quantities (h/2pi), 3h/2pi, 2h/pi) The integer n is used to label the orbits.

Key Experiments

2.6 de Broglie’s Hypothesis ●

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Einstein showed that light exhibited a wave-particle relationship. ○ In some experiments, light behaved like a wave and sometimes behaved like a beam of photons. Diffraction ○ Light is a wave ○ Observed when light passes through a hole or slit whose size is comparable to the wavelength of light. Photoelectric effect ○ Light is particle like Louis de Broglie stated that if light could behave like both a wave and a beam, so can particles. λdB =

h mv

λdB - de Broglie wavelength mv - momentum

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The significance of de Broglie’s hypothesis is that a complete description of the behaviour of an electron in an atom must incorporate wave-particle duality.

2.7 Heisenberg Uncertainty Principle (H.U.P.) ● ● ●

Warner Heisenberg recognized that it is impossible to isolate an observer from the system he/she is studying Heisenberg said that if we tried to measure the position (x) of electrons, we will change its momentum (p) and vice versa. He derived this relationship to measure both position and momentum △p ≥

h 4pi△x

△x - uncertainty in the position of the particle △p -uncertainty of the momentum of the particle ●

HUP tells us that it is impossible to determine both the position and momentum of a particle with absolute certainty. ○ The smaller the uncertainty in the particle's position, the greater uncertainty in its momentum ○ We know the position of the particle but unsure of where it is going

2.8 The “New” Quantum Theory for Describing Electrons in Atoms ● ●

de Broglie - the electron exhibits a wave particle duality Heisenberg - the exact behaviour of an electron cannot be determined.

Schrodinger Equation ●

Described the behavior of a single electron moving about the nucleus.

Ψ - mathematical function that depends on (x,y,z) V - potential energy associated with electron-proton interaction (+e)(−e) V (x, y, z) = 4piεo r r - √x2 + y 2 + z 2

εo - permittivity of vacuum constant ●

The unknowns of Schrodinger equation are E and Ψ.

Meaning of ● ● ●

Ψ is a mathematical function Referred to as wave function Ψ itself does not have physical interpretation, however, |Ψ|2 does have physical meaning

Interpretations: 1. Born interpretation a. Emphasizes the particle-nature of the electron. 2. Suggests that the electron is smeared out into a charge cloud a. The density of the cloud at a particular point represents the probability of finding the electron there b. So, denser regions of the cloud represent locations where the electron is more likely to be found. ● ● ●

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Each stable state of the H atom has a unique mathematical function, Ψ, the square at which gives us the probability of finding the electron at a particular point An orbital is a mathematical function, Ψ, whose |Ψ|2 gives us the probability of finding the electron at a particular point. Each state of the H atom has a unique set of integers, quantum numbers, that identifies properties of the orbital ○ n - principal quantum number (n = 1, 2, 3, … etc) ■ Determines size of orbital ○ l - orbital angular momentum quantum number (l = 0, 1, 2, … n-1) ■ Determines shape of orbital ○ ml - magnetic quantum number (ml = 0, ∓1, ∓2, … ∓ l) ■ Tells us the number of distinct orientations that are allowed for a particular orbital. Each stable state of the H atom has a well defined energy R

E n =− ( nH2 ) RH = 2.179 x 10-18  J

Energy Level Diagram for H

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To simplify the labeling of the energy levels, chemists use the following letter designations for the possible values of l ○ l=0 ■ s ○ l=1 ■ p ○ l=2 ■ d ○ l=3 ■ f

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Diagram above for the H atom, which is a one electron system The electron in the H atom can exist in any one of an infinite number of these levels.

Graphical Representations of H Atom Wave Functions ●

There are mostly 3 variable functions of the wave function for the H atom Ψ = R(r)Y (θ, Φ) R(r) - radical factor Y (θ, Φ) - angular factor

Probability Density Plots (“scatter point” plots): ●

A density plot is like a scatter plot.

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These diagrams show that: ○ s orbitals are spherical ○ p orbitals are dumbbell shaped ○ Orbitals can have radial and angular nodes. Radial Nodes (# of radial nodes = n-l-1) ○ Corresponds to a given value of r where R=0 ■ Where r changes from positive to negative or vice versa. ○ Represented by a circle (in a 2-D diagram) or sphere (in a 3-D diagram). Angular Nodes (# of angular nodes = l) ○ Corresponds to the points where Y changes sign. ○ Appear as surfaces such as planes or cones ○ The greater the value of l the greater number of angular nodes and the greater number of lobes the orbital has.

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Boundary Surface Plots (“ballon” pictures) ● ●

A boundary surface defines a region of space within which the probability of finding an electron is high (90%-100%) It tells us about the shape and orientation of the electron cloud

Radical Factors, R(r) ●

Depends on the values of n and l for the state in the question

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R(r) (big R) decreases exponentially as r (little r) increases R(r) crosses the r-axis, n-l-1 times. We say that R(r) has n-l-1 radial nodes For s states (i.e. l=0) R(r) has its maximum at r=0 NOT A NODE IF STARTS AT ZERO.

Radial Electron Densities - plots of R(r)2 vs. r

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These plots tell us: ○ How the probability of finding the electron changes as we move away from the nucleus in a certain direction ○ How the density of the electron cloud changes as we move away from the nucleus in a certain direction General features: ○ Series of maxima decrease as r increases. ○ # of radical nodes = n-l-1 ○ # maxima = n-l ○ For s states, the density is greatest at the nucleus ○ For p, d, f, etc, states, the density is 0 around the nucleus

Radial Distribution Plots - plots of r2 R(r)2 vs. r

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All plots consist of a series of maxima that get progressively larger as r increases # of maxima = n-l All plots start at zero rmp increases as n increases ○ Orbital

1s

2s

3s

rmp

53pm

~300pm

~750pm

rmp decreases as l increases  ○ orbital

2s

2p

rmp

~300pm

~200pm

In Conclusion ●

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The state of an electron is specified completely by the following set of quantum numbers ○ n ○ l ○ ml ○ s ○ ms n, l, ml characterize a region of space (an orbital) s and ms characterize the electron’s spin

Module 3: Multielectron Atoms and the Periodic Table 3.1 Multielectron Atoms ● ●

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The results obtained for the H atom help us understand how 1 electron behaves when it interacts with a single nucleus However, it we had He, we would have 2 electrons and would have to worry about 3 seperate interactions, both electrons interacting with the nucleus and electrons interacting with each other. We can use Schrodinger’s equations to help us but the hard part will be to solve the equation Fortunately, we do not have to solve the equation for every atom to understand how the electrons in a multielectron atom “pack around” the nucleus.

Penetration and Shielding (NOT TESTED) Orbital Energy Diagram for Multielectron Atoms ● ●

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n defines a “shell” ○ “n=1 shell”, an “n=2 shell” etc. l defines a subshell ○ For each shell, we have different n  different subshells because for a given value of n, the quantum number l can have one of n different values ■ 0, 1, … n -1. ■ For example the n=3 shell, we can have 3 subshells: a “3s subshell”, “a 3p subshell”, and a “3d subshell”. The energy and size of a given orbital (i.e. 1s) both increase as Z increases ○ As Z increases, the attraction between the nucleus and any given electron increases. The increases attraction lowers the energy of the orbital and causes the orbital to contract. For a multielectron atom, the orbitals in the same “shell” are not of the same energy

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Because of electron-electron repulsions, the subshells are not of the same energy in a multielectron atom. In a given shell, the “s” subshell is the lowest in energy, then “p”, then “d”, etc.

3.2 Ground State Electron Configurations for Neutral Atoms ●

There are 3 basic rules that help us predict how the electrons in an atom distribute themselves among the possible states to achieve the lowest possible energy for the atom.

Pauli Exclusion Principle ●

NO TWO ELECTRONS CAN HAVE THE SAME SET OF QUANTUM NUMBERS n, l , ml, and ms.

Subshell

# of orbitals (2l +1)

Max # of electrons

ns

1

2

np

3

6

nd

5

10

nf

7

14

ng

9

18

Aufbau Procedure.

Hund’s Rule ●

If there are not enough electrons to fill completely a set of energetically degenerate, the lowest energy arrangement is the one which has the maximum number of parallel spins. ○ Parallel spins = lower energy

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When electrons have parallel spins, they avoid each other to a greater extent So, they shield each other less and this increases the attraction each electron feels towards the nucleus.

3.3 The Periodic Table

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Rows are periods Columns are groups To make electron configurations, just read across table

3.4 Ground-state Electron Configurations for Monatomic Ions ● ●

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Monatomic ions (O- , Cl- , S+ , Ni2+  , etc.) Negative monatomic ions (monatomic anions) ○ Write the electron configuration for the neutral atom first ○ Then use (n+l) to add electrons to the appropriate orbitals Positive monatomic ions (monatomic cations) ○ Write the electron configuration for the neutral atom first ○ Then, remove electrons from orbitals with the highest value of n first.

3.5 Atomic Properties and Periodic Trends ●

Electron configurations of atoms change in a predictable way as we move across a period and down a group

Paramagnetic and Diamagnetic Atoms ● ● ● ● ●

As a result of electron spin, each electron produces a magnetic field. If all of the electrons in an atom are paired up, then the magnetic field cancel so that there is no net magnetic field for the atom. If there are unpaired electrons then the magnetic fields do not cancel. Diamagnetic ○ All electrons are paired Paramagnetic ○ One or more unpaired electrons

Atomic Radii ● ●

The size between the atom is determined by measuring the distance between nuclei in a certain environment Atomic radii decreases across a period and increases down a group.

Ionization Energy ●

The energy required to remove an electron form a gas-phase atom

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Ionization energy decreases down a group and increases moving left to right. EXCEPTIONS: ○ Be>B ○ N>O

Electron Affinity ● ●

Energy change that accompanies the addition of an electron to a gas-phase. Electron affinity decreases down a group and increases moving left to right.

Summary

Module 4: Introduction to Chemical Bonding 4.1 Introduction to Chemical Bonding ● ● ● ● ● ● ●

Focusing on main group elements from the s and p block Ionic bonding ○ Electron transfer Covalent bonding ○ When election pairs are shared between a pair of electrons Metals from group 1 and 2 have low IE and low EA ○ Give electrons Atoms from groups 14-17 have large IE and large EA ○ Takes elections When metals from the s block combine with atoms from the p block they usually from an ionic compound. When atoms from the p block combine with each other, it usually forms a molecular compound.

Octet Rule ● ●

Based on the observation that noble gasses are unreactive ○ There must be a special stability associated with the noble gas configurations...