chemistry 121: atomic and molecular chemistry · 10/3/10 2 chemistry 121: atomic and molecular...

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Chemistry 121: Atomic and Molecular Chemistry Topic 3: Atomic Structure and Periodicity

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Topic 3: Atomic Structure and Periodicity Text Chapter 2, 8 & 9 3.1 Nature of light, elementary spectroscopy. 3.2 The quantum theory and the Bohr atom. 3.3 Quantum mechanics; the orbital concept. 3.4 Electron configurations of atoms 3.5 The periodic table: its historical development. 3.6 The periodic table: atomic structure & periodic trends.

Problem set 4 Problem set 4 answers


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Electromagnetic Radiation

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Wavelength - λ • “space” taken up by one cycle • units of distance normally stated as Å or m or cm, • 1 Å = 1 x 10-10 m = 1 x 10-8 cm

Example:


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Topic 2: Atomic Spectroscopy

How is Electromagnetic Radiation related to Atomic and Molecular energy?

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Topic 2: Atomic Spectroscopy Planck’s Quantum Theory: A Quantum is the smallest quantity of energy that can be emitted (or absorbed) in the form of EM.

E = h v where: h is Planck’s constant, which is h = 6.63 x 10-34 J s Energy is always emitted (or absorbed) in whole number multiples of hv

The Photoelectric Effect: Albert Einstein proposed that light is composed of particles, called photons. Each photon has an energy content of; E = h v

Energy above a specific threshold can dislodge electrons from a metal surface. This phenomenon can be used to construct a photon detector.


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Energy “Storage” in Atoms and Molecules:

Atoms and molecules have can store energy only in very specific ways. In other words, they have very specific and defined energy states. Since the energy of a photon is defined by it’s frequency, only photons with very specific energy can be absorbed by a given atom or molecule. Subsequently, if an atom or molecule is in an excited state and then returns to a less energetic state, photons with specific frequencies will be emitted.

Etot = Eelec + Evib + Erot + Etrans


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Sodium Absorption Spectrum

Hydrogen Emission Spectrum

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Atomic Energy States:

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Determination of Energy Difference based on Formula:

What is the wavelength of a photon (in nm) emitted during a transition from a Ni =5 to a Nf = 2 state in the Hydrogen atom?


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Dual Nature of the Electron:

Louis de Broglie: If photon waves can behave as particles, can particles behave as waves? Assume e- moves as a wave in it’s orbit. For a stable standing wave the relationship between circumference and wavelength is;

2 π r = n λ

de Broglie also suggested that the relationship between the wave and particle properties of the electron was;

Where; h is Planck’s Constant, m is the mass and u is the velocity.

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Quantum Mechanics Heisenberg Uncertainty Principal: It is impossible to know simultaneously both the momentum p (defined as mass times velocity) and the position of a particle with certainty. Mathematically;

Where; Δx and Δp are the uncertainties in the position and momentum, respectively

Example: The hydrogen atom has a radius of the order of 0.050nm. Assuming that we know the position of an electron to an accuracy of 1.0% of the hydrogen radius, calculate the uncertainty in the velocity of the electron. Compare this value with the uncertainty in the velocity of a baseball of mass 0.100 kg (100 g) and radius 0.050 m (diameter 10 cm) whose position is known to an accuracy of 1.0% of its radius.


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Example: The wavelength for a 100 g baseball thrown at 35.0 m/s is;

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Quantum Mechanics and the Schrödinger Equation:


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Quantum Numbers: From quantum mechanics, three main quantum numbers (QN) are required to describe an atomic orbital. These are called the Principal Quantum Number (n), the angular momentum quantum number (l), and the magnetic quantum number (ml ). An additional Quantum number, the Electron Spin Quantum number (ms) is needed to describe the state of an electron within an atomic orbital.

•  Principal Quantum Number (n): This QN can have the integer values; 1,2,3,4, etc. In Hydrogen the value of n determines the energy. As n becomes larger, the distance from the orbital to the nucleus becomes larger.

•  Angular momentum quantum number (l): This QN tells us the shape of the orbital. The value of l is related to the principal QN, with l having the possible values of 0 to (n-1). ∴ for a n of 1, l can only be 0; for n=2, l can be 0 or 1; for n=3, l can be 0, 1 or 2; etc., Each value of l has been assigned a unique letter “name”, such that l = 0 = s, l = 1 = p, l = 2 = d, l = 3 = f, l = 4 = g and l = 5 = h. s → sharp, d → diffuse, Strong (principle)→p


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Quantum Numbers (continued):

Magnetic quantum number (ml ): This value describes the orientation of the orbital in space. The value of ml depends on the value of the angular momentum (l), where for each value of l there is the following sets of ml; -l, (-l+1), ...0, ... (+l -1), +l

Therefore, there are (2l +1) integral values of ml. •  For an l = 0 = s state there would be (2x0+1)=1 ml states this would have a value of 0 •  For an l = 1 = p state there would be (2x1+1)=3 ml states these would have values of (-1,0,1) •  For an l = 2 = d state there would be (2x2+1)=5 ml states these would have values of (-2,-1,0,1,2)

Electron Spin Quantum number (ms): These result from the magnetic field generated by the spinning electron. Only 2 values possible; +½ and -½.

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Energies of Orbitals:

In the case of the Hydrogen atom, the relative energies of the orbitals were adequately described by the principal QN and the relationship presented below;


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Electron Configuration:

The four QNs enable us to completely label any electron in any orbit in any atom by a 4 number “address”. The electronic configuration describes how the electrons are distributed among the various atomic orbitals (AOs).

Recall that the number of electrons present in a neutral atom is indicated by its Atomic Number, Z.

The notation for describing electronic configuration is;

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The notation for describing electronic configuration is;


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Pauli Exclusion Principal: For multi-electron elements, the Pauli exclusion principal applies; no two electrons in an atom can have the same four quantum numbers. Therefore for Helium, the proper electronic configuration must be;

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Shielding Effect and Energetics:

Why is the 2s orbital more stable than the 2p orbital?

The 1s orbital must be filled before the n=2 orbitals are filled. Therefore, the n=2 (and above) orbitals are “shielded” from the stabilizing attraction to the nucleus. The electron(s) in the 2s orbital has a greater probability of being near the nucleus that the 2p orbital does, therefore, the 2s orbital is shielded less and is stabilized more. The relation between this type of stabilization and the angular QN is; s>p>d>f>....


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Hund’s Rule: Consider Carbon with 6 electrons;

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Paramagnetic substances are those that are attracted by a magnet. This occurs in elements were there is net unpaired e-. (Always for odd # e-)

Diamagnetic substances are slightly repelled by a magnet. Occurs when the electron spins are paired.


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Some rules: •  Each shell or principal level of quantum number, n, contains n sub-shells. Example: for n = 2, then there are two sub-shells (two values of l) of momentum quantum numbers 0 and 1.

•  Each sub-shell of quantum number l contains 2l + 1 orbitals. Example: For a p orbital l = 1, then there are three p orbitals.

•  No more than 2 electrons per orbital

•  The maximum number of electrons in a quantum number equals 2n2. Example: for n = 2, the max # is 2 x 22 = 8; n=3; max =18

Aufbau Principal: The Building up principal. As protons are added, one by one to the nucleus, electrons are also added.

Noble Gas Core: shows in brackets the noble gas that preceded the element being considered. ie for Mg [Ne]3s2 ; where, [Ne] is the noble gas core.

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Key Equations:


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Periodic Trends:

The electrons in the Noble Gas Core of an element are usually not involved in chemical bonding or reactions. The Valance electrons are those electrons “outside” the Noble gas core and these are responsible for the chemistry of the element. For Example; all the alkali metals have similar chemistry and an analogous configuration [Noble gas core]ns1;

whereas, the halogens also have a similar chemistry and a [Noble gas core]ns2np5 core. The electrons in the filled ns2 shells do not contribute very much to the chemistry of the halogens are not usually considered valance electrons.

The electronic configurations of ions (Cations and Anions) are derived from their neutral configuration with the addition or subtraction of electrons as appropriate. Most ions are isoelectronic with a noble gas electronic configuration.

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Periodic Trends in Physical Properties:

•  Effective Nuclear Charge: A key concept. Inner shell electrons are closer to the nucleus than outer shell electrons. These inner shell electrons can partially shield or reduce the attractive force that the outer electrons “feel”.

Zeffective = Z - σ where; Z is actual nuclear charge and σ is the shielding const.

• Atomic Radius: The size of an atom. For most species determined by one-half the distance between two bound nuclei.

Ionic Radius: The ionic radius is the radius of a cation or an anion. This tracks atomic radius, except cations are smaller and anions are larger.


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Ionization Energy: The minimum energy required to remove an electron from a gaseous atom in it’s ground state. This is commonly expressed in kJ/mol.


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Bohr Model – Closer evaluation: In the Bohr model, all orbitals are shells defined by the principal quantum number. In other words 2s and 2p orbitals have the same energy. 3s, 3p and 3d orbitals also have the same energy. This is true only in 1 electron atoms such as Hydrogen.

Calculate Ionization energy of Hydrogen;

ΔE = RH ( ni2

1

nf2

– 1 ) = hν

As nf goes to infinity for hydrogen starting in the ground state:

hν = RH ( ni2

1 ) = RH

This also works for hydrogen-like species such as He+ and Li2+.

hν = -Z2 RH


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Relative Energy levels:

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Orbital Shapes: The square of the wave function,Ψ2, represents the probability of finding an electron in a specific orbital. This allows us to visualize an orbital shape.

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The p Orbitals (l = 1, ml = -1, 0, 1): Nodal plane results in a two-lobe shape; three p orbitals symmetric along x, y and z axes; highly directional.


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The d Orbitals (l = 2; ml = -2, -1, 0, 1, 2): Two nodal planes result in a four-lobe shape. Shaped like a cloverleaf

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Energy Levels: in multiple electron atoms, the electron-electron repulsions cause the different subshells to be at different energies

Pauli Exclusion Principle: no two electrons in the same atom can have the same four quantum numbers; each electron has unique set of four quantum numbers


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Why do certain orbitals lie lower than others in terms of energy? e.g., 2s is lower than 2p

•  The more stable an orbital, the lower its energy is (more negative).

•  The energy of a 2p orbital is slightly higher than a 2s orbital even though both of them are in the n = 2 shell

• Compare radial distribution curves for a 2s and a 2p orbital. •  2s has greater penetration, so core electrons do not shield 2s electrons as effectively.

Zeff(2s) > Zeff(2p)

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Transition metals: the 10 elements from Scandium to Zinc (and below) electrons in These elements occupy the d orbitals

Lanthanides (or rare earth metals): the 14 elements from atomic number 57 through 70: These correspond to the 14 electrons occupying the 4f orbitals

Actinides: the 14 elements from atomic number 89 through 102. These correspond to the 14 electrons occupying the 5f orbitals: these elements are radioactive and most are not found in nature

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Ionization Energy: The minimum energy required to remove an electron from a gaseous atom in it’s ground state. This is commonly expressed in kJ/mol.

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Ion Electron Configurations 1) Cations (+) of main group elements have lost electrons in the reverse order to that in which they were added under the Aufbau principle.

Consider sodium:

Na 1s2 2s2 2p6 3s1

Na+ 1s2 2s2 2p6 closed shell, noble gas e- configuration [Ne]

2) Anions (-) have gained electrons until an ns2np6 outer electron configuration is obtained.

Consider sulfur:

S [Ne] 3s2 3p4

add 2 electrons S2- [Ne] 3s2 3p6

closed shell, looks like [Ar]


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Metals: •  Shiny solids •  Moderate to high melting point (solids at room temperature) •  Good thermal and electrical conductivity •  Malleable and ductile •  Located in the left and lower ¾ of the Periodic Table. •  Low IE ⇒ Lose electrons in reactions

Reactions of metals: •  Formation of metal oxides: e.g., 2Ni (s) + O2 (g) → 2NiO (s) (ionic solid)

•  Oxides act as bases: metal oxide + water → metal hydroxide e.g., Na2O (s) + H2O → 2NaOH (aq)

Note: Not all metal oxides are soluble in water.

•  Oxides react with acids: metal oxide + acid → salt + water e.g., NiO (s) + 2HCl (aq) → NiCl2 (aq) + H

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Non-Metals •  Not shiny (Dull and brittle solids) •  Melting points generally lower than those of metals •  Poor thermal and electrical conductivity •  Located in the upper right of the Periodic Table

•  High (-) EA ⇒ Gain electrons in reactions


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Reactions of non-metals: When non-metals react with metals, non-metals tend to gain electrons because of their high and negative electron affinities (to fill outer most p subshell ⇒ noble gas):

metal + non-metal → salt

e.g., 2Al (s) + 3Br2 (l) → 2AlBr3 (s)

Most non-metal oxides are acidic: non-metal oxide + water → acid

e.g., CO2 (g) + H2O → H2CO3 (aq)

SO2 (g) + H2O → H2SO3 (aq)

Non-metal oxides react with bases to form salts and water:

non-metal oxide + base → salt + water

e.g., CO2 (g) + 2NaOH (aq) → Na2CO3 (aq) + H2O

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chemistry 121: atomic and molecular chemistry · 10/3/10 2 chemistry 121: atomic and molecular...

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