Units 5-8

Chapter 5: Gases

Barometer/manometer- used to measure pressure

Boyle, Charles, Gay-Lussac, Avogadro

• Boyle’s Law
  • The product of pressure times volume is a constant, provided the temperature remains the same
    • P is inversely related to V
    • The graph of P versus V is hyperbolic
• At constant temperatures, Boyle’s law can be used to find a new volume or new pressure
  • P1V1=k=P2V2   or P1/P2=V1/V2
• Law works best at low pressure
• Gases that obey this law are called ideal gases
• Charles’ Law
  • The volume of a gas increases linearly with temperature provided the pressure remains constant
    • V=bT  or V/T=b
    • V1/T1=V2/T2   or  V1/V2=T1/T2
    • Temperature must be measured in Kelvin
      • 0 K = absolute zero
• Gay-Lussac’s Law
  • Deals with pressure and temperature
    • P1/T1=P2/T2
• Avogadro’s Law
  • For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles (n)
    • V=an  or  V/n=a
    • V1/n1=V2/n2

Dalton’s Ideal Gas Law

• Ideal Gas Law
  • PV=nRT
    • R=0.08206 (L*atm/K*mol)
• Limitations of the Ideal Gas Law
  • Works well at low pressures and high temperatures
  • Most gases do not behave ideally above 1 atm pressure
  • Does not work well near the condensation conditions of a gas
• Dalton’s Law of Partial Pressure
  • “For a mixture of gases in a container, the total pressure exerted is the sum of the pressures each gas would exert if it were alone”
  • It is the total number of moles of particles that is important, not the identity or composition of the gas particles
    • P(total)= P1 + P2 + P3+ …
    • P(total)= n(total)*(RT/V)

Gas Stoichiometry

• STP
  • 0 degrees C or 273 K
  • 760 torr, 1 atm
  • Molar volume
    • 1 mole= 22.4 L
    • Density
      • D=M/V
      • N= (grams of substance/ molar mass)

Kinetic theory

• Postulates of the KMT Related to Ideal Gases
  • The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be zero
  • The particles are in constant motion. Collisions of the particles with the walls of the container cause pressure
  • Assume that the particles exert no forces on each other.
  • The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas

Explaining Observed Behavior with KMT

• P and V (T = constant)
  • As V is decreased, P increases
    • V decrease causes a decrease in the surface area. Since P is force/area, the decrease in V causes the area to decrease, increasing the P
• P and T (V = constant)
  • As T increase, P increases
    • The increase in T causes an increase in average kinetic energy. Molecules moving faster collide with the walls of the container more frequently, and with greater force
• V and T (P = constant)
  • As T increases, V also increases
    • Increased T creates more frequent, more forceful collisions. V must increase proportionally to increase the surface area, and maintain P
• V and n (T and P constant)
  • As n increases, V must increase
    • Increasing the number of particles increases the number of collisions. This can be balanced by an increase in V to maintain constant P
• Dalton’s law of partial pressures
  • P is independent of the type of gas molecule
    • KMT states that particles are independent, and V is assumed to be zero. The identity of the molecule is therefore unimportant

Temperature, energy, particle velocity

• Root Mean Square Velocity
  • Velocity of a gas is dependent on mass and temperature.
  • Velocity of gases is determined as an average
  • M = mass of one mole of gas particles in kg
  • R = 8.3145 J/K·mol
    • joule = kg·m2/s2
• Equation:

 

Mean Free Path

• Average distance a molecule travels between collisions
  • 1 x 10-7 m for O2 at STP

Effusion/diffusion

• Effusion
  • Movement of a gas through a small opening into an evacuated container (vacuum)
  • Graham’s Law of Effusion:
    • Rate for effusion for gas 1/ rate or effusion for gas 2= the square root of molar mass of gas 2/ molar mass of gas 1
• Diffusion
  • The mixing of gases
  • Diffusion is complicated to describe theoretically and mathematically

Chapter 6: Thermochemistry

• energy- the capacity to do or produce heat
• law of cinservation of energy-  energy can be converted from one form to another but can neither be created nor destroyed
• Potential energy is due to position or composition
• Kinetic energy- due to the motion of the object and depends on the mass of the object (m) and its velocity (v)

KE= (1/2)mv2

• Temperature- a property that reflects the random motions of the particles in a particular substance

• Heat- involves the transfer of energy between two objects due to a temperature difference
• work- force acting over a distance
• state function (aka state property)- a property that is independent of pathway
• system- the part of the universe on which we focus attention on (products and reactants)
• surroundings- everything else in the universe (the reactions container)
• exothermic- energy flows out of the system
  • In an exothermic process, the bonds in the products are stronger than those of the reactants. The opposition is true from an endothermic reaction
• endothermic- energy flows into the system
• thermodynamics- the study of energy and its interconversions
• first law of thermodynamics- the energy of the universe is constant
• internal energy (E)- the sum of the kinetic and potential energies of all the “particles” in the system
• enthalpy (H)= a state function

H=E+PV

• At constant pressure, exothermic means delta H is negative, endothermic means delta H is positive
• calorimetry- the science of measuring heat; based on observing the temperature change when a body absorbs or discharges energy as heat.
• heat capacity (C)= (heat absorbed/ increase in temperature)
• specific heat capacity- the energy required to raise the temperature of one gram of a substance by 1 degree Celsius
• Molar heat capacity- the energy required to raise the temperature of one mole of a substance by 1 degree Celsius
• Hess’s Law: In going from a particular set of reactants to a particular set of products, the change in enthalpy is the same whether the reaction takes place in one step or a series of steps
• Standard Enthalpy of Formation- the change in enthalpy that accompanies the formation of one mole of a compund from its elements with all substances in their standard states.

Chapter 7: ATomic Structure and Periodicity

Note: Wavelength (λ)—distance between consecutive peaks or troughs in a wave

Frequency (v)—number of waves that pass a given point per second

Speed (c)—measure in mters/second

Relationship: λv=c

Planck/Einstein/Bohr atom developments

• Max Planck and Quantum Theory
  • Energy is gained or lost in whole number multiples of the quantity hv
    • Frequency = v
    • Planck’s constant = h = 6.626 x 10-34 J·S
      • DeltaE = nhv
• Energy is transferred to matter in packets of energy, each called a quantum

Einstein and the Particle Nature of Matter

• EM radiation is a stream of particles – “photons”
  • E(photon)=hv=(hc)/wavelength

Energy and mass are inter-related

• E= mc2

Bohr Model

• Quantum Model
  • 1. The electron moves around the nucleus only in certain allowed circular orbits
  • 2. Bright line spectra confirms that only certain energies exist in the atom, and atom emits photons with definite wavelengths when the electron returns to a lower energy state
  • 3. Energy levels available to the electron in the hydrogen atom
    • E=-2.178×10^-18 J (Z²/n²)
      • n = an integer Z = nuclear charge J = energy in joules

Calculating the energy of the emitted photon

1. Calculate electron energy in outer level
2. Calculate electron energy in inner level
3. Calculate the change in energy (∆E)a. ∆E = energy of final state – energy of initial state
4. Use the equation:

a. λ=hc/∆E

to calculate the wavelength of the emitted photon

• Energy Change in Hydrogen atoms
  • Calculate energy change between any two energy levels
    • ∆E=-2.178×10^-18 J ((1/n_final²)-(1/n_initial²))
• Shortcomings of the Bohr Model

1. Bohr’s model does not work for atoms other than hydrogen
2. Electron’s do not move in circular orbits

Quantum theory – quantum numbers

• Principal Quantum Number (n)
  • n corresponds to the periods in the periodic table
  • relates to the size and energy of the orbitals
  • Integral values: 1, 2, 3 …
  • Indicates probable distance from the nucleus
    • Higher #= greater distance
    • Great distance= less tightly bound= higher energy
• Angular Momentum Quantum (l)
  • Integral values from 0 to n-1 for each principal quantum number n

Indicates the shape of the   atomic orbitals
Table   7.1 Angular momentum quantum numbers and corresponding atomic orbital numbers
Value   of l	0	1	2	3	4
Letter   used s p d f g	s	p	d	f	g
#   of orbitals/ subshells	1	3	5	7	9

• Magnetic Quantum Number (ml)
  • Integral values from l to –l, including zero
  • Magnetic quantum number relates to the orientation of the orbital in space relative to the other orbitals
• Spin Quantum Number
  • An orbital can hold only two electrons, and they must have opposite spins
  • Spin can have two values +1/2 and -1/2

		Table   .2
n	l	orbital designation	ml	# of orbitals
1	0	1s	0	1
2	0	2s	0	1
	1	2p	~1, 0, 1	3
3	0	3s	0	1
	1	3p	~1, 0, 1	3
	2	3d	~2,~1, 0, 1, 2	5
4	0	4s	0	1
	1	4p	~1, 0, 1	3
	2	4d	~2,~1, 0, 1, 2	5
	3	4f	~3, ~2, ~1, 0, 1, 2, 3	7

Electron configuration/orbital diagram

• Size of orbitals
  • Defined as the surface that contains 90% of the total electron probability
  • Orbitals of the same shape grow  larger as n increase
• s Orbitals
  • spherical shape
  • nodes (areas where probability of finding an electron is equal to 0)  (s orbital of n=2 or greater)
• p Orbital
  • two lobes each
  • occur in level n=2 or greater
  • each orbital lies along an axis (2p_x, 2p_y, 2p_z)
    • 3p has more complex probability than 2p
• d Orbital
  • occur in levels n=3 and greater
  • two fundamental shapes
    • four orbitals with four lobes each, centered in the plane indicated in the orbital label
    • fifth orbital is uniquely shaped- two lobes along the z axis and a belt centered in the xy plane
• f Orbital
  • occur in levels n=4 and greater
  • highly complex shapes
  • not involved in bonding in most compounds
• Orbital energies
  • All orbitals with the same value of n have the same energy
    • “degenerate orbitals” (hydrogen only)
• The lowest energy state is called the “ground state”
• When the atom absorbs energy, electrons may move to higher energy orbitals- “excited state”

NOTE: Oddities for electron configuration

• Cr—- 1s2s2p3s3p4s¹3d⁵
• Cu (+1 or +2)—1s2s2p3s3p4s¹4s¹⁰

Aufbau, Hund’s, Pauli exclusion rules

• Pauli’s exclusion principle: in a given atom no two electrons can have the same set of four quantum numbers
• Aufbau Principle: the principle stating that as protons are added one by one to the nucleus to build up the elements, electrons are similarly added to hydrogen-like orbitals.
• Hund’s rule: the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli exclusion principle in a particular set of degenerate orbitals, with all unpaired electrons having parallel spin

Periodic Trends in periodic table

• Ionization Energy – the energy required to remove an electron from an atom
  • Ionization energy increases for successive electrons
  • Ionization energy tends to increase across a period
    • electrons in the same quantum level do not shield as effectively as electrons in inner levels
    • irregularities at half-filled and filled sublevels due to extra repulsion of electrons paired in orbitals, making them easier to remove
• Ionization energy decreases with increasing atomic number within a group
  • electrons farther from the nucleus are easier to remove
• Electron Affinity – the energy change associated with the addition of an electron
  • Affinity tends to increase across a period
  • Affinity tends to decrease as you go down in a period
    • electrons farther from the nucleus experience less nuclear attraction
    • Some irregularities due to repulsive forces in the relatively small p orbitals
• Atomic Radius
  • Determination of radius
    • half of the distance between radii in a covalently bonded diatomic molecule – “covalent atomic radii”
• Periodic Trends
  • Radius decreases across a period
    • increased effective nuclear charge due to decreased shielding
  • Radius increases down a group
    • addition of principal quantum levels

Heisenberg uncertainty principle

• “There is a fundamental limitation on how precisely we can know both the position and momentum of a particle at a given time”

4p

∆x * ×∆ (mv) ≥ h/4(pi)

• ∆x = uncertainty in the particle’s position
• ∆ (mv) = uncertainty in the particle’s momentum
• The more accurately we know the position of any particle, the less accurately we can know its momentum, and vice-versa

Chapter 8: Bonding: General Concepts

Coulomb’s Law

E=-2.178*10^-19 J*nm (Q₁ Q₂ / r)

• Used to calculate the energy interaction between a pair of electrons and to calculate the repulsive energy when two like charged ions are brought together
  • E= energy in joules
  • Q₁ and Q₂ are numerical ion charges
  • R= distance between ion centers in nanometers
  • Negative sign indicates an attractive force

Bond polarity (affected by electronegativity–?) – Dipole moment

• Dipolar molecules
  • Moles with a somewhat negative end and a somewhat positive end (a diploe moment)
  • Molecules with preferential orientation in an electric field
  • All diatomic molecules with a polar covalent bond are dipolar
• Molecules with polar bonds but no dipole moment
  • Linear, radial, or tetrahedral symmetry of charge distribution
    • Carbon dioxide= linear
    • CCl4= tetrahedral

Energy of bond formation

• Average Bond Energies

Process Energy                     Required (kJ/mol)

CH4(g) –> CH3(g) + H(g)                    435

CH3(g)–> CH2(g) + H(g)                     453

CH2(g)–> CH(g) + H(g)                        425

CH(g) –> C(g) + H(g)                             339

Total                                                           1652

Average                                                       413

• Multiple bonds
  • Single bonds- 1 pair of shared electrons
  • Double bond- 2 pairs of shared electrons
  • Triple bond- 3 pairs of shared electrons
  • NOTE: As the number of shared electrons increases, the bond length shortens
• Bond energy and Enthalpy (using bond energy to calculate approximate energies for reactions)

1. ∆H= sum of the energies required to break the old bonds (endothermic)  + sum of the energies released in forming new bonds (exothermic)

Ionic/covalent bonding

• Ionic bonds
  • Electrons are transferred until each species attains a noble gas electron configuration
• Covalent bonds
  • Electrons are shared in order to complete the valence configuration of both atoms

Lewis structures – resonance – formal charge

~Lewis Structures

EX:

 

• Electrons and Stability
  • “the most important requirement for the formation of a stable compound is that the atoms achieve noble gas configurations

  Duet rule

  • Hydrogen, lithium, beryllium, and boron form stable molecules when they share two electrons (helium configuration)
• Octet Rule
  • Elements carbon and beyond form stable molecules when they are surrounded by eight electrons
• Writing Lewis Structures
  • Rules
    • Add up the TOTAL number of valence electrons from all atoms
    • Use a pair of electrons to form a bond between each pair of bound atoms. Lines instead of dots are used to indicate each pair of bonding electrons
    • Arrange the remaining atoms to satisfy the duet rule for hydrogen and the octet rule for the second row elements

~ Resonance Structures

• When more than one valid Lewis structure can be written for a particular molecule
• The actual structure is an average of the depicted resonance structures

~ Formal Charge

• Number of valence electrons on the free atom

Number of valence electrons assigned to the atom in the molecule

• Lone pair (unshared) electrons belong completely to the atom in question
• Shared electrons are divided equally between the sharing atoms
• The sum of the formal charges of all atoms in a given molecule or ion must equal the overall charge on that species
  • If the charge on an ion is -2, the sum of the formal charges must be -2
• Using Formal Charge to Evaluate Lewis Structures

1. If nonequivalent Lewis structures exist for a species, those with the formal charges closest to zero, and with negative formal charges on the most electronegative atoms are considered the best candidates
2. Only experimental evidence can conclusively determine the correct bonding situation in a molecule

VSEPR model – shapes

Valence Shell Electron Pair repulsion

1. The structure around a given atom is determined principally by minimizing electron-pair repulsion
2. Non-bonding and bonding electron pairs will be as far apart as possible

• Effect of unshared electron pairs
  • The ideal tetrahedral angle is 109.5
  • Lone (unshared) electron pairs require more room than bonding pars (they have greater repulsive forces) and tend to compress the angles between bonding pairs
  • Lone pairs do not cause distortion when bond angles are 120 or greater
• VSEPR and Multiple Bonds
  • For the VSEPR model, multiple bounds count as one effective electron pair
  • When a molecule exhibits resonance, ANY of the resonance structures can be used to predict the molecular structure of the VSEPR model
• How well does VSEPR work?
  • For non-ionic compounds, VSEPR works in most cases