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PChem1Final

Final test of Physical Chemistry 1-UW Platteville

QuestionAnswer
the goal of chemical potential is to express any thermodynamic property of an equilibrium system in terms of easily measured quantities
consider the simplest possible system-single phase of pure substance, like liquid water. at the temperature and the pressure of the system chemical potential = molar Gibbs free energy in a particular phase
mui is the Gibbs energy per mole of component "i", i.e. the partial molar Gibbs free energy
partial quantity of partial molar Gibbs free energy quantity not affected by adding another component but the total is affected
Gibbs energy is made up of chemical potential
regardless of the nature of the process, the transfer proceeds from a higher chemical potential to a lower chemical potential
the flow from high to low chemical potential will continue until chemical potential has been equalized in all phases of the system
just like difference in temperature is the driving force for the flow of heat from one phase to another, a difference in chemical potential is the driving force for the flow of chemical species, i, from one phase to another
spontaneous processes go from high chemical potential to low chemical potential until they reach equilibrium
at equilibrium there cannot be any spontaneous processes so the chemical potentials are equal
the chemical potential and its downhill drive to equilibrium will be the basis of the study of phase transitions, chemical reactions, etc.
ex. write the phase equilibrium conditions for a liquid solution of acetone and water in equilibrium with its vapor you get a mixture w/ some vapor above lq which is a mixture of both components, both components are in equilibrium with it's chemical potential between the two phases but the chemical potential of each component is not equal
we know initial Gibbs, but concentration during a reaction is constantly changing therefore Gibbs energy is constantly changing as the reaction progresses
to be spontaneous G has to <0 so we need (amuA + bmuB) > (cmuC +dmuD)
in thermodynamics we try to preserve the form of equations that are developed for ideal systems. This is the thought behind the introduction of the activity aJ of the substance
activity for a pure solid or a pure liquid in the standard state equals 1
mu nod is the standard chemical potential
for a pure gas at standard state p/p0
for a pure solute at standard state [J]/c0
dynamic equilibrium example cars moving on or off a bridge
static equilibrium example tug of war, equal strength so the rope doesn't move
chemical equilibrium is an example of dynamic equilibrium
chemical equilibrium occurs when opposing reactions are proceeding at equal rates
kinetics tell us how fast a reaction reaches equilibrium
opposing reactions naturally lead to equilibrium
equilibrium can be reached by either direction, reverse or forward reaction
Kp equilibrium constant using partial pressure of gases
Kc equilibrium constant using concentrations
large K lots of products (equation shifts far to the right)
small K lots of reactants (far to the left)
homogeneous phase in the same phase
heterogeneous equilibrium different phases
solvents, solids, and liquids are not included when writing equilibrium constant
why are solids and liquids not included when writing equilibrium constant because they're "constant" and M/v ratio stays constant in the dynamic equilibrium; P-chem level: the activities of (s) and (l) in standard state equal 1
if K=Q reaction is at equilibrium
if K>Q more reactants
if K < Q more products
Le Chatlier's principle "if a system at equilibrium is disturbed by a change in temperature, pressure, or the concentration of one of the components, the system will shift its equilibrium position so as to counteract the effect of the disturbance"
if you increase the amount of reactants equilibrium shifts to the right
Pressure-Volume changes do not change K as long as temperature is constant they instead change total pressures
temperature changes and equilibrium exo and endothermic process have heat as a product and reactant respectively
increase temperature of an endothermic reaction the equilibrium shifts right
increase temperature of an exothermic reaction the equilibrium shifts left (more reactants)
catalysts lowers activation energy; increase rate of both forward & backward reactions proportionally; doesn't change composition of reaction or K
if the reaction is exothermic deltaH < 0 and deltaS>0 deltaG<0 and K>1 at all temperatures
if the reaction is exothermic deltaH<0 and deltaS<0 deltaG<0 and K>1 provided that T<deltaH/deltaS
if the reaction is endothermic deltaH>0 and deltaS>0 deltaG <0 and K>1 provided that T>deltaH/deltaS
if the reaction is endothermic deltaH>0 and deltaS<0 deltaG<0 and K>1 at no temperature
endothermic reaction deltaH>0
exothermic reaction deltaH <0
at equilibrium deltaG = 0; deltaH = TdeltaSnod
deltafGnod > 0 is unstable with respect to its elements
spontaneity is a thermodynamic tendency that might not be realized at a significant rate in practice
thermodynamic equilibrium constant is independent of pressure
K is independent of pressure does not mean that the equilibrium composition is independent of the pressure and its effect depends on how the pressure is applied
if the gases are perfect, addition of inert gas leaves all the partial pressures of the reacting gases unchanged
partial pressure of a perfect gas is the pressure it would exert if it were alone in the container, so the presence of another gas has no effect
pressurization by the addition of an inert gas has no effect on the equilibrium composition of the system (provided the gases are perfect)
when a reaction at equilibrium is compressed, the reaction responds by reducing the # of molecules in the gas phase (in this case by producing the dimers represented by the linked spheres) if a system at equilibrium is compressed then the reaction will adjust to minimize the increase in pressure; reduces the number of particles in the gas phase
exothermic reactions increased temperature favors the reactants
endothermic reactions increased temperature favors the products
dependence of the equilibrium constant on the temperature is expressed by the van't Hoff equation; ln(K2)-ln(K1)=-(deltaH/R)({1/T2}-{1/T1})
for most substances (excluding water and a few other exceptions) the molar volume of the liquid phase is greater than that of the solid phase
for a solid or liquid, the molar volume is almost independent of pressure therefore to a good approximation: Gm(Pf)-Gm(Pi)=Vm(Pf-Pi)
molar volumes of gases are large therefore Gibbs energy depends strongly on the pressure; Gm(Pf)-Gm(Pi)=RTln(Pf/Pi)
using molarities for K only gives you an approximate value because you're making the assumption it's an ideal dilute solution
because the standard states refer to pure materials, the standard chemical potentials in this expression are the standard molar Gibbs energies of the (pure) species
Q refers to an arbitrary stage of the reaction and K is the value of Q at equilibrium
if the concentration of a substance in an equilibrium mixture is 0.010 M, its activity is 0.010M/1M =0.01
when you replace the activities, the resulting expression is an approximation however such approximations could be a problem (e.g. electrolyte solutions even when dilute)
K=eq constant b/c derived in activities & activities are dimensionless there K has no units
fugacity activity of a gas
the standard state of fugacity, f0 is the value that the fugacity would have if the gas behaved ideally at 1 bar pressure i.e. f0=P0
f and P are related by fA = gammaAPA where gamma is the fugacity coefficient
as f approaches P, P approaches what and gamma approaches 0; gamma approaches 1
] as gamma approaches 1, [A] approaches 0
what is delta n for: N2O4 (g) yields 2NO2 2-1 = 1
for a solid or liquid the molar volume is dependent or independent of pressure independent
phase transitions are changes of phase without change of chemical composition
a substances has a spontaneous tendency to change into the phase with the lowest molar Gibbs energy
below 0 degrees Celsius, water tends to go from lq to s therefore what can be inferred about the chemical potential mui lq>mui(s) because it goes from high to low chemical potential
phase diagrams describe the phase properties as a function of state variables such as temperature and pressure
the phase diagram of a pure substance shows the regions of pressure and temperature at which its various phases are thermodynamically stable
the liquid-vapour phase boundary terminates at the critical point
at the triple point, solid, liquid, and vapor phases are in dynamic equilibrium
the normal freezing point is the temperature at which the liqiud freezes when the pressure is 1 atm
the normal boiling point is the temperature at which the vapor pressure of the liquid is 1 atm
the standard boiling point is the temperature at which the vapor pressure reaches 1 bar
the critical point is where liquid-vapor equilibrium ends
the critical point is the last point where you can distinguish from liquid and vapor phases because anything above that gives a supercritical fluid
suppose two phases are in equilibrium at a given pressure and temperature. If we change the pressure, we must adjust the temperature to a different value to ensure that the two phases remain in equilibrium
the Clausius-Clapeyron equation relates the temperature dependence of he vapor pressure of a liquid or a solid to deltaHvap or deltaHsubl
for the Clausius-Clapeyron equation we assume that the vapor behaves as a perfect gas and the enthalpy of vaporization is constant over the temperature range of interest and the molar volume of a gas is much greater than that of a liquid
can 4 phases of a single substance ever be in equilibrium no because F=C-P+2
the number of components in a system is the minimum number of independent species necessary to define the composition of all the phases present in the system
how many components does pure water system have C=1
how many components does a mixture of ethanol and water have C=2
the number of degrees of freedom, F, of a system is the number of intensive variables (ex. pressure, temperature, or mole fractions) that can be changed independently without disturbing the # of phases in equilibrium
when F=1 for 2 phases meaning you can vary one variable, ex. pressure, but the moment you change P, T becomes fixed
when the triple point lies above 1 atm the liquid cannot exist at normal atmospheric pressures whatever the temperature
two phases are considered to be in mutual equilibrium when the temperature, pressure, and chemical potential of each component are the same in each phase
consider the ideal gas reaction: PCl5 = PCl3 + Cl2. When He is added at constant temperature & volume in an equilibrium mixture at 25 degrees Celsius, indicate whether the equilibrium shifts to the right, left, or neither constant T, V addition of He doesn't affect the partial pressures of the gases therefore there is no shift
consider the ideal gas reaction: CO + 1/2O2 = CO2 for which deltaHnodR=-283.0 kJ/mol. Predict the change in the partial pressure of CO2 as the temperature is increased at constant total pressure it will decrease following Le Chatlier's principle because the reaction is exothermic
Quantum mechanics can be described as laws governing the behavior of microscopic particles such as electrons and nuclei
quantum mechanics deals with systems that are not part of everyday macroscopic experience, and the formulation of quantum mechanics is math based and abstract
essentially all of chemistry is a consequence of the laws of quantum mechanics
if we want to understand chemistry at the fundamental level of electrons, atoms, and molecules, then we must understand quantum mechanics
after its discovery, quantum mechanics was used to develop concepts that explained chemical properties. However, quantum mechanics was of little practical value because of the very difficult calculations needed to apply quantum mechanics to chemical systems
in present times, the extraordinary computational power of modern computers allows quantum mechanical calculations to give accurate chemical predictions in many systems of chemical interest
the basic constituents of matter are atoms
Newton's Laws apply universally; Newtonian mechanics explained macroscopic behavior of matter, planetary motion
classical mechanics predicts precisely specified locations and momenta at each instant (deals with the laws of motion of macroscopic objects whose speeds are small compared with the speed of light)
in the late 19th century, some people believed that the theoretical structure of physics was complete and there was nothing else to learn
experimental evidence showed up that could not be explained by classical physics and these results led to the development of quantum theory and the theory of relativity
an understanding of atomic structure, chemical bonding and molecular spectroscopy must be based on quantum theory
quantum mechanics describes the rules that apply to electrons in atoms and molecules
quantum mechanics is not deterministic but is probablistic
visible light is one type of electromagnetic radiation
when a solid is heated, it emits light; classical physics pictures light as wave consisting of oscillating electrical and magnetic fields (electromagnetic wave)
electromagnetic waves are synchronized oscillations of electric and magnetic fields that propagate at the speed of light
frequency is the number of cycles the wave undergoes per second; expressed in s-1 or hertz (Hz)
wavelength is the distance between any point on a wave and the corresponding point on the next crest (trough) of the wave
in a vacuum, all types of electromagnetic radiation travel at 3.00 X10^8 m/s which is a physical constant called the speed of light
amplitude of an electromagnetic wave is a measure of the strength of its electric and magnetic fields
amplitude is related to the intensity of radiation which we preceive as brightness for visible light
rotational spectroscopy takes places using what type of waves microwaves
vibrations use infared and visible light which means that rotational spectroscopy gets super imposed on IR; UV-vis has rotations and vibrations super imposed
different solids emit radiation at different rates at different temperature meaning you can associate temperature with a color scale
a blackbody is an idealized object that absorbs all electromagnetic radiation that falls on it
a good approximation of a blackbody is a cavity with a tiny hole because radiation that enters the hole is repeatedly reflected within the cavity; at each reflection a certain fraction of the radiation is absorbed by the walls of the cavity; large # of reflections causes virtually all radiation to be absorbed
when a blackbody is heated the walls emit light equal to what it absorbed because no light is reflected or transmitted
the rate or radiation emitted per unit surface area of a blackbody is a function of only its temperature and is independent of the material of which the blackbody is made
classically blackbody radiation cannot be explained because radiation from a blackbody is a result of e- oscillating w/ a certain frequency; energies of the electronic oscillators reponsible for the emission of radiation can have any value; well it cannot exactly have any value it wants
Rayleigh-Jeans Law is a classical law approximating the intensity of radiation emitted by a blackbody
Rayleigh-Jeans Law had great deviation at low wavelengths
the ultraviolet catastrophe also called the Rayleigh–Jeans catastrophe, was a prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power
the ultraviolet catastrophe stated that cool objects should radiate in the visible and UV regions
in 1900 Max Planck announced that he had discovered a formula that would give highly accurate fit to the observed curves of the blackbody radiation
Planck considered the walls of the blackbody to contain electric charges that oscillated (vibrated) at various frequencies
it was understood at the time when Planck was working that the origin of blackbody radiation is due to the vibration of electric dipoles formed by atomic nuclei and their associated electrons which emit radiation at the frequency at which they oxcillate
from Maxwell's electromagnetic theory of light, it was known that electromagnetic waves are produced by accelerated electric charges
a charge oscillating with a frequency, v, will emit radiation of that frequency
Planck made a few assumptions: energy of the oscillator was proportional to an integral multiple of frequency; E=nhv where n=0,1,2,... and h was the proportionality constant
Planck made an adjustment to Rayleigh-Jean's Law by plugging in his equation into theirs
Planck showed that his added to Rayleigh-Jean's gave excellent agreement with the experimental data for all frequencies, wavelengths, and temperatures if h has the value 6.626X10^-34
Planck constant was found to be 6.626X10^-34 by using his adjustment to Rayleigh-Jean's equation and solving for different frequencies, wavelengths, and temperatures
in classical physics, energy takes on a continuous range of values and a system can gain or lose any amount of energy but Planck's ideas were a direct contradiction to classical physics by saying there were only certain values (it was quantized)
the Latin word quantum means how much
in quantum mechanics the energy of a system is quantized, meaning that the energy can take on only certain values
Planck also proved his derivation of the Rayleigh-Jean's Law using the Wien displacement Law: lambdamaxT = 2.90X10^-3 mK
in astronomy the theory of blackbody radiation is used to estimate the surface temperature of stars
in the early 19th century the French scientists Dulong and Petit determined the heat capacities of a number of monoatomic solids
Molar heat capacities of all monoatomic solides are the same and close to 25 J/K*mol
if classical physics were valid, the equipartition principle could be used to infer that the mean energy of an atom as it oscillates about its mean position in a solid is kT for each direction of placement (for 3 directions of motion) and the derivative was taken and found to equal 25 J/K*mol
significant deviations of heat capacities were observed from Dulong and Petit's deviation of molar heat capacities at low temperatures
spectroscopy is the detection and analysis of the electromagnetic radiation absorbed, emitted, or scattered by a substance
Balmer, Rhydber, and others found an empirical formula that correctly reproduces the observed H-atom spectral frequencies
the Rydberg equation and the value of the constant are based on data rather than theory
the Rydberg equation has two sets of integers which can be described as different series
the Lyman series ends at nb = 1; seen in the UV
the Balmer series ends at nb = 2; seen in the visible
the Paschen series ends at nb= 3; seen near the IR
the Bracket series ends at nb = 4; seen in the IR
if intensity is constant e-s begin coming out only at a specific wavelength
if you cross the threshold that e-s begin to emerge they come out faster (speed increases, KE increases if mass doesn't change)
energy is proportional/inversely proportional to wavelength inversely proportional
after you cross the threshold of frequency KE increases and frequency increases
Einstein drew on Planck's idea of quantized energy
work function corresponds to ionization energy of metals
what energy isn't used for work function goes into what when incoming energy equals h(nu) 1/2 mv^2
nu nod is the threshold frequency where KE= 0
at KE=0 hv = work function
when alpha particles were shot at metal they deflected as opposed to going right through meaning they must have hit something at the center of the atom
Rutherford's model of the atom led to Bohr's model
Bohr said that the e-s can't just be in any orbit or they would kill the atom
photoelectric effect is that when photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal
experimental characteristics of photoelectric effect KE of e-s increases w/ frequency but is independent of intensity of the radiation; if frequency is above the threshold e-s are ejected even at low light intensities; no e-s are ejected if the frequency is less than the threshold value
the threshold frequency differs for most metals and lies in the ultraviolet for most metals
from the classical picture, the photoelectric effect would expect that the KE of the emitted e-s to increase with an increase in light intensity and photoelectric effect should occur at any frequency provided the light is sufficiently intense
in 1905 Einstein explained the photoelectric effect by extending Planck's concept of energy quanitzation to electromagnetic radiation
Einstein expanded Planck's when extended Rayleigh-Jean's Law
Einstein proposed that in addition to its wavelike properties, light could also be considered to consist of particle like entities (quanta)
Ephoton= h(nu)
work function is the energy required to remove an electron from the metal to infinity, analogue of ionization energy
in 1911 Rutherford proposes nuclear model: atom can be thought of as a 'microscopic solar system' in which the e-s orbit the nucleus
Bohr took Rutherford's idea and said that the e-s can't just be in any orbit or they would kill the atom
classical physics states than an e- in orbit around an atomic nucleus should emit electromagnetic radiation (photons) continuously, b/c it's continually accelerating in a curved path; the resulting loss of energy implies that the e- should spiral into the nucleus...(aka atoms can't exist)
Bohr postulates H has only certain stationary states, atom doesn't radiate energy while in a stationary state; going from a higher to lower level releases a photon; e- in stationary state moves in a circle around nucleus; allowed orbits follow e-s angular momentum
Bohr called energy levels stationary states
the force holding the e- in a circular orbit, according to Bohr, is the coulombic force of attraction between the proton and the e-
Bohr balanced the coulombic force with the centrifugal force (b/c moving in an orbit)
n=1 corresponds to the state of lowest energy; ground state energy
negative sign indicates that the energy states are bound states; i.e. the energies given by the Bohr orbits radius equation are less than when the p+ and e- are infinitely apart (n=infinity)
n>1 is also called an excited state
at ordinary temperatures hydrogen atoms, as well as most other atoms and molecules, are found exclusively in the ground electronic states
state of higher energy are called excited states and an atom or molecule in that state will relax back to the ground state and give off energy in the form of a photon
Bohr's equation had good agreement with the experimental value of the Rydberg constant
ionization energy is the energy required to take an e- from the ground state to the first unbound state, which is obtained by letting nb=1 and na=infinit
limitations of ionization energy, Bohr's model, and Rydberg's equation failed to predict the spectrum of any other atom other than hydrogen
Bohr model is a one-electron model and works for He+, Li2+, and Be3+
wave particle duality is an extension of the Bohr theory to explain the spectra of atoms when more than one e- failed; the fact that Bohr theory works for hydrogen is somewhat of an accident
de Broglie proposal (1923) if light can be particle-like at times, why should matter not be wave-like at times
quantization occurs in wave motion such as seen in sound waves; when a string is plucked it can vibrate at its fundamental frequency with overtones being n(nu) where n is an integer; frequencies lying between these mulitplies of nu are not allowed
de Broglie proposed that a material particle with a momentum would have a wavelength lambda given by lambda = h/p where p=mv momentum
does de Broglie's relationship of lambda = h/p apply to all particles yuppers; ex. baseball; e-; the difference is the degree by which it matters to the object
Davisson and Germer experiment scattering of e- beam from the nickel crystal shows a pattern characteristic of a diffraction experiment where waves interfere constructively & destructively in different regions
classical experiments had shown matter to be particle-like and energy to be wave-like, but de Broglie, Davisson, and Germer showed that the distinction between a particle and a wave is meaningful only in the macroscopic world, not the atomic world; aka wave-particle duality
Heisenberg Uncertainty Principle states that the more precise you know the position the less precise you known the momentum and vice versa
in the classical view of the world a moving particle has a definite location at any instant whereas a wave is spread out in space but an e- has the properties of both a wave and a particle
uncertainty in the linear momentum parallel to the axis q and deltaq is the uncertainty in the position along that axis
the basic approach of microscopy is illuminating a small area of a sample and collecting light with a microscope
the resolution of a microscope is on the order of wavelength of light used as a probe
conventional microscopes that use visible light are blind to features in the nanometer range
the wavelength of light is an important factor in the resolution of a microscope. The greatest resolving power in optical microscopy is near the UV light, the shortest effective imaging wavelength
under most circumstances microscopists use white light generated by tungsten-halogen bulb to illuminate the specimen
in electron microscopy a beam of e- w/ a well-defined de Broglie wavelength (wave particle duality) replaces the lamp found in traditional light microscopes and instead of glass or quartz lenses, magnetic fields are used to focus the beam
because of the Broglie wavelength, microscopes have the best resolving power at low wavelengths
in transmission electron microscopy, TEM, the e- beam passes through the specimen and the image is collected on a screen; more resolution than SEM but can't be done on every sample; needs a super thin slice w/ an e- beam shining through)
in scanning electron microscopy, SEM, the e-s scattered back are detected & the electrical signal is sent to a video screen; an image is obtained by scanning the e- beam across the surface of the sample (3D view)
typical resolutions of TEM and SEM instruments are about 2 nm and 50 nm respectivevly; it follows that e- microscopes cannot resolve individual atoms (which have diameters of about 0.2 nm)
for e- microscopes only certain samples can be observed under certain conditions
for e-microscopes the measurements must be conducted under high vacuum b/c air molecules can cause difraction
for TEM observations the samples must be very thin cross-sections of a specimen (hard to make); cannot be used to study living cells
for SEM observations the samples must be made on dry samples; cannot be used to study living cells
Created by: 530848841