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# P chem test 2

### yay P-Chem Test 2

how is Lattice Energy related to the stability of an ionic solid directly stability of an ionic solid
can lattice energy be determined directly by experiment no
Lattice energy the energy required to completely separate a mole of a solid ionic compound into its gaseous ions
Born-Haber cycle formation of an ionic compound as a series of well-defined steps and use Hess's law to put these steps together in a way that gives us the lattice energy of the desired compound
ex. Born-Haber cycle for NaCl using two different routes one gives you heat of formation the other helps you find lattice energy
consider an ideal gas inside a cylinder fitted with a piston. Let the initial state be T, Vi and the final state be T, Vf. The change of state can be brought about in many ways but the two simplest are 1. free expansion against zero external pressure (w=0, q=0) 2. reversible, isothermal expansion ( w = -nRTln(Vf/Vi and q = nRTln(Vf/Vi))
isothermal expansion of a perfect gas: deltaU equals 0
internal energy is unchanged by expansion of a perfect gas in an isothermal situation because only average distance between the molecules is the only thing that changes; average speed & therefore total KE remains the same; no intermolecular interactions so deltaU is independent of average separation so the internal energy is unchanged by expansion
is deltaU of a sample of perfect gas at a given temperature independent of the volume it occupies yes
heat capacity H = q/deltaT
at constant volume deltaU = qv
at constant pressure deltaH qp
heat capacity at constant volume Cv= qv/deltaT = deltaU/deltaT
for an infinitesimal change in temperature, dT and infinitesimal change in dU means that Cv = dU/dT
for infinitesimal small changes Cp = dH/dT
True or False: Enthalpy is always greater than the internal energy of the system True
True or False: the difference between enthalpy and internal energy of the system decrease with Temperature false
why is internal energy a function of two and not three variables function of V, T, and P but because there is an equation of state this states that two of the variables make the third variable is fixed
internal energy varies with the temperature and the volume of the sample, but we are interested only in its variation with the temperature with constant volume
Is Cv,m = Cv/n intensive or extensive property intensive
heat capacity is used to relate a change in internal energy to a change in temperature of a constant-volume system
if the range of temperature is small can it be ignored in relation to the variation of heat capacity? yes
Kirchhoff's Law describes the enthalpy of a reaction's variation w/ T changes; directly related
for a gas behaving ideally with constant moles and a closed system deltaH = deltaU +nRdeltaT
for a gas behaving ideally with constant Temperature and a closed system deltaH = deltaU + RTdeltan
calculate the change in moles: 2H2 (g) + O2(g) yields 2H2O (l) -3 mol
relationship between heat capacities for ideal gases Cp - Cv = nR; gamma = Cp/Cv = Cpm/Cvm
for gases Cp > Cv gamma is > 1
for an ideal monoatomic gas Cv= 3R/2
for an ideal monoatomic gas Cp = Cv + R = 5R/2
why is Cv useful? you can solve for Cp and find enthalpy
adiabatic process is not the same as isothermal processes
adiabatic process one with no heat transfer into or out of a system; q=0
a process that happens so quickly there is no opportunity for heat transfer to occur is an example of an adiabatic process
when the cork is popped open in a champagne bottle this is an example of adiabatic process; the pressurized gases expand into the outside air so rapidly that there is no time for them to exchange heat with their surroundings
as the expanding gases do work on their surroundings in an adiabatic process their internal energy and temperature both drop; ex. why a cork shows water vapor condense
when an ideal gas expands adiabatically a decrease in temperature is expected; no work is done but no heat enters the system; deltaU falls and b/c deltaU = sumKE + sumPE Temperature falls
1st law of thermodynamics says that work done by system has to come at the expense of something therefore happens at the expense of deltaU; if deltaU decreases KE decreases and therefore T decreases and some gas condenses to some liquid and we get the mist around a champagne bottle
reversible adiabatic expansion dw = -Pdv is a universal truth; dU= dq (goes to 0) + dw = dw; dU = CvdT = dw = -PdV = -nRTdV/V (P and V related so we can't take it out of the integral b/c its a reversible process)
an adiabatic free expansion of an ideal gas is isothermal; b/c dw = -PdV = 0; dU = dq + dw = 0
adiabatic expansion/compression of an ideal gas under constant P Cvdt = dw = -PdV; a relationship between initial and final states is obtained by integration so we get Cv(Tf-Ti)=-P(Vf-Vi) because P=Pex
can you use Boyle's Law for an adiabatic process? Explain No; can't use for an adiabatic process b/c it happens so infinitesimally fast there is no opportunity for heat transfer and the P and V changes are fast
only way you can get dw in an adiabatic process is dU = dw and dU= CvdT; deltaU = CvdeltaT = nCvmdeltaT
first law of thermodynamics tells us that energy is conserved; neither created nor destroyed; can be transferred between a system and the surroundings; can be converted from one form to another; deltaU = q + w
the first law does not address the extent to which energy is conserved, converted, or transferred
spontaneous process a process that proceeds on its own accord without any outside assistance; occurs in a definite direction
processes that are spontaneous in one direction are non-spontaneous in the opposite direction
the fact that a process is spontaneous does not mean that it will occur at an observable rate
acid-base neutralization is an example of a fast spontaneous reaction
a rusting iron nail is an example of a very slow spontaneous reaction
thermodynamics can tell us the direction and extent of a reaction but tells nothing about the speed of the reaction
in a reversible process a system is changed in such a way that the system and its surroundings can be restored to their original state by exactly reversing the change
an irreversible process is one that cannot be simply reversed to restore the system and its surroundings to their original state
a block of ice melts when we place it in a hot (70 degree Celsius) metal box is an example of an irreversible process; heat flows from the box into the ice and water
a block of ice at 0 degrees Celsius can be melted if we put it in a 0 degrees Celsius metal box is an example of a reversible process; by infinitesimally raising or lowering the temperature of the box we can make heat flow into the ice to melt it or make heat flow out of the water to refreeze it
reversible processes are what kind of thermodynamic processes equilibrium processes with the system always in thermodynamic equilibrium
a reversible process is idealized so it cannot be precisely obtained in the real world
free expansion of a gas is what kind of process irreversible; non-equilibrium processes in that the system is not in thermodynamic equilibrium at any point until the end of the process
true or false disorder = chaos false
usual definition of disorder unorganized/random arrangement of particles
exploding firecracker is an example of disorder; you don't know where the pieces will land
entropy S; the measure of disorder in thermodynamics
entropy is synonymous with disorder
ex. hot and cold bodies and thermodynamics hot gives heat to cold; 1st law says cold can give heat to hot but this doesn't b/c its easy to go from energy to heat but heat is not completely converted into energy
is converting mechanical energy completely converted into heat yes; this happens everytime we use a car's brakes to stop it
can heat be completely converted into energy no but there are many devices that can partiallyconvert heat to mechanical energy
2nd law of thermodynamics state in terms of entropy a quantitative measure of the degree of disorder or randomness of a system; heat engine
heat engine any device that transforms heat partly into work or mechanical energy
Kelvin statement of the Second Law of thermodynamics no process is possible in which the sole result is the abbsorption of heat from a reservoir and its complete conversion into work
for an engine to do some work some energy must be dispersed
a ball at rest on a surface has never been observed to leap spontaneously upwards; an upward leap of the ball would be equivalent to the conversion of heat from the surface into work; causes the vibrations of the molecules to be distributed between the ball and the floor molecules
True or false entropy is a state function true
for an isothermal process deltaS = qrev/T which works for more than just reversible processes
all real rocesses that occur of their own accord are irreversible (reversible process being an idealization) and these process are also spontaneous
alternative definition of the 2nd Law of Thermodynamics total entropy of the uuniverse increases in any spontaneous process
we can look at entropy on two levels macro and micro
looking at a coin toss as 50% heads and 50% tails is a macro view
looking at a coin toss as coin 1 was heads, coin 2 was tails, coin 3 was tails is a micro view
there can be many microscopic states that correspond to the same macroscopic description
the state with the most disorder has the most microscopic states possible
equation for number of total possible outcomes (possible options)^N and N = number of repeat trials you have
the leas probable outcomes for flipping coins are the states that are all heads or all tails; aka completely ordered
the most probable outcome of tossing N coins is that 1/2 are heads & 1/2 are tails
macroscopic description "half heads, half tails" by itself tells you very little about the state (heads or tails) of each individual coin; the system is disordered b/c we know so little about the microscopic state
consider a mole of an ideal gas containing Avogadro number of molecules P,V,T = macroscopic state; microscopic would require stating position & velocity for each molecule; at certain P,V,T the gas may be in any one of the large # of microscopic states, depending on position& velocities of its NA of molecules
if a gas undergoes a free expansion into a greater volume, the range of possible positions increases as does the # of possible microstates; the system becomes more disordered & we say that the entropy has increased
if w=# of possible microscopic states for a macroscopic state: when tossing 4 coins w=1 for all heads or all tails; w=4 when 3 heads and one tails
Entropy, S, of a macroscopic state is given by the Boltzmann formula S=kln(w) where k = R/NA
use Boltzmann formula to show that increasing # of microstates increases S S=kln(w) as w increases S increases because they're proportionate
when S = 0 or w=1 (because kln(1) = 0) the system is completely ordered
the entropy of a closed system can never decrease because a closed system can never spontaneously undergo a process that decreases the # of possible microscopic states
What if all the air in your room spontaneously moved to one half of the room, leaving a vacuum in the other half of the room? the probability of this happening is not 0, but is so small that it is incredibly unlikely to occur
the second law of thermodynamics tells us that the essential character of any spontaneous change is that it is always accompanied by an overall increase in entropy
spontaneous processes have a positive deltaS universe
during melting the number of accessible microstates increases and so does the entropy; not all of the H bonds break # of kinds of motion increase entropy increases
in a thermodynamic cycle the overall change in a state function = zero
the most efficient heat engine cycle is the Carnot cycle consisting of 2 isothermal process & two adiabatic processes
the 2nd law of Thermodynamics says that not all the supplied heat can be used to do work, Carnot efficiency sets the limiting value on the fraction of the heat which can be used
In a Carnot Cycle, the processes involved are responsible & involve no change in entropy therefore it's an idealization
no real engine processes are reversible and all real physical process involve some increase in entropy
Carnot Cycle has 4 steps 2 isothermal, 2 adiabatic
an adiabatic process is not an isothermal process
adiabatic process means q= zero; no heat going in or out or a process that happens so quickly there is no opportunity for heat transfer to occur
champagne bottle 1st law w done by system w has to come @ the expense of something therefore happens @ expense of deltaU&deltaU is decreasing; if ideal gas&follow Kinetic theory therefore KE&T decreases & some gas condenses to some (lq)& we get the mist around the bottle
an adiabatic free expansion of an ideal gas is also isothermal
the conceptual value of the Carnot cycle is that it establishes the maximum possible efficiency for an engine cycle operating between Th and Tc
it is not practical engine cycle because the heat transfer into the engine in the isothermal process is too slow to be practical
if you installed a Carnot engine in your car, it would increase gas mileage, but you would be passed on the highway by pedestrians
heat flow happening during isothermal processes which means tiny change in work to prevent T from increasing; you have to put heat in, which would increase T unless you added heat in infinitesimally small changes so equilibrium could be reached
reversible process are slow due to infinitesimally small changes
you can only build machines that hold a set amount of Volume so you have to try and compensate to maximize efficiency but if you compensate too much you will end up extending more work
since internal energy is a state function, it does not depend on whether the path is reversible or irreversible but dqrev/T is >= dqirr/T
Clausisus Inequality dS is greater than or equal to dq/T
for a reversible process dS equals dq/T
for an irreversible chemical reaction or phase change dS is greater than dq/T
if the system is isolated from the surroundings the Clausius inequality implies dS is greater than or equal to 0
in an isolated system, the entropy cannot decrease when a spontaneous change occurs; irreversible process
reversible, isothermal expansion deltaS = qrev/T = nRln(Vf/Vi)
a phase change is reversible
phase change is at constant pressure so deltaH = qp, rev
all enthalpies of fusion are positive (melting is endothermic and requires heat)
entropies of fusion are positive
if the phase change is exothermic entropy is negative (entropy decreases b/c its freezing or condensing) for system but positive for surroundings b/c heat is released into them
at the transition temperature, the total change in entropy is zero
if the transition is endothermic (melting or vaporization) entropy change of the system is positive; entropy of the surroundings decreases by the same amount and the overall chagnge is 0
to find entropy of a change that is spontaneous and irreversible a reversible path must be found
the third law of thermodynamics is a statistical law of nature regarding entropy
at T=0, all energy of thermal motion has been quenched, and in a perfect crystal all the atoms or ions are in a regular, uniform array
at absolute zero, all lattice units are in their lattice sites, devoid of thermal motion
as the temperature is increased above 0 K, the atoms or molecules gain energy and their vibrational motion increases
at absolute zero, all the units of the lattice do not have any thermal motion therefore there is only one microstate
the entropy of the lattice increases with increasing T because vibrational motion causes the atoms or molecules to have a greater number of accessible microstates
residual entropy S>0 and T=0
ice has a residual entropy of 3.4 J/Kmol hydrogen bonds between neighbouring water molecules; there is a degree of randomness in which two bonds are short and which are long (short O-H; long O...H)
entropy increases as a function of temperature from absolute 0; the vertical jump on a graph refers to a phase change
the third law of thermodynamics allows us to determine absolute entropies of substances
entropy of a pure crystalline substance is 0 at 0 K
entropies reported on the basis that S(0)=0 are called third-law entropies
when the substance is in its standard state at the temperature T, the standard (Third-Law) entropy is denoted Snod(T)
S nod is called molar entropy values; standard molar entropies; standard state is 1 atm/1bar
just as solutions of cations cannot be prepared in the absensce of anions, the standard molar entropies of ions in solution are reported on a scale in which the standard entropy of the H+ ions in water is taken as zero at all temperatures; S(nod)(H+, aq) = 0
ion entropies vary on the basis that they are related to the degree to which the ions order the water molecules around them in solution small, highly charged ions induce local structure in the surrounding water, and the disorder of the solution is decreased more than in the case of large, singly charged ions
dAT,V is < or = 0
dGT,P is < or = 0
Helmholtz Energy A = U -TS
Gibbs Energy G = H-TS
criteria for spontaneity dAt,v < 0; dGt,p < 0; deltaSuniv>0
a decrease in Helmholtz energy means a change is spontaneous
dAt,v = 0 when a reaction is at equilibrium when neither the forward nor the reverse process has a tendency to occur
why do we use Gibbs more than Helmholtz energy we work more often with constant pressure than with constant volume
at constant temperature and pressure, chemical reactions are spontaneous when dGt,p =< 0
the criteria for equilibrium when neither the forward nor the reverse process has a tendency to occur is dGt,p = 0
deltaSuniverse is what for a spontaneous process >0
a positive deltaSuniv implies that deltaG is less than 0
if deltaG is negative the reaction is spontaneous in the forward direction
if deltaG is zero the reaction is at equilibrium
if deltaG is positive the reaction in the forward direction is non-spontaneous; work must be supplied from the surroundings; the reverse direction is spontaneous
it is more convenient to use deltaG as a criterion for spontaneity than to use deltaSuniv because deltaG relates to the system alone and avoids the complication of having to account for the surroundings
non-expansion work means any work other than that arising from the expansion of the system; ex. electrical work, mechanical work
at constant temperature and pressure, maximum additional non-expansion work equals dG (aka "free" energy)
if deltarG < 0 reaction is exergonic (work-producing) b/c the process is spontaneous, it can be used to drive another process, such as another reaction, or used to do non-expansion work
in biological cells, the oxidation of carbohydrates act as the heavy weight that drives other reactions forward and results in the formation of proteins from amino acids, muscle contraction, and brain activity
delta r G > 0 is endergonic
endergonic work-consuming; the reaction can be made to occur only by doing work on it (ex. electrolysing water to reverse its spontaneous formation reaction)
exergonic work-producing
for a system with expansion work only dwnon-expansion = 0
by convention deltaf G nod (H+, aq) = 0
standard Gibbs energies of formation of the elemnts in their reference states are 0 b/c their formation is a 'null' reaction
fundamental Gibbs equations dU=TdS-PdV; dH = TdS +VdP; dA = -SdT=PdV; dG=-SdT + VdP but these cannot be used to solve problems
when are the fundamental Gibbs equations valid for a closed system with no change in composition and with constant temperature and pressure
How do the fundamental Gibbs equations change if the composition of the system changes? concentrations in the reaction are changing and chemical potential helps us measure the change in concentration
chemical potential is a measure of how much the free enthalpy(or free energy) of a system changes (using Gibbs energy) if you add or remove a number of particles of the particle species while keeping the number of the other particles (and the temperature T and the pressure p) constant:
for a pure substance mu i is the molar Gibbs free energy
thermodynamics the study of the transformations of energy and, in particular, the transformation of heat into work and vice versa
thermodynamics was originally formulated by physicists and engineers interested in the efficiency of steam engines
how do steam engines work water is heated and boils and the expanding steam does work to propel the locomotive
in chemistry, thermodynamics deal with the energy out pout of chemical reactions answering questions such as why reactions reach equilibrium, their composition at equilibrium, and how reactions in electrochemical (and biological) cells can be used to generate electricity
classical thermodynamics provides useful relations between observable properties of bulk matter
statistical thermodynamics theory of the connection between atomic and bulk thermodynamic properties
work energy used to cause an object with mass to move; done to achieve motion against an opposing force
heat energy used to raise the temperature of an object
thermodynamic system examples reaction vessel, an engine, an electrochemical cell, a biological cell
thermodynamics popcorn example pot is placed on stove, energy added to popcorn by heat, popcorn expands & does work to exert an upward force on the lid to move it; state of popcorn change b/c v,t, and p all change
thermodynamic process a process where there are changes in the state of a thermodynamic system
surroundings the region outside of the system and are where we make our measurements; ex. large water bath; so huge has either constant v or constant p; effectively remains the same size
universe system + surroundings
open system can exchange both energy and matter with its surroundings; open flask
closed system can exchange energy but not matter with its surroundings; stoppered flask
isolated system can exchange neither matter nor energy with its surroundings; (not perfect) insulated thermos
diathermic walls that permit heating as a mode of transfer of energy; e.g. metal container
adiabatic walls that do not permit heating even though there is a difference in temperature; q=0
exothermic a process in a system that releases energy as heat; e.g. combustion of coal
endothermic a process in a system that absorbs energy as heat e.g. endothermic dissolution of ammonium nitrate in water in instant cold-packs that are included in some first-aid kits
expansion work =-PexdeltaV; when a system expands against an opposing pressure
free expansion expansion against 0 opposing force; Pex=0 therefore w = 0; ex. when a gas expands into a vacuum
how can we achieve the greatest amount of work reversible process
the work of reversible isothermal expansion of a gas is equal to the area beneath the corresponding isotherm evaluated between the initial and final volumes
can we have a reversible process in the real world? no it's an idealized process
internal energy sumKE + sumPE = U; the grand total energy of the system; we cannot actually measure this but we can deal with the changes in internal energy
if the system is a glass of H2O, placing it on a high shelf increases the gravitational PE arising from the interaction between the glass & the earth but has no effect on the interactions between the molecules so the internal energy of the H2O does not change
a system may exchange energy with its surroundings as heat or as work. Internal energy of a system changes in magnitude as heat is added to or removed from the system or as work is done on it or by it; deltaU =q+w
internal energy doesn't know if you are changing work or heat; acts like a bank with two types of currency
if a system is isolated from its surroundings then internal energy is 0; q=0, w=0
intensive properties do not depend on the amount of the sample being examined; ex. temperature, melting point, density
extensive properties depend on the quantity of the sample; ex. mass, volume
state function doesn't care how you got there, just cares about being there, ex. internal energy, enthalpy, entropy; depends on initial and final
heat and work are not state functions
enthalpy state function; H=U+w (usually just PV work)
enthalpy is more useful than internal energy because qp is easily measured
H is state function but q is not. Is there a contradiction? yes but under specific conditions it can be remedied; 1. constant pressure 2. PV work only
specific heat the amount of heat that must be added to one gram of a substance to raise its temperature by 1K/1degree C
heat capacity the amount of heat required to raise its temperature by 1K
A tomato plant is an open system. True or false? True
if the compression factor Z<1, it indicates that repulsive forces are dominant. True or False? Explain. False; for an ideal gas Z=1; Z<1 attractive forces are dominant and there are a lower number of molecular collisions
calorimetry the study of heat transfer during physical and chemical processes
calorimeter a device for measuring energy transferred as heat
heat capacity of the calorimeter is determined by combustion of a sample that releases a known quantity of heat and measuring the temperature change (usually benzoic acid)
what effect does reversing a reaction have on deltaH? reverse the sign
what effect does multiplying coefficients by 2 do to deltaH? multiply it by 2
Hess's Law states that if a reaction is carried out in a series of steps deltaH for the overall reaction will equal the sum of the enthalpy changes for the individual steps
the overall enthalpy change for the process is independent of the number of steps or the particular nature of the path by which the reaction is carried out. Why? it's a state function therefore Hess's Law is true
standard enthalpy of formation (deltaH nod f) enthalpy change that results when one mole of a compound is formed from its elements at a pressure of 1 atm/1 bar
bond dissociation energy the enthalpy change required to break a particular bond in one mole of gaseous molecules
all bond enthalpies are positive b/c it takes energy to break a bond so you have to put energy in
bond enthalpy tables are usually not accurate because they don't take into account the chemical environment
the standard enthalpy of formation of ions in solution is a special problem because it's impossible to prepare a solution of just cations or just anions; charge has to be neutralized so we have to set a 0 which is delta rH(H+, aq)=0
Created by: 530848841