Quiz 2 Flashcards
How do you calculate Cp for an ideal gas?
Cp = Cv +nR
Why is Cp larger than Cv?
not only do we increase the temperature when we add heat, but we also do pressure volume work against atmospheric pressure
What is the general definition of Cv? Cp?
Describe the energy of an ideal gas.
The energy of an ideal gas is purely kinetic, for an ideal gas the internal energy only depends on temperature not volume or pressure
What is the enthalpy state function?
H = U + PV
What is the relationship between enthalpy and heat at constant pressure? What conditions does this equation depend on?
dH = dQp
- mechanical equilibrium between system and surroundings (reversible process)
- no additional work other than pv work
What is the si unit for volume and how does that relate to L?
m3
1 L = 0.001m3
What is described by the two work equations for isothermal expansion?
the work the system does on the surroundings
Equation for work the system performs on the surroundings when heating a solid liquid or gas reversibly under constant pressure
w= -p(v2 - v1)
- pV work upon reversible heating at constant external pressure
Internal energy equation for heating a liquid with phase transition?
w= -p(v2 - v1)
but also:
dU = Cvm(T2-T1)
What does isobaric mean?
same pressure
What does isochoric mean?
same volume
How do you calculate dH during a phase change?
What does thermochemistry study?
the heat transferred in chemical reactions
Why are standard states important?
- so we can measure relative changes in dH
- like sea level
What is the standard state?
- the most stable state of a material at 1 bar and a specified temperature
What are the standard states of gas, solid, liquid, and solution?
Gas - pure gas at 1 bar
Solid - crystalline solid at 1 bar
Liquid - states of the liquid at 1 bar
Solution - substance in a solution with conc 1M and at pressure of 1 bar
What is the standard enthalpy of formation?
- the reaction enthalpy for the formation of the compound from its elements in their reference states
What is the reference state of an element?
its most stable form under standard conditions (1 bar, pure element, specified T)
What does the definition of standard enthalpy of formation imply?
makes the standard enthalpies of formation of elements in their reference states zero at all temperatures (enthalpies of “null” reactions)
What is Hess’s Law?
If two or more chemical equations are added to give another chemical equation the corresponding enthalpies are added
What is a spontaneous process?
- Occurs without ongoing outside intervention
- although reverse processes are also possible, they require work to be done
- all processes that require work are non-spontaneous
What is entropy? (words)
a measure of energy dispersal
Describe entropy - conservation and function
- entropy is a state function - need to find the amount of reversibly exchanged heat qrev as the system is going from the initial to the final state, even when the process is irreversible
- unlike energy, entropy is not conserved; the entropy of an isolated system increases in the course of a spontaneous process
What are two classes of processes?
spontaneous and nonspontaneous
Why does a ball not bounce as high on the next bounce?
The energy that is concentrated in the ball is dispersed in the surroundings.
Hallmark of spontaneous change
direction of change that leads to the dispersal of the total energy in the universe
What is entropy intimately related to?
- excitation of vibrational modes are related to heat transfer - we can easily accept that entropy is intimately related to heat transfer
What is the basic entropy equation?
When are these equations true?
H = U +pV
dH = dU +pdV
- first definition is true under all conditions (general definition of enthalpy)
- second definition is true only under constant pressure
What is the equation for enthalpy change upon reversible heating under constant pressure (no phase change)?
dH = nCpm(T2-T1)
How do you use enthalpy state transition equations when adding?
- if it is in the reactants (make -)
- if it is in the products add as is
Entropy is a ______ function
state
- change applies to reversible and irreversible processes
What is the message of the clausius inequality?
a process can occur spontaneously if the total entropy of the universe increases in the course of the process
Describe the Clausius inequality in the case of reversible and irreversible processes.
How do you calculate enthalpy at a temperature other than 25?
What is the Clausius inequality?
Explain the basic interaction between energy and probability and give the equation.
What did our money experiment show?
- energy is randomly and dynamically exchanged between molecules in discrete amounts (energy is quantized)
- it is just as probable for a high energy molecule to lose or gain energy when it meets a lower energy molecule
- when the average distribution of energy moved to a higher value the distribution broadened, and fewer students had no money
How is entropy defined in classical thermodynamics?
Δ S = qrev / T
How is entropy defined in statistical thermodynamics? How do you describe this in words?
S = klnW
- entropy as a measure of microstates (W) in which a particular distribution of the total energy over the energy levels of the system can be realized
What does W represent?
- the number of ways in which a distribution of a given amount of energy over the molecules of the system can be formed
What is W tied to?
- W is tied to the temperature of the system, when we add heat to the system the number of ways in which the available energy can be distributed increases, increasing Ssys
What occurs when increasing energy quanta?
-if the same amount of energy was exchanged in larger amounts there would be fewer ways of distributing the money and more molecules would be in their ground state (lowest energy state)
What did our game simulate?
the exchange of vibrational quanta
How does container size effect energy level spacing?
- increasing the width of a container decreases the spacing between translational energy levels, so more energy levels become accessible at a fixed internal energy - this is why gas expands into a vacuum
How can you change the accessible microstates?
- Can decrease the volume by doing work on the system, this increases the spacing and lowers the number of accessible microstates at the same U
- Transferring energy in the form of heat into the system increases the U and therefore the number of accessible microstates (spacing unchanged)
What is heat capacity?
the energy dispersed in a substance per unit temperature (j/k)
Describe temperature during a phase transition.
- during a phase transition T doesnt change
How does entropy change as you change temperature? (without phase transition)
How does entropy change as you change temperature (with phase transition)?
What is the first law of thermodynamics?
- energy conservation
- energy of the universe is conserved
- Δ U = q + p
What is the second law of thermodynamics?
- spontaneity of processes
- the entropy of an isolated system increases in the course of a spontaneous change
- Δ S universe = Δ S system + Δ S surroundings > = 0
- (equality applies to a system at equilibrium)
What is the third law of thermodynamics?
The entropy of a perfect crystal at absolute zero is zero
What is the origin of mixing ideal gases?
origin of entropy of mixing is better described as the entropy of dilution
What does “the entropy increases” mean?
“a change will always occur in the direction of the more probable distribution of energy”
Describe small and large systems in reference to energy and probability?
Small systems like ours (26 students) will exhibit fluctuations (deviations from the most probable distribution). However, large systems (consisting of a large number of molecules) do not exhibit any significant fluctuations (such states are called equilibrium states).
When will the entropy be positive?
When W2 > W1
What can you calculate heat/ enthalphy of in regards to phase changes?
- heat/enthalphy of fusion, vaporization, condensation, freezing
- Fusion and vaporization are positive quantities because we need to break intermolecular bonds
Compare H2O and n-octane in terms of joules of heat available per gram. (H2O = -141.78kj/g) (n-octane = -48.25kj/g)
Since the amount of heat available per gram of water is higher than n-octane the heat of formation of water is higher than that of n-octane
What is the equation for the molar entropy of a gas?
- The molar entropy of a gas is intimately related to its molar volume (as measured by partial pressure)
ΔSsys = Rln (Pi/Pf)
What does Gibbs free energy do (as a function)?
it is a state function that predict the spontaneity of processes at constant p and T
Given the heat of freezing, how do you calculate ΔG at 273.15 and 263.15 K of H2O changing from liquid to solid?
What is the definition of Gibbs Free Energy at constant temperature and pressure?
- ΔG = the maximum amount of non-expansion work a system can do
- the system must operate reversibly or else this maximum amount of work will be less
Equation for pressure dependence of Gibbs free energy for an ideal system:
ΔG = nRTlnP2/P1
Describe gibbs free energy for an ideal gas expansion/compression: (type of effect)
Gibbs free energy for ideal gas expansion/compression is purely an entropy effect, not an enthalpy effect
- ΔH is not pressure dependent for an ideal gas
What is RT?
RT = 2.5 kj/mol
This is the thermal energy available at room temperature (300k)
What are the 4 types of intermolecular forces?
dispersion/vanderwaals, dipole-dipole, h-bonding, ion-dipole
Dispersion/Vanderwaals:
- present in all molecules/atoms
- 0.05 - 20+ kj/mol
- dispersion force can become very strong and even stronger than the others for molecules of high molar mass
Dipole - Dipole
- polar molecules
- 3 - 20+ kj/mol
H-bonding
- Molecules containing H bonded to F ,O or N
- 10 - 40 kj/mol
Ion-dipole
- Mixtures of ionic compounds and polar compounds
- 30 - 100+ kj/mol
Strength of a covalent C-H bond
420kj/mol
What is coulomb’s law?
F & q1q2/r^2
- the closer the charges the stronger the force
- cutting the distance of separation by 1/2 increases the force by 4x
What is the driving force for helix formation?
- hydrogen bonding stabilized peptide secondary structure
- in the random coil conformation there are many different rotational and translational modes available to the atoms - entropy is dispersed over many energy levels, there are fleeting H-bonds
- in the helical structure H-bonds form between peptide units, as a result the folded state is enthalpically stabilized
- folding removes rotational and translational modes, therefore it is low in entropy
What is the physical basis for the hydrophobic effect?
- a small hydrophobic region <1nm is diameter does not disrupt hydrogen bonding
Can a reaction occur in an isolated system that leads to a decrease in the entropy of the system?
The reaction cannot occur in an isolated system that leads to a decrease in the entropy of the system. This is because as per the second law of thermodynamics, there is no exchange of energy and material between system and surrounding.
Describe an irreversible and reversible process in context of ideal gas expansion.
- Irreversible process occurs when the pressure is suddenly changed, rather than in small amounts
- A reversible process is when the system remains in mechanical equilibrium, in the case of ideal gas expansion the pressure changes in small enough increments that pex =pgas
What occurs to the energy levels during the phase transition water to ice?
the energy levels of the system decrease
Explain the sign of ΔSsys for the phase transition of water to ice?
If the energy levels of the system decrease this means that more microstates can be achieved with the same internal energy and there is an increase in entropy or the dispersal of energy is greater because more microstates can be achieved
What are quantities A and B on the graph?
Enthalpy of fusion, enthalpy of vaporization
Provide a physical explanation for the different magnitudes of enthalpy of fusion and enthalpy of vaporization
- more freedom of gas than liquid caused by different modes
- greater volume change
Describe the modes accessed by heavier molecules?
The vibrational levels of the heavier molecules are lower, therefore more populated at room temperature
How do small and large cavities impact the hydrophobic effect?
- Small spherical cavities do not disrupt hydrogen bonding, but require re-organization of the H-bonding network around the cavity
- Large spherical cavities disrupt H-bonding, resulting in a liquid-vapor-like interface
How do small and large cavities (particle/s and aggregates) impact the scaling of ΔG in the hydrophobic effect?
Hydrophobic aggregation is _________ and __________
entropic and enthalpic
What are two graphs that demonstrate gibbs free energy of hydration? What are the axes?
What does the driving force for hydrophobic assembly mean? What do the graphs show?
- If we have a sufficient number of small particles such that they can assemble into an aggregate >1nm in R, then the hydration gibbs free energy of the aggregate is at 1, (bottom point) but the free energy of the particles scales with the total volume
- the difference (2 - 1) is the driving force
- If you have a high concentration of these particles then they will assemble into an aggregate >1nm, and aggregation is favored
Describe the behavior of entropic and enthalpic aggregation at high temp. How does this effect the driving effect at high temp?
- Enthalpic : some h-bonds are already disrupted at high temp so the penalty for the gibbs free energy of hydration for the aggregate is less
- Entropic : if you exclude some volume from hydrogen bonding that effect will be more pronounced at high temp, can access more configurations in your hydrogen bonding network at high temp
- The driving effect will be stronger at high temp (more negative)
∫dx
∫dx = x
∫x dx
∫x dx = 1/2 x^2
∫x^2 dx
∫x^2 dx = 1/3 x^3
What is the work done on an ideal gas at constant pressure?
W = -nR(T2 - T1)
Positive ΔS
increasing dispersal of energy
negative ΔS
decreasing dispersal of energy
1 g/cm^3 =
1000000 g/m^3
J to L atm
1 J = 0.0099 L atm
