CHM 306 Midterm 2

A vessel containing a liquid is opened inside an evacuated chamber. Will you see a liquid-gas interface if the volume of the initially evacuated chamber is (a) less than critical volume (b) a factor of 10 larger than the critical volume (c) a factor of 1.05 larger than the critical volume.

(a) No, because the liquid and gas are not distinguishable above the critical density. (b) No, because all liquids will evaporate (c) Yes, because the density is less than the critical density

What equation is the isothermal compressibility?

(dV/dP) @ constant T

what is the most probable velocity for a 1D gas velocity distribution

0 m s^-1

For NO3 with a singly degenerate ground state, what would the electronic partition function be?

1

The timescale for collisional transfer of rotation energy (R-->R) from one diatomic molecule to another at standard conditions is

10^10 seconds

Assuming 19F2 and 35Cl2 have the same bond length, which molecule do you expect to have the largest rotational constant (B)?

19F2

For a 2 component system a specific temperature and pressure, liquid and solid coexist how many degrees of freedom do we have for this system under these conditions

2

For a two component system at a specific temperature and pressure, liquid and solid coexist. How many degrees of freedom do we have fore this system under those conditions?

2 phase rule f = c - p + 2

the electric field at a point 1nm from a point dipole of 1D is

3 x10^5 V/cm

Which expression corresponds to the variance of the distribution P(x)?

<x^2> -<x>^2

Which of the statements is true about the dependence of U on V at constant T for a gas? A. U is independent of V at constant T for an ideal gas B. U is dependent of V at constant T for a real and ideal gas C. U can increase or decrease as V decreases at constant T for a real gas D. U is dependent on V at constant T for a real gas E. U must be reversible

A C and D A. U is independent of V at constant T for an ideal gas C. U can increase or decrease as V decreases at constant T for a real gas D. U is dependent on V at constant T for a real gas

An ideal gas in thermal contact with the surroundings is cooled in a irreversible process at constant pressure, which of the following statements is true.. A. entropy tot > 0 B. entropy surr >0 C. change in entropy>0 D. change in entropy surr<0

A and B A. entropy tot > 0 B. entropy surr >0

Which of the following statements about how the Debye-Hückel screening length changes with changes in the temperature, solvent dielectric constant, and ionic strength of an electrolyte solution are true? A. Increasing T increases the screening length. B. Increasing T decreases the screening length. C. Increasing εr increases the screening length. D. Increasing ionic strength increases the screening length.

A and C A. Increasing T increases the screening length. C. Increasing εr increases the screening length.

Which of the following statements about the phase diagram (qp v T) is correct? A. The zero slope of the curves in the liquid + solid and liquid + gas regions occurs is a result of two phase coexistence. B. The slope of the curves in the solid and liquid regions is proportional to the heat capacity. C. The slope of the curves in the solid and liquid regions is inversely proportional to the heat capacity. D. The total amount of heat taken up in the liquid + solid region is proportional to ΔHvaporization.

A and C A. The zero slope of the curves in the liquid + solid and liquid + gas regions occurs is a result of two phase coexistence. C. The slope of the curves in the solid and liquid regions is inversely proportional to the heat capacity.

A few minutes after opening a dishwasher after the wash cycle and before the dry cycle, you observe that ceramic plates are dry, and that plastic storage containers are wet. Which of the following statements can provide an explanation for this observation? A. The heat capacity of a ceramic plate is greater than that for a plastic storage container. B. The mass of a ceramic plate is greater than that for a plastic storage container. C. The enthalpy of vaporization of water is small compared to the heat capacity of a ceramic plate. D. The relative humidity in the kitchen is less than 100%. E. The relative humidity in the kitchen is greater than 100%.

A and C A. the heat capacity of a ceramic plate is greater than that for a plastic storage container C. The enthalpy of vaporization of water is small compared to the heat capacity of a ceramic plate

The reaction A + B → C + D is at equilibrium for ξ = 0.1. Which of the following statements about the reaction is true? A. ΔG0f for A + B is smaller than ΔG0f for C + D. B. ΔG0f for A + B is larger than ΔG0f for C + D. C. ΔG = 0 for ξ = 0.1. D. ΔG > 0 for ξ = 0.1.

A and C A. ΔG0f for A + B is smaller than ΔG0f for C + D. C. ΔG = 0 for ξ = 0.1.

Which of the following statements is true? A. ΔH0R = ΔU0R if all reactants and products are liquids or solids. B. ΔH0R = ΔU0R if all reactants and products are in their standard reference states. C. ΔH0R = ΔU0R if the change in the number of moles of gaseous species in the reaction is zero. D. ΔH0R = ΔU0R if the reaction takes place at 1 bar. E. ΔH0R = ΔU0R if the reaction takes place at 298.15 K.

A and C A. ΔH0R = ΔU0R if all reactants and products are liquids or solids. C. ΔH0R = ΔU0R if the change in the number of moles of gaseous species in the reaction is zero.

Which of the following statements is true? A. Tabulated values of standard entropies of some aqueous ionic species are negative. B. Tabulated values of standard entropies of aqueous ionic species are always negative. C. Tabulated values of standard entropies of aqueous ionic species are always positive. D. Tabulated values of standard entropies of aqueous ionic species can be negative or positive.

A and D A. Tabulated values of standard entropies of some aqueous ionic species are negative. D. Tabulated values of standard entropies of aqueous ionic species can be negative or positive.

What is the difference between configurations and microstates?

A configuration is a general arrangement of energy while a microstate is a specific arrangement of energy

Which of the following statements is true about the dependence of U on V at constant T for a gas? A. U is dependent of V at constant T for an ideal gas B. U is independent of V at constant T for real and ideal gas C. U can increase or decrease as V decreases at constant T for a real gas D. U is dependent on V at constant T for a real gas E. U must be reversible

A, C, D A. U is dependent of V at constant T for an ideal gas C. U can increase or decrease as V decreases at constant T for a real gas D. U is dependent on V at constant T for a real gas

Raoult's law for a solution of A and B will be better obeyed when

AA interactions, BB interaction, and AB interactions are about the same

Why are there no points in the liquid phase diagram for sulfur that shows rhombic and monoclinic solid phases in equilibrium with liquids and gaseous sulfur?

According tot he Gibbs phase rule, four phases of a pure substance cannot coexist

Which of Ne or Ar has the larger van der Waals parameter b?

Ar has the larger van der Waals parameter b because Ar atoms are larger than Ne atoms

The value of the Boyle temperature increases with the strength of the attractive interactions between molecules. Which of the following properly lists the Boyle temperatures of the gases Ar, CH4, and C6H6 in increasing order?

Ar, CH4, C6H6

Under what conditions does 𝛾±→1 for electrolyte solutions?

As m -> 0 We know that the activity is close to 1 at very small concentrations, so that can correspond to small molalities.

Why does the liquid-gas coexistance curve in a P-T phase diagram end at the critical point ?

At the critical point, the gas and liquid have the same density, and can no longer be distinguished. this is also true for all point on the liquid-gas coexistance curve extended beyond the critical point.

9.3 At the point when the L2 phase disappears, the temperature increases beyond 94C and the vapor composition changes along the i-j curve. Why does the vapor composition change along the i-j curve?

At the point when the L2 phase disappears, we are left with the dilute solution of butanol in water. The composition of the vapor is given by point i, and the composition of the solution is given by the point g. As more vapor is produced ,Zbutanol decreases and the boiling temperature increases. The composition of the liquid and the vapor is given by the ends of a tie line crossing the L1 + V region. We see that the liquid follows the composition on the curve g-k-0, and the vapor follows the composition along the curve i-j-0.

Gibbs Phase Rule

F = C - P + 2 f = degrees of freedom c = number of components p = number of phases at equilibrium for a system of any conditions !

8.20 Is the following statement correct? Because dry ice sublimes, carbon dioxide has no liquid phase

False. Carbon dioxide has a liquid phase above the triple point but not at 298K

A van der Waals gas undergoes an isothermal reversible expansion under conditions such that z<1. Is the work done more or less than if the gas followed the ideal gas law?

For a reversible expansion, Pexternal=P. Because V>Videal, for z<1, deltaV<detlaVideal.

The entropy of two liquids is increased if they mix. How can immiscibility be explained in terms of thermodynamic state functions?

Given a binary solution, miscible ideal solutions can be described with no differences in the interactions between A-A, B-B, and A-B. Entropy of mixing substance A and B is spontaneous if the substance is miscible. If the interactions between A-A and B-B are greater than the reactions between A-B, the entropy is non spontaneous and the solutions are described as immiscible. For immiscible substances, the enthalpy of mixing and volume of mixing would not be expected to equal - as it does for miscible solutions.

9.10 What can you say about the composition of the solid at temperatures less than the eutectic temperature in the figure below on a microscopic scale?

Gold and silicon are not miscible in all proportions. Below the eutectic temperature, the solid is non-uniform and consists of gold and silicon small crystallites.

The water gas shift reaction can be stated as...

H2O + CO → H2 + CO2

by convention q and w are both positive when:

Heat is added to the system and work is done on the system

9.11 Is a whale likely to get the bends when it dives deep into the ocean and resurfaces? Answer this question by considering the likelihood of a scuba diver getting the bends if he or she dives and resurfaces on one lung full of air as opposed to breathing air for a long time at the deepest point of the dive.

Henrys law suggests that a solubility of a gas in a solution is dependent upon the partial pressure of the pure substance. Atmospheric pressure increases with decreasing altitude. High levels of dissolved nitrogen in the blood cause a decompression sickness termed "the bends". It would be unlikely that the whale would have the bends.

Give a molecular level explanation as to why the surface tension of Hg(l) is not zero.

Hg atoms have a strong attractive interaction. The atoms at the surface of a droplet have fewer nearest neighbors than an atom in the liquid. They experience a net force perpendicular to the surface that will lead to a pressure increase inside the droplet

Why does water have several different solid phases, but only one liquid and one gaseous phase?

Liquid and gaseous phases are disordered, so that except for special cases such as superfluid and normal He(l), there is no way to distinguish two different liquid or gaseous samples of the same pure substance.

A triple point refers to the point in a P-T phase diagram for which three phases are in equilibrium. Do all triple points correspond to a gas-liquis equilibrium?

No, if there are several solid phases, there can be a triple point corresponding to the equilibrium among three solid phases.

will the fugacity coefficient of a gas above the Boyle temperature be less than 1 at low pressures?

No, the integral is always greater than zero for this case. Therefore y>1 for all P

9.6 For a pure substance, the liquid and gaseous phases can only coexist for a single value of pressure at a given temperature. Is this also the case for an ideal solution of two volatile liquids?

No. An ideal solution of two volatile liquids can exist over a range of pressures that are limited by the pressure for which only a trace of liquid remains, and the pressure for which only a trace of gas remains.

Can equilibrium with respect to the concentration of Ar and H2 be attained in the system? If so, what can you say about the partial pressure in each part of the system? Pure H2 |||| H2 + Ar

No. H2 can diffuse through the membrane but Ar cannot. The partial pressure of H2 will be equal on both sides of the Pd membrane at equilibrium.

A molecule has a carbonyl group. What contribution to the Cvm does the stretching vibration of this group make to a gas phase sample of this molecule at a temperature of 3000000K ?

R

9.5 Explain the usefulness of a tie line on P-Z phase diagram

The tie line allows the composition of the liquid and vapor phases to be determined geometrically for a given total composition and pressure. Specifically, the ratio of moles in liquid and vapor phase is inversely proportional to the ratio of the tie line distances. Tie lines are horizontal lines that connect liquid to vapor-liquid phases and vapor-liquid to vapor phases. These lines help determine the mole fraction of each component in both liquid (x) and vapor (y) phases in the binary solution

9.13 The entropy of two liquids is lowered if they mix. How can immiscibility be explained in terms of thermodynamic state functions?

The two liquids are immiscible if ΔHmixing > 0 and |ΔHmixing | > |TΔSmixing |. The liquids are immiscible if ΔGmixing = ΔHmixing − TΔSmixing > 0.

Raoult's Law

The vapor pressure of one component above a solution is proportional to the mole fraction of that component in the solution. P_A = X_A * P_total

A Van der Waals gas undergoes an isothermal reversible expansion under conditions such that z>1. Is the work done more or less than if the gas followed the ideal gas law?

The work done is more than if the gas followed the ideal gas law.

9.2 Fractional distillation of a particular binary liquid mixture leaves behind a liquid consisting of both component in which the composition does not change as the liquid is boiled off. Is this behavior characteristic of a maximum or minimum boiling point azeotrope?

This behavior is characteristic of a max-boiling azeotrope. After initially giving off the more volatile component, the liquid remaining tends to the composition of the max boiling point at intermediate composition. After the more volatile component has boiled away, the azeotrope evaporates at constant composition.

Why does the triple point in a P-T diagram become a triple line in a P-V diagram?

This is the case because a gas and a liquid are in equilibrium for the range of values of volume from that of the pure liquid to that of the pure gas at a given temperature

Why are the triple point temperature and the normal freezing point very close in temperature for most substances?

This is the case because the freezing point changes only slightly with pressure.

List the molecular motions in order of increasing distance between energy levels.

Translational, Rotational, Vibrational, Electronic

What energetic degrees of freedom are considered when applying statistical mechanics to Ar?

Translations and electronic

When considering the equilibrium involving the ground-state dissociation of a diatomic into atomic constituents, what energetic degrees of freedom are considered?

Translations, rotations, vibrations, and the dissociation energy of the diatomic

The law of corresponding states implicitly assumes

Two parameters are sufficient to describe the intermolecular potential

A system containing argon gas is at pressure P1 and temp T1. How would you go about estimating the fugacity coefficient of the gas?

Use the critical constants of the gas to determine the reduced pressure and temperature. With these results, estimate the fugacity coefficient using figure

How does the diffusion coefficient (D) for a gas scale with average speed (vave)?

Vave

8.13 How can you get a P-T phase diagram from the P-V-T phase diagram?

You can get a P-T phase diagram by projecting a P-V-T phase diagram on the P-T plane

By looking at the a and b values for the van der Waals equation of state, decide whether 1 moles of O2 or H2O has ther higher pressure at the same value of T and V

a is significantly larger for H2O. Therefore the attractive forces between H2O molecules are greater than between O2 molecules. Consequently, O2 will have a higher pressure

Gaussian distribution

normal distribution

what is the ratio of D(1H2)/D(2H2)?

sqrt. 2

Explain the significance of the Boyle temperature

the Boyle temp provides a way to classify the way in which z varies with P at low values of P for different gases. If T>Tb, z increases with increasing P; it T>Tb, z decreases with increasing P. At the Boyle temp, the repulsive and attractive interactions cancel one another out so that the gas behaves ideally over a larger range of pressure than at other temperatures

consider the comparison made between accurate results and those based on calculation using the van der Waals and Redlich-Kwong equations of state. is it clear that one of these equations of state is better than the other under all conditions?

the Redlich-Kwong gives more accurate results for almost all of the values of pressure. However, it is not better under all conditions

Which of Ne or Ar has the larger van de Waals parameter a?

the degree to which the electron charge cloud is polarizable determines a. Ar has the larger van der Waals parameter a because it has more electrons and is therefore more polarizable

7.10 Explain why the oscillations in the two-phase coexistance region using the Redlich-Kwong and van der Waals equations of state do not correspond to reality

the oscillations predict that as V increases, P will increase. No real gas exhibits this behavior

the water gas shift reaction is a moderately exothermic reversible reaction. Why is the reaction run at high temperatures industrially?

the reaction is kinetically favored at high temperatures

Why do the temperature versus heat curves in the solid, liquid, and gas regions of a graph have different slopes?

the slopes of the curves are equal to the inverse of Cp.m which has different values for all three phases

7.20 An equation states that the total pressure in a mixture of gases is equal to the sum of the partial pressure. Is this equation valid for real gases?

this is only valid if the molecules do not interact with one another or if the pairwise interactions for all of the different gases are equal.

7.1 Using the concept of the intermolecular potential, explain why two gases in corresponding states can be expected to the the same value for z

two different gases will have different values for the depth of the intermolecular potential and for the distance at which the potential becomes positive. By normalizing P, T, and V to their critical values, the differences in the intermolecular potential are to a significant extent also normalized

What is degeneracy?

when a particle has two or more states available at a given energy

for reactive mixture of ideal gases we can calculate the equilibrium constant in terms of pressure, mole fraction and/or molarities. When are these equilibrium constants equal?

when ΔV = 0

The temperature dependence of the potential of a cells is vanishingly small. What does this tell you about the thermodynamics of the cell reaction?

Δ𝑆𝑅°=𝑛𝐹(𝛿𝐸°/𝛿𝑇) @ P 𝑎𝑛𝑑 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑛𝑜 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑐𝑒: ΔS𝑅°≈0, 𝑖.𝑒. 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑛𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑒𝑛𝑡𝑟𝑜𝑝𝑦

The reaction A + B ⇌ C+ D is at equilibrium for 𝜉=0. What does this tell you about the variation of Gpure with 𝜉?

∆𝑮𝒇° for A + B is less than that for C + D If the ∆_𝐺_𝑓_°_ for the reactants was much greater than that of the products, 𝝃 would be near 1.0. If the ∆_𝐺_𝑓_°_ of reactants and products were nearly the same, 𝝃 would be near 0.5.

Which of the following statements is true: A. A P-T phase diagram can be obtained from a P-V-T phase diagram by projection on the P-V plane. B. A pure substance can have several solid phases, but only one gas phase. C. The triple point in a P-T diagram can become a triple line in a P-V diagram. D. As the pressure is increased at 245°C, ice I is converted to ice II, showing that ice I has the higher density.

B and C B. A pure substance can have several solid phases, but only one gas phase. C. The triple point in a P-T diagram can become a triple line in a P-V diagram.

Which statement is true? A. The voltage between the terminals of a battery in which the contents are in chemical equilibrium is equal to the standard potential. B. The electrode of a battery at which oxidation takes place is not the same for charging and discharging. C. More work can be extracted from a fuel cell than a combustion engine for the same overall reaction. D. If you double all the coefficients in the overall chemical reaction in an electrochemical cell, the equilibrium constant and the emf change by the same factor.

B and C B. The electrode of a battery at which oxidation takes place is not the same for charging and discharging. C. More work can be extracted from a fuel cell than a combustion engine for the same overall reaction.

Which of the following statements about the experimental determination of standard cell potentials is true? A. Standard cell potentials are determined by setting the activity of all species to one. B. Standard cell potentials are determined in very dilute solutions and calculating activity coefficients using the Debye-Hückel limiting law. C. Standard cell potentials are determined in solutions where the activity is near one and calculating activity coefficients using the Debye-Hückel limiting law. D. Standard cell potentials are determined at 298.15K.

B and D B. Standard cell potentials are determined in very dilute solutions and calculating activity coefficients using the Debye-Hückel limiting law. D. Standard cell potentials are determined at 298.15K.

Which of the following processes is spontaneous? A. the reversible isothermal expansion of an ideal gas B. the vaporization of superheated water at 102 C and 1 bar C. the constant pressure melting of ice at its normal freezing point by the addition of an infinitesimal quantity of heat D. the adiabatic expansion of a gas into a vacuum E. The reversible adiabatic expansion of a gas

B and D B. the vaporization of superheated water at 102 C and 1 bar D. the adiabatic expansion of a gas into a vacuum

Why is deltH sublimation = deltH fusion + deltH vaporization?

Because H is a state function, deltaH has the same value for solid, liquid, gas, and intermediates, as long as the initial and final states are the same for these two processes

8.1 Why is it reasonable to show the u versus T segments for the three phases as straight lines? More realistic curves would have some curvature. Is it the curvature upward or downward on a u versus T plot?

Because S increases slowly with T, the realistic curves will curve downward, but not very rapidly

the value of the Boyle temperature increases with the strength of the attractive interactions between molecules. Arrange the Boyle temperatures of the gases Ar, CH4, and C6H6 in increasing order

Because the strength of dispersive interations increases with the number of electrons and atoms, Ar<CH4<C6H6

tabulated values of standard entropies of aqueous ionic species can be negative or positive because

Because the structure of the solvent is affected by the presence of the ionic species

Q9.14 Explain why colligative properties depend only on the concentration, and not on the identity of the solute molecules.

Colligative properties depend on changes in the entropy of the solution when the solution is dissolved, which is determined by the concentration of the solution not their identity or structure.

9.1 Why is the magnitude of the boiling point elevation less than that of the freezing point depression?

The boiling point elevation is less than the freezing point depression because the chemical potential of the vapor is a much more steeply decreasing function of temperature than the solid. This is due to the relation du=-SmdT at constant P and the fact that the molar entropy of a vapor is much larger than that of a solid. When the uliquid curve is displaced down by the addition of the solute, the intersection of the uliquid curve with the usolid curve and the ugas curve determines the shift in the freezing and boiling temps. Because the magnitude of the slope of the ugas curve is greater than that of the usolid curve, Tb moves up less than Tm moves down.

As the pressure is increased at -45, ice I is converted to ice II. Which of these phases has the lower density?

The higher density phase is more stable as the pressure is increased, according to LeCatelier's principle. Therefore ice I is the less dense phase

Explain why chemists doing quantitative work using liquid solutions prefer to express concentration in terms of molality rather than molarity.

The molality of a solution is preferred unit because it is independent of P and T. A kilogram of a substance is a conserved quantity, independent of temperature and pressure. The volume, however, changes as T or P are varied because the thermal expansion coefficient and the isothermal compressibility are not zero. Moles per kilogram is thus a more useful concentration unit than moles per liter, which changes with the thermodynamic state.

What does a partition function represent?

The normalization factor for the probability distribution.

What is the physical origin of the pressure difference across a curved liquid-gas interface?

The origin is the cohesive forces in the liquid. Across an interface, the resultant force vector is not zero in magnitude. If the interface is curved, the resultant force tends to minimize the surface area, leading to a pressure difference across the interface

At a given temperature, a liquid can coexist with its gas at a single value of the pressure. However, you can sense the presence of H2O above the surface of a lake by the humidity, and it is still there is the barometric pressure rises or falls at constant temperature. How is this possible?

The statement that at a given temperature, a liquid can coexist with its gas at a single value of the pressure holds for a system with only one substance. For the case described, the system consists of water and air. The change in barametric pressure is equivalent to an external pressure exerted on a liquid. This will change the vapor pressure only slightly.

What is it meant by "weight" of configuration?

Weight is equal to the number of microstates corresponding to a given configuration

A gas is slightly above its Boyle temp. Do you expect z to increase or decrease as P increases?

above the Boyle temp (dz/dP)t > 0, so z increases as P increases

Why is it possible to set the ground-state vibrational energy to zero when constructing the vibrational partition function?

because the quantity of interest is the energy of excited vibrational energy levels relative to the ground state, not the absolute energies

8.19 What can you say about deltH vaporization of a liquid as the temperature approaches the critical temperature?

deltHvap decreases slowly far from the critical temperature and rapidly as it approaches the critical temperature where it has the value zero.

A van der Waals gas undergoes an isothermal reversible expansion under conditions such that z > 1. Is the work done more or less than if the gas followed the ideal gas law?

for a reversible expansion, Pexternal= P. Because V>Videal, for z>1, deltV?deltVideal. therefore abswork= integralPdV > integralPdVideal

7.19 You have calculated the pressure exerted by ethane using the ideal gas law and the Redlich-Kwong equation of state. How do you decide if the repulsive or attractive part of the molecular potential dominates under these conditions?

if PR-K > Pideal, repulsion dominates if PR-K< Pideal, attraction dominates

Is the ratio of the fugacity to pressure greater to or less than one if the attractive part of the interaction potential between gas molecules dominates?

if the attractive interactions dominate, P<Pideal, so f/P <1

For a given set of conditions, the fugacity of a gas is greater than the pressure. What does this tell you about the interaction between the molecules of the gas?

if the fugacity is greater than the pressure, the repulsive part of the potential dominates the interaction between the molecules

Why is the standard state of fugacity (fo), equal to the standard state of pressure, Po?

if this were not the case the fugacity would not become equal to the pressure in the limit of low pressure

A vessel containing a liquid is opened inside an evacuated chamber. For which of these situations will you see a liquid-gas interface? If the volume of the initially evacuated chamber is: i) Less than the critical volume? ii) A factor of 10 larger than the critical volume? iii) A factor of 1.05 larger than the critical volume?

iii) A factor of 1.05 larger than the critical volume?

The chemical potential for a solution...

is always less than that of the pure solvent