CHEM 341

PHYSICAL CHEMISTRY

FINAL EXAM

 

 

Name_____________KEY____________________

 

 

ID#_______________________________________

 

Your name is worth 1 point, Merry Xmas.

Do not open this exam until told to do so. The exam consists of 16 pages, including this one. Count them to insure that they are all there. The last five pages of the exam are the lists of constants and equations. No additional notes are allowed. You should only have your exam, writing implements and a calculator on your desk.

 

 

 

 

 

 

Do not write in the area below

Page

Score

1

1/1

2-7

/99

8

/25

9

/25

10

/25

11

/25

Total

/200

 

For each of the following problems, a right answer is worth 3 points, a wrong answer results in -1 points and no answer is scored as a zero. You do not need to justify your answer.

1) In general, the temperature of a system is most accurately described as:

  1. a measure of the heat entering a system
  2. a measure of the kinetic energy of a system
  3. a measure of the total energy of a system
  4. a measure of the heat generated by a system

 

2) During the isothermal expansion of an ideal gas:

  1. q = 0
  2. q < w
  3. q = w
  4. w = -q

 

3) At constant pressure, when CsCl is dissolved in water, the beaker becomes quite cold to the touch. The enthalpy change for dissolving CsCl in water is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

4) For an isothermal expansion of an ideal gas, the change in enthalpy is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

5) For an adiabatic compression of an ideal gas, the change in internal energy is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

6) An ideal gas is compressed isothermally and reversibly from 2 liters to 1 liter, then expanded adiabatically and reversibly back to 2 liters. The overall change in temperature of the gas is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

7) The freezing of liquid water to form ice

  1. results in uptake of heat from the surroundings
  2. results in release of heat to the surroundings
  3. results in no transfer of heat to or from the surroundings
  4. whether heat is taken up or given off during freezing depends on the temperature

 

8) When a spontaneous, endothermic reaction occurs at constant temperature and pressure, the entropy change of the surroundings is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

9) When a spontaneous, endothermic reaction occurs at constant temperature and pressure, the entropy change of the system is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

10) Consider a mixture of ice and water at equilibrium in an adiabatic container. Heat is transferred into the system until half the ice melts. The resulting change in temperature of the system will be

  1. an increase
  2. a decrease
  3. no change
  4. impossible to tell

 

11) Consider the transfer of heat between a hot block of copper and a cold block of copper. Which of the following is true?

  1. The entropy change is positive in both blocks
  2. The entropy change is negative in both blocks
  3. The entropy change in the cold block is opposite in sign and smaller in magnitude compared to the entropy change in the hot block
  4. The entropy change is the cold block is opposite in sign and larger in magnitude compared to the entropy change in the hot block

 

12) For the process of heat transfer between the hot and cold blocks in the last problem, the free energy change is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

13) For a spontaneous chemical reaction, the enthalpy change is:

  1. positive
  2. negative
  3. zero
  4. impossible to tell

 

14) At 20 C and 1 atm, the chemical potential of ice is

  1. greater than the chemical potential of liquid water.
  2. equal to the chemical potential of liquid water.
  3. less than the chemical potential of liquid water.
  4. this depends on the amounts of ice and water present.

 

15) Upon dissolving salt into a mixture of ice and water at equilibrium, the temperature of the mixture will:

  1. increase
  2. decrease
  3. stay the same
  4. impossible to tell

 

16) You can cause ice to melt by exerting pressure on it. This means that:

  1. the molar volume of ice is greater than that of liquid water
  2. the molar volume of ice is less than that of liquid water
  3. the molar volume of ice is equal to that of liquid water
  4. impossible to tell

 

17) Carbon tetrachloride and water are immiscible. That is, they do not mix together. This means that:

  1. the entropy (for the system) of mixing is negative
  2. the free energy of mixing is negative
  3. the enthalpy of mixing is positive
  4. none of the above

 

18) What is the maximum number of phases that can be present in a two component system?

  1. 2
  2. 3
  3. 4
  4. 5

 

19) When the reaction Aß à B is at equilibrium, the reaction free energy is:

  1. zero
  2. one
  3. 2.303
  4. impossible to tell

 

20) If I add salt to water, the chemical potential of the water will:

  1. increase
  2. decrease
  3. stay the same
  4. impossible to tell

 

21) After dissolving 0.01 M NaOH in pure liquid water, the pH is approximately (assuming all activity coefficients are 1.0):

  1. 2
  2. 12
  3. 9
  4. 16

 

22) If one dissolves an equal amount of the conjugate base and the conjugate acid form of a molecule in a beaker of water, the final pH will be approximately (assuming activity coefficients are all one):

  1. Equal to the pKA of the molecule.
  2. Equal to the pKB of the molecule.
  3. pH 7.0.
  4. pH 14.0.

 

23) According to the Debey-Huckle theory, the activity (not the activity coefficient!) of NaCl in a 0.1 molal aqueous solution is:

  1. greater than 0.1
  2. less than 0.1
  3. equal to 0.1
  4. the answer will depend on the situation

 

24) The anode of an electrochemical cell is always:

  1. positive
  2. negative
  3. uncharged
  4. the answer will depend on the situation

 

25) For a spontaneous electrochemical reaction, the zero current potential (E) is:

  1. greater than zero
  2. zero
  3. less than zero
  4. impossible to tell

 

26) The rate of a chemical reaction has units of:

  1. s-1
  2. M/s
  3. M-1s-1
  4. Depends on the reaction order.

 

27) The reaction A ß à B has an equilibrium constant of 10. This means that:

  1. The rate constant for the forward reaction is ten times bigger than that of the reverse reaction.
  2. The rate constant for the reverse reaction is ten times bigger than that of the forward reaction.
  3. The sum of the forward and reverse rate constants is 10.
  4. You cannot say anything about rate constants from thermodynamic data.

 

28) For the irreversible reaction A à B, doubling the concentration of B will cause the rate of change of A (dA/dt) to:

  1. increase by a factor of two
  2. decrease by a factor of two
  3. stay the same
  4. impossible to tell

 

29) For the elementary reaction, A+B+C à D, the units of the forward rate constant are:

  1. s-1
  2. Ms-1
  3. M-1s-1
  4. M-2s-1

 

30) What molecular properties give rise to the red color of the paint on a stop sign?

  1. There are molecules in the paint whose electronic orbitals have an energy spacing equal to the energy of red photons, but not the energy of blue or green photons.
  2. There are molecules in the paint whose electronic orbitals have an energy spacing greater than the energy of red photons, closer to the energy of green or blue photons.
  3. There are molecules in the paint that absorb all visible light and emit red light, which is what we see.
  4. Only red light has the right energy to stimulate emission from excited electronic orbitals in the molecules in the paint, and what we see is this emission.

 

31) When you measure the absorbance spectrum of a complex organic dye molecule in solution, you typically find that it is 10 - 30 nanometers wide. A likely explanation for the spectrum being so broad is:

  1. The deBrogli wavelengths of the electrons in the molecule are large, resulting in an uncertainty in the energy spacing between orbitals.
  2. Because the light is traveling so fast, its energy and therefore wavelength is uncertain.
  3. The molecules in the cuvette all have slightly different conformations or environments and this results in a distribution of photon energies absorbed.
  4. Fluorescence is shifted to the red of absorbance and this broadens the spectrum.

 

32) Your mirror is probably made of a piece of glass with an aluminum backing. Almost all the light that hits the mirror reflects back. Only about 5% of the light that hits the surface of the glass in your window reflects back. The reason why light reflects so well from the aluminum surface compared to the glass surface is:

  1. Metal is much harder than glass and therefore photons undergo purely elastic collisions.
  2. Metals have conduction bands that allow electrons to move freely, generating a counter electric field to the photon. The bound electrons in glass cannot do this as efficiently.
  3. The magnetic field of the photon sets up an equal and opposite magnetic field in the metal. Glass is not influenced by magnetic fields, so little reflection is observed.
  4. The electric field at the surface of a metal is much larger than that found at the surface of a glass, and this repels the photons.

 

33) Phophorescence arises from:

  1. Formally "forbidden" emission from triplet states of a molecule.
  2. Molecules left in a thermally excited state after light absorption that glow.
  3. Relaxation among vibrational levels in the ground and excited states that results in loss of energy as heat prior to emission.
  4. Chemical reactions between molecules that result in light emission.

 

 

Each of the following problems is worth 25 points. You must show your work or reasoning for credit!

34) 40 grams of ice at 0 C is placed in 100 mls of water at 25 C in an adiabatic container. What is the final temperature when the system comes to equilibrium? How much ice will there be (in grams) and how much water (in mls) at equilibrium? The density of water is 1.00 g/ml under these conditions.

The heat required to bring 25 C water to 0 C: q = nwater CP DT =

(5.56 moles)(75.5 J/(K mole))(25 K) = 10,500 J

How much ice will this much heat melt? q = nice DHfus; 10,500 J = nice (6008 J/mole)

nice = 1.75 moles. This is 1.75 moles x 18 g/mole = 31.4 grams. Since this is less than the 40 grams of ice we started with, ice and water are still present at equilibrium so the temperature must be O C. 40 - 31.4 grams is 8.6 grams which is how much ice remains. The amount of liquid water is just 100 mls + 31.4 grams x 1 ml/g = 131.4 mls.

 

35) 3.00 moles of an ideal gas is expanded isothermally against a constant pressure of 1 atm from 2.0 liters to 10.0 liters at a temperature of 20.0 C.

Determine each of the following for this process (express all energies in Joules and entropy changes in J/K):

w = -PDV = -(1atm)(8 l) = -(101.3 J/l)(8 l) = -811.2 J

 q = -w (since DU = 0) = 811.2 J

  DU = 0 (since isothermal ideal gas)

 DH = 0 (since isothermal ideal gas)

 DSSYS = qrev/T = -wrev/T = nRln(VF/VI) = 40.14 J/K

 DSSUR = -qsys/T = (-811.2 J)/(293 K) = -2.77 J/K

Is this process spontaneous (explain why or why not)?

It is spontaneous. The total entropy change for the system is greater than zero (adding the change in energy for the system and for the surroundings together above).

 

36) For the reaction A + B à C ß à D, the rate constant for the first irreversible reaction forming C is k1, for the reaction from C to D the rate constant is k2f and for the reverse reaction from D to C the rate constant is k2r. These rate constants have the following values: k1 = 2.00 M-1s-1, k2f = 1.00 s-1, k2r = 5.00 s-1. The initial concentrations of each of the components in the reaction (A, B, C and D) is 0.100 M.

  1. First, write down the differential rate equations for each component in the reaction (just write down the equations; do not evaluate them).

d[A]/dt = -k1 [A][B]

d[B]/dt = -k1 [A][B]

d[C]/dt = k1 [A][B] - k2f [C] + k2r [D]

d[D]/dt = k2f [C] - k2r [D]

b) Evaluate the initial rates of [A], [B], [C] and [D] change for this reaction (before any A, B, C or D is used up)

d[A]0/dt = -(2.00 M-1s-1)(0.1M)(0.1M) = -0.02 M/s

d[B]0/dt = -(2.00 M-1s-1)(0.1M)(0.1M) = -0.02 M/s

d[C]0/dt = (2.00 M-1s-1)(0.1M)(0.1M) - (1.00 s-1)(0.1M) + (5.00 s-1)(0.1M)

= 0.42 M/s

d[D]0/dt = (1.00 s-1)(0.1M) - (5.00 s-1)(0.1M) = -0.40 M/s

 

c) Determine the final (equilibrium) concentrations of each component.

 

[A]eq = 0.00 M [B]eq = 0.00 M [C]eq = 0.25 M [D]eq = 0.05 M

At equilibrium, [A] = [B] = 0 since the first reaction is irreversible. That means all of the material is in C and D which implies that [C] + [D] = 0.3 M. From the fact that we are at equilibrium we can say that K = [D]/[C] = k2f/k2r = 0.2. Solving the two equations for [C] and [D] gives the values listed above.

 

 

 

37) One thing we work on in my lab is the process of photosynthesis. The light driven reactions of photosynthesis convert light energy into chemical energy using the overall reactions diagramed below. The light energy is stored by generating an oxidant, P+, and a reductant, Q-. The final state, P+ Q- is higher in energy than the initial state, P Q, and therefore some of the light energy is stored.

In the organisms that we study, light at a wavelength of 860 nm is absorbed by the pigment P. During the lifetime of the excited state of P (P*), an oxidation reduction reaction occurs forming oxidized P (P+) and a reduced quinone (Q-). The half reaction P+ + e- à P has a standard potential of about 0.500 V. The half reaction Q + e- à Q- has a standard potential of about 0.00 V.

  1. What is the energy difference between the ground state of the system, P Q, and the excited state, P* Q? Report this energy in Joules per mole of P Q undergoing the reaction.

    For one molecule, E = hc/l = 2.31 x 10-19 J. Multiplying by Avagodro's number to give the number of joules for a mole of reactants gives 139,100 J/mole.

     

     

  2. What is the standard free energy difference between the ground state PQ and the state P+ Q-? Report this in Joules per mole as well.

    P à P+ + e- -0.500 V

    Q + e- à Q- 0.000 V

    ____________________

    P + Q à P+ + Q- -0.500 V

    converting potential to reaction free energy: DrG0 = -nFE0 = 48,300 J/mole

  3. Assuming that all of the light energy is available as free energy in the excited state P* Q, what fraction of the light energy absorbed at 860 nm is retained in the final product, P+ Q-?

(48.3 kJ/mole)/(139.1 kJ/mole) = 0.347