Tuesday, 2 October 2012

Physical Chemistry Mock Midterm Answer Key

Disclaimer: Use at your own risk. The definitions, short answers, and calculations may not be correct or fully correct. Hope it is helpful and please leave comments if you have found any discrepancies. Also, while doing this exam, I discovered many questions were poorly phrased for which I apologize. (One mistake has already been caught by somebody! Please help me catch more!) 


Physical Chemistry Mock Midterm Exam

**disclaimer: I have no idea exactly what will be on the midterm exam beyond what was listed by the professor in class, although I do know these section headings are accurate. This mock midterm is written only as a study tool. It’s usefulness is debatable.

Part I: Definitions (20%)

Provide definitions for each of the following terms. Do NOT give any examples of the terms or you will lose marks.  (1 mark per definition, -1 mark if example given)

1) System: the part of the universe of interest

2) Isolated system: system that exchanges neither matter nor energy with the surrounding

3) closed system: system that exchanges matter but not energy with the surroundings

4) open system: system that exchanges both matter and energy with the surroundings

5) surroundings: the rest of the universe, excluding the system or part of the universe of interest

6) Zeroth Law of Thermodynamics: If A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A is in thermal equilibrium with C

7) Thermal Energy: the energy around us in the translational, rotational, vibrational states

8) Internal Energy: the energy needed to create the system from atoms, the thermal energy (kinetic energy of motion – moving, rotational and vibration) and bond energy – the electrostatic energy of the attraction and repulsion of nuclei, does not include PV work

9) Heat: transfer of energy by conduction, radiation, convenction; path dependent

10) Work: energy transferred by a force acting on a distance; path dependent

11) First Law of Thermodynamics: delta U = q + w, where q is the heat added to the system, and w is the work done on the system, and delta U is the change in internal energy

12) Reversible Path: a path that depends only on the initial and final states of the system

13) Nonreversible Path: a path that depends on the method used to achieve the final state from the initial state

14) State Function: a property whose change is only dependent on the initial and final states of a system

15) Heat Capacity (also include definition for molar heat capacity and specific heat capacity):  the amount of heat required to raise the temperature by 1­K, dependent on the translational, rotational and vibrational states of the molecules
molar heat capacity: the amount of heat required to raise the temperature by 1­K per 1 mol of substance
specific heat capacity: the amount of heat required to raise the temperature by 1K per 1 kg of substance

16) Translational States: this in my humble opinion, is an unfair question as the mathematics involving this definition go back to particle in a box and are a bit complicated.

A better question would be: How do you eliminate the translational states of a molecule?

Answer: By taking a frame of reference.

17) Rotational States: same as angular momentum, denoted by Jmj where J goes from 0 to infinity, -J < mj < +J

18) Vibrational States: given in integer values from 0 to infinity

19) Equiparition of Energy: the division of energy amongst all of the degrees of freedom of the molecule (this definition may be incomplete, however with the content of the course thus far, and its not rigorous nature, I suspect it may be ok)

20) Bond Energy: the energy required to break a chemical bond into its constituents  

21) Hess’s Law: state functions do not depend on the path

22) Heat of Formation of a Molecule: the heat required to form a molecule from its elements

22) Heat of Combustion of a Molecule: the heat required to burn a molecule (react with gaseous oxygen) to usually produce gaseous carbon dioxide and liquid water

23) Enthalpy: H = U + PV where U is the internal energy of a system, P is the pressure of the surroundings, and v is the volume of a system

26) State: the parameters that are measured and describe a system under those conditions

Part II: Calculations
Provide all work, including appropriate equations, notation, and manipulation.

Try (or retry) calculations from the textbook without looking at the solutions manual.
For a good selection of questions do:

Energy, Heat, Work

3, 4, 6, 10 (this question might require you to do 9 or something, sorry)

Thermochemistry

15, 17, 21, 24, 29, 32, 34

Equiparitioning of Energy 

1)   Calculate the number of degrees of freedom for carbon dioxide. Estimate the molar heat capacity of the substance.

2)   Calculate the number of degrees of freedom for methane. Estimate the molar heat capacity of the substance.



Part III: Short Answers

1)   What type of system is a coffee cup calorimeter? What type of system is a bomb calorimeter? Compare and contrast.

A coffee cup calorimeter is a closed system. Matter cannot leave the system, but energy can. A bomb calorimeter is an isolated system, so both matter and energy cannot leave the system.

2)   If system A is 25ºC and system B is 25ºC, and system C is in equilibrium with system B, what can we conclude about the temperature of system C and its relationship with system A?

Using the Zeroth Law of Thermodynamics, we know that since system C is in equilibrium with system B, it must have the same temperature of 25ºC. System C may be in thermal equilibrium with system A if it is in contact with system A, or if it is in contact with system B and system B is in contact with system A. But the problem doesn't include enough information to make a solid conclusion about the relationship of system C and A. 

3)   Draw potential energy diagram of a diatomic molecule. Label the place of greatest repulsion, A. Label the place of greatest stability, B. Label zero point, C. Label and show the bond energy. Draw in the largest state (rotational/vibrational/translational) , and discuss the placement and magnitude of the other states (rotational/vibrational/translational).



4)   Is the maximum work done by the system reversible or irreversible? Explain referring to a P versus V diagram.

The maximum work done by the system is reversible. It is done along the same isotherm (at constant temperature), and depends on only the final and initial states, not the path. In an isothermal expansion or compression, the process is very slow, and so the work done by or on the system is replaced by the heat into or out of the system for a change of internal energy of zero. (There is a nice diagram on page 58 of the text that you could refer to with this answer.)

5)   Using the definition of enthalpy, show that it is equal to the heat at constant pressure.


6)   Define both the heat capacity at constant volume and the heat capacity at constant pressure.


7)   Is work a state function? Explain.

No, work is not a state function, as it is path dependent. (Using a car, crane or helicopter to move an object all takes different amounts of energy to reach the final state)

8)   Discuss how differential calorimetry finds the unknown heat capacity of a substance.

Differential calorimetry compares a sample of unknown heat capacity with a sample of known heat capacity called the reference sample. This reference must be well-defined over a large range of temperatures, and not undergo a phase transition. Then you test the two samples. If the unknown undergoes a phase transition, a peak on a heat versus temperature graph will appear. Comparing this value with the value of the known heat capacity of the reference sample will aid in calculating the heat capacity of the unknown. qs - qr

9)   What is the standard enthalpy of formation of oxygen gas?

As oxygen gas is in elemental form, its standard enthalpy of formation is zero.

10)                   Why is the bond energy always positive?

The bond energy is the amount of energy required to break a molecule into its constituents. Energy is usually required to put into the system (positive) to break a chemical bond.

11)                   Hydrogen gas only has 2 rotational degrees of freedom. Explain why.

Hydrogen gas can rotate along the three axes. However, the x and y axes exhibit much greater rotation for a linear molecule as does the z axes, since the x and y axes contain the two atoms whereas the z axis does not and so is not as greatly effected.

12)                   Discuss the effects of temperature when comparing calculated heat capacities using equiparitioning of energy and the actual measured heat capacity values.

At warmer temperatures, there is greater agreement of the calculated heat capacities with the actual heat capacity values. At colder temperatures there is less agreement between the calculated and actual heat capacities. This is because the vibrational molecules are more widely spaced and energy cannot move as freely between vibrational modes, so a transition requires a more significant (or sufficiently large quantum) amount of energy.



Part IV: True or False
This section will NOT be on the exam, however, it may provide a good snapshot as to whether the definitions are understood.

1)   Heat leaves the system. q is positive.             True/False q is negative.
2)   Energy is stored in chemical bonds.             True/false energy is stored in the degrees of freedom of a molecule
3)   The system does work. w is negative.             True/false
4)   Internal energy does not depend on PV work.             True/false
5)   Bond energy is usually greater than thermal energy.             True/false
6)   A diatomic gas has 2 degrees of translational energy.             True/false A diatomic gas has 3 degrees of translational energy and 2 degrees of rotational energy.
7)   PV work is positive for an expansion of a gas.             True/false PV work is negative for the expansion of a gas and positive for the compression of a gas.
8)   The lowest vibrational state is at the zero point.             True/false The lowest vibrational state is slightly above the zero point.  
9)   The heat capacity at a phase change is infinite.            True/false
10) Vibrational states are the same as angular momentum.             True/false Rotational states are the same as angular momentum.

Part V: Bonus Questions

1)   Show that PV=nRT is a state function using partial derivatives and Euler’s Theorem for Exactness without referring to Appendix C. (Just kidding! Bad joke I know.)

Refer to post titled “Friday Night State Functions.” But seriously we don't have to know this.

2)   Describe your experience and opinion of the textbook with regards to whether you have the e-book or hardcopy, its acquisition and availability, its use as a study tool, and to what level it corresponds to and complements the lectures.

I have heard many (at least 5 opinions not my own) nuanced responses to this question, and they all have strikingly similar themes.


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