Physical chemistry questions due in 24 hours

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CHEM 4508-01, Summer 2014 Exam 2, July 11 9:10-11:30 am

Please write clearly and neatly! Show all work to receive credit.

1. (35 pts, total) The canonical ensemble can be applied to a system consisting of two different components, which we will call a and b. Just like the molecular partition function can be divided into terms for each type of energy, the overall partition function for the two component system can be broken into two terms:

Qtotal =Qa ⋅Qb In this problem we will look at such a case.

a. (15 pts) Find an expression for the total entropy in terms of the two individual entropies. Remember, the entropy is

S = kBT ∂lnQ ∂T

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+kB lnQ

b. (20 pts) Write out the entropy for the specific case of two 2-level spin systems. The energy of a spin system depends on the magnetic moment,

! µ , and an external

magnetic field, ! B . We will assume that the magnetic field is either parallel (when the

spin is “up” or “+”) or antiparallel (when the spin is “down” or “–”) to the magnetic moment. The energy for this is

E = ! µ ⋅ ! B =±µB

where we have dropped the vector notation in deference to the ± signs.

Q1   /35   Q2   /30   Q3   /40   Q4   /35   Q5   /25   Total   /165  

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2. (30 pts, total) An object at temperature T1 is placed in contact with a heat reservoir at T2 (T2 > T1). The object has a constant pressure heat capacity of CP that remains constant over the temperature range involved. Determine the TOTAL change in entropy, i.e. ∆Ssystem + ∆Ssurrounding, for the process of bringing the object into thermal equilibrium with the reservoir. Is the total ∆S positive, negative, or zero?

Remember: ∆S = δq Tinit

final ∫ =

CpdT Tinit

final ∫

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3. (40 pts) Consider the following hypothetical equation of state: P = AT3 /V

where A is a constant and P, V, and T are pressure, volume and temperature, respectively. The internal energy for the matter is found to follow the equation:

U = BTn ln(V /V0)+ f (T) where B, n, and V0 are all constants, and f(T) is a function in T only. Find the numerical value for n and the value of B in terms of A. The following equations will be very handy:

dS = dU +PdV

T

dS = ∂S ∂T "

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dT + ∂S ∂V "

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%

& ' T

dV

dU = ∂U ∂T "

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& ' V

dT + ∂U ∂V "

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%

& ' T

dV

∂ ∂V

∂S ∂T "

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& ' V

"

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& '' T

= ∂ ∂T

∂S ∂V "

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& ' T

"

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& '' V

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4. (35 pts, total) The following mechanism has been proposed for the reaction between hydrogen bromide and oxygen to produce bromine and water:

HBr + O2 → k1

HOOBr

HBr + HOOBr→ k2

2 HOBr

HBr + HOBr→ k3

H2O+Br2

a. (5 pts) What is the overall stoichiometric equation? b. (30 pts) What is the rate law for the reaction, assuming HOBr and HOOBr are at steady state?

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5. (25 pts) In the space below, write about your p-chem 2 experience. You can write a list of things you learned, a list of things that interested you, or an explanation of some concepts that were meaningful to you, OR draw a picture that summarizes your feelings about the course. Poems are also acceptable. However, do not expect to get full credit for writing a bunch of nonsense! For example, transcribing the words to “Humpty Dumpty” does not constitute an acceptable answer; neither does a long narrative about my shoes (which are sweet, but not directly related to the course)! Anyway, have fun!