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CoColluummbbiiaa UUnniivveerrssiittyy in the City of New York New York, N.Y. 10027
Chemistry C2407x 2002 First Exam George Flynn September 26, 2002 Total Points: 150 75 Minutes
All questions are NOT weighted equally. I have attempted to order the questions from the least difficult to the most difficult, but "beauty is in the eye of the beholder", so skip around to find the problems that are easiest for you. Good luck!
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Co Colluummbbiiaa UUnniivveerrssiittyy in the City of New York New York, N.Y. 10027
Chemistry C2407x 2002 First Exam George Flynn
September 26, 2002 Total Points: 150 75 Minutes
All questions are NOT weighted equally. I have attempted to order the questions from the least difficult to the most difficult, but "beauty is in the eye of the beholder", so skip around to find the problems that are easiest for you. Good luck!
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Problem 1: (35 points) [Oxtoby Problems 4.41-4.43] a)(10 points) Compute the root-mean-square speed of H 2 molecules in hydrogen gas at a temperature of 300 °K. The molecular weight of H 2 is 2 gm/mole. Show all reasoning clearly.
d)(5 points) Compute the ratio of the root-mean-square speed of He at the surface of the sun, where the temperature is 6000 °K, to the root-mean-square speed of He in interstellar space, where the temperature is 100 °K. The atomic weight of He is 4 gm/mole. Show all reasoning clearly.
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Problem 2: (20 points) 2.00 moles of diatomic N 2 gas and 1.00 moles of monatomic He gas are confined to a rigid container of fixed volume V. a)(10 points) Calculate the heat absorbed by this gas mixture in the vessel of fixed volume, if the temperature is raised from 250 °K to 350 °K. Show all reasoning clearly.
b)(10 points) Imagine now that the sample of 2.00 moles of N 2 gas and 1.00 moles of He gas is transferred to a cylindrical container with a moveable, frictionless piston that holds the gas at a constant pressure of 2.00 atm. Determine the heat absorbed by this sample if its temperature is raised from 350 to 400 °K at constant pressure. Show all reasoning clearly.
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Problem 3: (50 Points) A 1.0 liter bulb is evacuated until the pressure of gas inside the bulb is negligible. Unfortunately, there is a hole in the bulb that allows air to leak into the bulb and the pressure to rise to 1.00× 10 -6^ Atm after 1.00 hour. In what follows, use exact kinetic theory formulas from the free formula sheet. You may assume that the surrounding atmosphere of gas is pure N 2 (MW= gm/mole) at one atmosphere pressure and that the temperature is constant at 275 °K. The pressure of the gas surrounding the bulb never changes because the volume of the surroundings is infinite compared to the volume of the bulb.
a) (5 points) Determine the average speed of N 2 molecules in this problem. Show all reasoning clearly!
b) (10 points) What is the number density ρs (number of molecules/cm^3 ), of N 2 molecules in the surrounding atmosphere? Show all reasoning clearly.
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e)(10 points) Determine the rate (molecules/sec) at which molecules leak into the bulb over the 1 hour period from the data given. Show all reasoning clearly.
f) (10 points) What is the area of the hole in the bulb through which the gas leaks? Show reasoning clearly.
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Problem 4 (45 points) In the binary collision theory of chemical reactions, the energy needed to “climb the barrier” EA to the transition state comes from the kinetic energy of relative motion of the reactants, A and B. Suppose instead that this form of energy is completely useless in promoting the reaction between A and B. (This often turns out to be true for reactions with large EA because the number of energetic molecules in the high energy tail of the Boltzmann Distribution at low to moderate temperatures is very small.) However, “internal” energy added to either of the molecules by the absorption of light can be effective in promoting chemical reaction. Suppose that only molecule A is capable of absorbing light and let the energy added to molecule A by light absorption be EL. A mixture of A and B is subjected to continuous irradiation by a laser beam producing a constant fraction fA of excited A molecules with energy EL. We designate the excited A molecules as A. You may assume that the speed distribution for A is identical to that for A before excitation with light. In what follows, you may wish to consult the Free Formula Sheet for definitions of the “All or Nothing” and Arrhenius models.
a)(10 points) If P(EL) is the reaction probability when an A molecule of energy EL (i.e. an A* molecule) encounters any B molecule, write an expression for the reaction rate using concepts from the binary collision model. Show all reasoning clearly.
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Show all reasoning clearly. (Be careful, this question is more subtle than it may appear! There are three different “kinds” of collisions.)
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