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Physical Chemistry Name_________________________________ Chemistry 453 June 6, 2008
EXAM 2
Directions: Write clearly and indicate your reasoning. Always show the details of your work. For numerical problems work the answer completely out and put your final answer in a box. Be specific. Total: 100 pts. +. Information: R = 8.314 J/mol-K. T(K) = T(°C) + 273.15.
1. The Rates of Chemical Reactions (a) Radon-222 is a radioactive gas with a decay half-life of 3.823 days. What is the decay constant of (^222) Rn?
(b) What fraction of an original sample of 222 Rn will remain after 11.47 days?
(c) Plotting the data. Consider a reaction that is second-order in a single reactant A. How should the data for [A] and time (t) be plotted to yield a straight line? Show a plot to the right, and tell what the slope is equal to.
(d) Temperature dependence. If the rate of a chemical reaction doubles in going from 10°C to 30°C, what is its activation energy E (^) a?
(e) Biological examples. A handout you received gave a number of examples of biological phenomena that follow an Arrhenius form. Describe two examples from this handout. Explain how a complicated biological process involving many steps can display such a simple overall behavior.
2. Kinetics terminology (a) Fill in the blanks with the best answers. The rate law expression for a reaction is obtained from
___________________. For a reaction whose rate law expression is rate = 1.5x10^15 [A]^2 [B]^1 the overall
order of the reaction is ________________. In a reaction mechanism the “rate-limiting step” is the
_______________ step. Whereas the deterministic kinetic analyses given in our textbook are “equation-
based”, the cellular automata simulations of these same phenomena are “___________-based.”
(b) What is a “pseudo first-order” reaction? Give a general example.
(c) Consider the pre-equilibrium reaction mechanism shown below. Give the differential equation expressions for the rates of change of the concentrations [A], [B], and [C]. k 1 k 3 A == B → C k
3. First-order reactions. (a) Suppose that one has a sequence of reactions A → B → C. | Sketch the general form that can be expected for the changes in | the populations of A, B, and C with time. Label your curves. | Conc. | | |_______________________ t
(b) For a competitive reaction in which reactant A can decay A → B (k1 = 0.05 s -1^ ) or A → C (k 2 = 0. s -1^ ), what will the decay of [A] look like? (Plot this below.) What will be the rate constant for the decay of the A population?
A → B ↓ C
6. Cellular automata simulations. (a) In your cellular automata simulations of the decay of 2500 ingredients a plot of ln(N) vs. time t (iterations) should give a straight line ln(N) = mt + b. What does the slope of this line represent?
(b) What is the numerical value of the y-intercept (b) in the above equation? Explain.
(c ) Under what conditions do the deterministic solution and the discrete solution for this example merge and become equal?
7. Transition state theory (TST). (a) By what mechanism (in words) does the transition state theory picture the reaction A + B → C + D to occur? Explain the complete process (going from reactants to products).
(b) One term that arises in TST is ΔS‡^. What does this term represent? For a bimolecular gas-phase reaction is ΔS‡^ positive or negative? Explain.
8. Photochemistry. To the right sketch a Jablonski diagram. Show the transitions for Abs, IC, ISC, F, and P, and state what these abbreviations stand for.
BONUS 1: What scientist originally developed TST?
BONUS 2: Sketch the form of the distribution of molecular velocities along a single dimension, and give the numerical values of the average and median velocities (vavg and v (^) med ) along this direction.
