NAME MON KEY CHEMISTRY 419 SPRING 2010 2103 Midterm Examination 2 April 22 2010 Answer each question in the space provided use back of page if extra space is needed Answer questions so the grader can READILY understand your work only work on the exam sheet will be considered Write answers where appropriate with reasonable numbers of significant figures You may use only the Student Handbook a calculator and a straight edge 1 10 points In the figure is shown the potential energy surface for the reaction AB C BC DO NOT WRITE IN THIS SPACE A 1 10 Indicate the following things by putting points or lines with labels a the transition state or saddle point b the entrance to the reactant channel for the reaction as written c the exit from the product channel for the reaction as written d a reactive event e an unreactive event 2 15 Be sure to label any points or lines you may draw on the graph carefully 6 10 3 20 4 15 5 15 7 15 TOTAL PTS 100 The entrance and exit channels are determined by which diatomic molecule starts and it will have the smallest separation in this case RAB must be small The transition state is the saddle point in the surface A reactive event starts in the reactant channel and ends in the product channel An unreactive event starts in the in reactant channel and ultimately moves back out through the reactant channel NAME CHEM 419 Midterm Exam 2 Spring 2010 page 2 2 15 points Lindemann developed a simple mechanism to explain certain unimolecular reactions The mechanism involves the interaction of the reactant molecule A with a mediator M to produce an excited state molecule A which ends up reacting to give product P The overall reaction is simple A P Here is the mechanism A M A M A k1 A M k2 A M k P v1 k1 A M v2 k 2 A M v3 k 3 A a To the right of each step as indicated write an equation for the velocity of the step in terms of the concentrations and rate constant b Assume that the excited state molecule is a reactive intermediate Give an expression for the steady state concentration of the reactive intermediate in terms of other concentrations and rate constants d A 0 dt d A v1 dt v2 v3 k1 A M k 2 A M k 3 A 0 Solving this equation gives the steady state concentration A c k1 A M k3 k 2 M Give the rate law for the Lindemann mechanism as a function of concentrations and rate constants The rate of reaction is given by the rate of creation of product which happens only in step 3 v k 3 A Substitution of the steady state concentration of the excited A molecules gives the final rate law v k 3 k1 A M k3 k 2 M Score for Page NAME CHEM 419 Midterm Exam 2 Spring 2010 page 3 3 20 points Insert the proper word or phrase from the list below into each of the following sentences to complete it appropriately a A reaction in which the reactant disappears exponentially is said to be of b A reaction in which the rate constant for disappearance of a reactant is equal to the sum of the rate constants for the appearance of two products is said to be a c FIRST PARALLEL REACTION order One means of measuring reactions that occur on short time scales is the PERTURBATION RELAXATION method d The activity of an enzyme is modeled by MICHAELIS MENTEN KINETICS e In competitive inhibition the of the Lineweaver Burk plot depends on the concentration of inhibitor f The unit of light intensity is WATT PER METER2 g The most common means of describing the temperature dependence of a rate constant is by reporting the ARRHENIUS h SLOPE parameters The so called inversion of the rate constant for electron transfer has been successfully predicted by MARCUS theory i In determining rate laws the concentrations of reactive intermediates are often determined by invoking the STEADY STATE j approximation Fluorescence resonance energy transfer involves the formation of a Arrhenius Eyring Joule Michaelis Menten kinetics Quenching Steady state Diffusion control First Lifetime Parallel reaction Second Stern Volmer plot DONOR ACCEPTOR COMPLEX Donor acceptor complex Intercept Lineweaver Burk plot Perturbation relaxation Sequential reaction Third Elementary step Intersystem crossing Marcus Pre equilibrium Slope Watt per meter2 Score for Page NAME CHEM 419 Midterm Exam 2 Spring 2010 page 4 4 15 points The decarboxylation of a keto acid is catalyzed by a decarboxylase to produce CO2 The rate of reaction can be determined by measuring the rate of appearance of CO2 The table lists the initial reaction velocity as the rate of formation of CO2 for various concentrations of the acid In these experiments the enzyme concentration was fixed From these data determine the maximum reaction velocity and the Michaelis Menten constant for this reaction keto acid mole dm 3 Initial velocity micromoles dm 3 s 1 1 keto acid dm3 mole 1 2 500 1 000 0 714 0 526 0 250 0 588 0 500 0 417 0 370 0 256 0 400 1 000 1 401 1 901 4 000 The appropriate plot is a Lineweaver Burk plot 1 v0 v max S 0 S 0 K m HINT The reaction rate law for Michaelis Menten kinetics is v 0 1 Initial velocity s dm3 micromole1 1 701 2 000 2 398 2 703 3 906 1 v max Km v max 1 S 0 In the third and fourth rows of the table are the inverses of the concentration and initial velocity A plot is shown below The slope of the line as determined in EXCEL is 0 617 s mole micromole 1 0 617 106 s Similarly the intercept is 1 467 s dm3 micromole 1 1 467 106 s dm3 mole 1 From the inverse of the intercept v max 6 817 10 7 mole dm 3 s 1 From this value and the slope the Michaelis Menten constant is Km 0 421 mole dm 3 1 initial velocity s dm 3 micromole 1 4 500 4 000 3 500 3 000 2 500 2 000 1 500 1 000 0 500 0 000 0 000 0 500 1 000 1 500 2 000 2 500 3 3 000 3 500 4 000 4 500 1 1 keto acid dm mole Score for Page NAME CHEM 419 Midterm Exam 2 Spring 2010 page 5 5 15 points Water has several vibrational modes Water has been of concern because the 13 million tons of water in the atmosphere may participate in so called global warming In the infrared spectrum a vibrational transition of water the symmetric stretch mode occurs at an energy of 3657 05 cm 1 a What is the frequency of a photon that corresponds to this energy c 2 99792458 10 8 m s 1 3657 05 10 2 m 1 1 09636 1014 Hz b Express that energy in joules E h hc 6 6260693 …