Chemistry 360 Spring 2015 Dr. Jean M. Standard April 27, 2015 Problem Set 14 (the last!) Good review problems in Engel & Reid (3rd Ed.): 36.1, 36.2, 36.3, 36.4, 36.5 1. A specific aqueous reaction that uses the solvent H2O as a reactant has a rate law given by Rate = k [ H 2O] [ A] , where A is the other reactant. Explain why in most circumstances this reaction can be defined in terms of pseudo first-order kinetics. What are € the units of the pseudo first-order rate constant? 2. A typical reaction mechanism involving an intermediate C is k A + B 1→ "" ←" " C k2 C k 3→ "" P. € The overall reaction is therefore € A +B " "→ P. Using the steady-state approximation for the intermediate C, determine the rate law for the production of the product, P. € 3. Ozone can be decomposed by the reactions k 1 → NO + O NO + O3 !! 2 2 k 2 → NO + O . NO 2 + O !! 2 a.) Determine the equation for the overall reaction. b.) Obtain a rate law for the formation of diatomic oxygen. c.) Obtain rate laws for the intermediates in the reaction. d.) Apply the steady-state approximation to the rate laws for the intermediates and obtain a simplified rate law for the formation of diatomic oxygen that depends upon the concentrations of ozone and NO only. Note that this is an unusual rate law as it still depends on the concentration of one of the intermediates (NO). 2 4. Consider the following mechanism for renaturation of a double helix from its two strands, A and B, k A + B 1→ "" ←" " unstable helix fast k2 unstable helix k 3→ "" stable double helix slow € Derive the rate equation for formation of the stable double helix. Apply the steady-state approximation to any intermediates. € 5. The enzyme fumarase catalyzes the hydrolysis of fumarate (C4H2O42–) to L-malate (C4H4O52–), fumarate + H 2O !! → L-malate . 3 -1 −6 The turnover number for the reaction is kcat = 2.5 ×10 s and the Michaelis constant is K M = 4.2 ×10 M . −4 Determine the rate of fumarate hydrolysis for an initial fumarase (enzyme) concentration of 2.0 ×10 M and −6 an initial fumarate (substrate) concentration of 1.0 ×10 M . 6. The following data were obtained for the reaction of carbon dioxide with water to form the bicarbonate ion; the reaction is catalyzed by the enzyme carbonic anhydrase. The data obtained includes the concentration of carbon dioxide (the substrate) and the measured rate of reaction, υ . [CO2], mmol L 0.66 0.76 1.51 3.78 0.0054 0.0064 0.0113 0.0205 –1 υ, € 7.57 11.4 15.1 0.0288 0.0342 0.0370 18.4 36.8 0.0388 0.0424 mmol L–1 s–1 € a.) Make a graph with rate on the y-axis and CO2 concentration on the x-axis. Estimate the turnover number k cat from the limiting asymptotic rate for large substrate concentration. Assume that the initial enzyme concentration [ E] o is 6.0×10–4 mmol L–1. € b). Estimate the Michaelis constant K M from the graph. € €