che110c_ps5_jba10 - CHE110C Problem Set 5(due June 2nd...

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CHE110C Spring 2010 Ames 1 PS5 Problem Set 5 (due June 2 nd ) 1. Some exercises with first-order kinetics A P , d A [ ] dt = k A [ ] . a. The integrated first-order rate law is usually expressed as [ A ] = [ A ] 0 e kt . Derive an alternative integrated first-order rate law expressed in terms of half life (t 1/2 ). (Hint: t 1/2 = ln(2)/k, substitute for k, and solve for [A] as a function of t.) b. Show that the time required for the reactant concentration to decrease from its starting value [ A ] 0 to some final concentration ( [ A ] = f [ A ] 0 ) is given by t f = − ln f k for a first-order process. 2. Consider the simultaneous formation of multiple products in a chemical reaction. Rate law = d A [ ] dt = ( k 1 + k 2 ) A [ ] a. Referring to problem 1b above, find t f for this process. b. Given the initial concentrations of products ( B [ ] 0 and C [ ] 0 ) are both zero, find kinetic expressions for the formation of B [ ] and C [ ] as a function of time in terms of A [ ] 0 . c. What is the final value of B [ ] C [ ] once the reaction is complete?
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