Chemical Reaction Kinetics Homework 9: Determining Reaction Orders and Time Requirements, Assignments of Physical Chemistry

Download Chemical Reaction Kinetics Homework 9: Determining Reaction Orders and Time Requirements and more Assignments Physical Chemistry in PDF only on Docsity! April 12, 2002 CH 342 S02, Homework 9 due Monday, April 13, 2002 This assignment will be covered in class. No late assignments will be accepted. Chemical Reaction Kinetics The following problem draws on information in 25.2. 1. The initial rate of consumption of A ro = -d[A]o/dt by a chemical reaction A + 2B! products is measured as a function of initial concentrations of four components A, B, C, and D. Results are tabulated below. Determine the values of the reaction orders for the empirical rate expression ro = [A]α [B]β [C]γ [D]δ . Assume the reaction orders can be values in increments of  1/2 only. Initial Concentration [mol/L] Initial Consumption Rate [mol/L s] A B C D 1.00 1.00 1.00 0.010 0.010 2.05 2.00 1.00 0.010 0.010 5.62 2.00 2.00 0.010 0.010 0.21 1.00 1.00 0.050 0.010 1.01 1.00 1.00 0.010 0.050 The following problems draw on information in 25.3. 2. A certain reaction is found to be first order in [A] with a rate constant of 4.5 105 s1. a) Starting from [A]o = 1.00 mol/L, how long is required (in s) for [A] to drop to 0.75 mol/L? Use the equation that relates concentration and time for a first order reaction. b) Starting from [A]o = 1.00 mol/L, how long is required (in s) for [A] to drop to half of its initial value? Use the equation for half-life for a first order reaction. Extra Credit: Consider a first order reaction in [A]. The time for concentration to decrease from an initial value [A]o to a value f [A]o can be expressed as t = ln( f ) t1=2= ln(2), where t1=2 is the half-life of the reaction. Derive (prove) the above expression. Extra Credit: Chemistry in Today’s World: Carbon 14 dating relies on the first order decay (removal) of 14C after a living organism dies while the amount of 12C stays constant. The first order half-life of 14C is 5,700 yrs. Analysis of a skeleton found in the UAH parking lot determines that it has a 14C concentration that is 40% of the value in living organisms today. How long ago did the animal die? 3. A certain reaction is found to be second order in [A] with a rate constant of 4.5 105 mol/L s. a) Starting from [A]o = 1.00 mol/L, how long is required (in s) for [A] to drop to 0.75 mol/L? Use the equation that relates concentration and time for a second order reaction. b) Starting from [A]o = 1.00 mol/L, how long is required (in s) for [A] to drop to half of its initial value? Use the equation for half-life for a second order reaction. Extra Credit: Consider a reaction that is second order in [A]. Prove the following: t(1=2)n = ∑2n1 k[A]o In the above formula, n is the number of periods that concentration will be cut successively in half. For example, when n = 3, concentration will be cut by a factor of 1/8 of its initial value [A]o in a period of 7/k[A]o. The following problem draws on information in 25.4. 4. The first order rate constant for a reaction A ! B is 2.5 107 s1. The equilibrium constant for the reaction is 0.45. What is the first order rate constant for the reaction B ! A? Use the relationship between forward and reverse rate constants and equilibrium constant. The following problems draw on information in 25.5. 5. A plot of ln(r) versus inverse temperature is attached at the end of this assignment. Determine the activation energy and pre-exponential for the chemical reaction. Activation energy Eact is determined from slope m as m =Eact=R. Pre-exponential ko is determined from intercept b as b = ln(ko). Extra Credit: Determine the uncertainty in activation energy from the data plot. 6. A certain reaction has an overall rate constant k = k1 + k2 where k1 = ko1 exp(E1=RT ) and k2 = ko2 exp(E2=RT ). Prove the true activation energy for the reaction has the overall form Eact = k1E1 + k2E2 k1 + k2 Overall activation energy is determined from the equation Eact = R d ln(r) d(1=T ) . 2