Rate law questions for physical chemistry?
Can not solve #'s 5 or 6
Biochemistry 5721 (AU 2016) Problem Set 7 Due: Friday, November 18, 2016 1. For the reaction:
2NO g + 2H2 g ? N2 g + 2H2 O(g) write the expressions for the overall rate of the reaction in terms of the following quantities: a)
d) NO /
H! O / 2. Chlorine gas reacts with carbon monoxide to produce phosgene according to the following
Cl2 g + CO g ? Cl2 CO(g) It is experimentally observed that when the concentration of CO is decreased 10-??fold, the rate of the reaction also decreases by a factor of 10, while when the concentration of Cl2 is increased 10-??fold, the rate of the reaction increases by approximately a factor of 30. a) Write down the rate law for this reaction in terms of a rate constant, k, and the
concentrations of Cl2 and CO.
b) What is the overall order of the reaction, and the orders with respect to Cl2 and CO?
c) What are the units of k for the reaction?
d) If the rate of the reaction at time t is equal to ?, and the concentrations of Cl2 and CO are
instantaneously increased by a factor of 2 and 3, respectively, what is the reaction rate in
units of ?.
3. The following reaction:
2I ? I2 is second order in [I]. If under a particular set of experimental conditions the rate constant has been measured to be = 8.2?10! M !! ? s !! , and the initial iodine concentration is 1.0 x 10-??4 M, calculate the iodine concentration after 2.0 ?s. 4. 64Cu is a radioactive nuclide of copper, with a half-??life of 12.7 h, that is commonly used in nuclear medicine applications either as an imaging or therapeutic agent. Calculate the number
of days required for an administered dose of 64Cu to drop to 0.10% of the initial amount
injected. Assume than the radioactive decay of 64Cu is a first-??order process and that the loss of
64Cu occurs only via radioactive decay. 5. Suppose that 1.00 L of 7.58 x 10-??3 M S2O32-?? is mixed with 1.00 L of 3.18 x 10-??3 M H2O2 at pH 7.0 and 25oC. These species react by two competing pathways according to the following reactions: !!
! + 4H2 O! ? 2SO! + 3H2 O + 2H !!
! + H2 O! + 2H ? S! O! + 2H2 O At the instant of mixing S2O32-?? is observed to be disappearing at a rate of 6.4 x 10-??7 M?s-??1, and at the same time H2O2 is observed to be disappearing at a rate of 9.1 x 10-??7 M?s-??1. a) Calculate the percentage of S2O32-?? that is reacting according to the first equation. b) It is observed that the concentration of H+ decreases with time. How many milliliters of 0.1 M HCl must be added per minute to keep the pH constant at 7.0. Hint: For part (b) you may assume that in spite of adding 0.1 M HCl, the total volume of the reaction mixture remains constant at 2.00 L. Check that your final result is consistent with this assumption. 6. In class we discussed ways to determine the order of a chemical reaction by plotting an appropriate function of the reactant concentration vs. time. Consider the reaction below: H2 g + Br2 g ? 2HBr(g) which is of order ? in Br2, i.e., = [Br2 ]!/! , where [?] refers to partial pressure in atm. a) What quantities should be plotted on the x and y axes in order to obtain a linear plot? b) What do the slope and intercept correspond to? c) Use your answers to parts (a) and (b) to extract the value for the rate constant, k, from the following set of experimental data. Make sure to specify the correct units for k. Time (min) 0 5 10 15 20 P(Br2) (atm) 1.000 0.960 0.915 0.870 0.820 Time (min) 25 30 35 40 45 P(Br2) (atm) 0.785 0.745 0.700 0.675 0.630 7. The reaction: N2 O2 g ? 2NO(g) is first order in the concentration of N2O2. a) Derive an expression for the time dependent behavior of the product concentration, [NO]. b) Given that: (i) the volume of the reaction is constant, (ii) the initial concentration of N2O2 is 1.0 mol/L and no NO is present at the start of the reaction, and (iii) the rate constant is k = 1.25 x 10-??2 s-??1, plot on the same graph the concentrations of N2O2 and NO as a function of time. 8. Consider the following base-??catalyzed reaction: OCl! (aq) + I ! (aq) ? OI ! (aq) + Cl! (aq) Use the following initial-??rate data to determine the rate law and the corresponding rate constant for the reaction. Run [OCl] (M) [I] (M) [OH] (M) Initial rate, ? (M?s-??1) 1 1.62 x 10-??3 1.62 x 10-??3 0.52 3.06 x 10-??4 -??3
2 1.62 x 10 2.88 x 10 0.52 5.44 x 10-??4 -??3
3 2.71 x 10 1.62 x 10 0.84 3.16 x 10-??4 4 1.62 x 10-??3 2.88 x 10-??3 0.91 3.11 x 10-??4 ? ? ?
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