The following mechanism was proposed for the reaction with overall stoichiometry A + B → R A → X X+ B➡R (K1, K-1) (k2) The expected intermediate X cannot be analytically detected during the reaction. Use the steady state principle for intermediate X to derive the differential kinetic equation for the formation of the product R, i.e. d[R] / dt. What will be the reaction order for the two limiting cases, i.e. if a) k2 >> k1, k-1 b) k2 << K1, K-1

What are the rate laws of mechanisms 1 and 2 for oscillating reactions if the second reactions were the rate-determining steps?

Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of 3104 g/mol that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalyzed reactions can be complex, at low concentrations this reaction can be described by a rate equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 g ( 0.15106 g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant. [Penicillin] (M) Rate (mol/L/min) 2.0106 1.01010 3.0106 1.51010 4.0106 2.01010

Define stability from both a kinetic and thermodynamic perspective. Give examples to show the differences in these concepts.

The rate of photodecomposition of the herbicide piclo- ram in aqueous systems was determined by exposure to sunlight for a number of days. One such experiment produced the following results. (Data from R.T. Hedlun and C.R. Youngson, “The Rates of Photodecomposition of Picloram in Aqueous Systems," Fate of Organic Pesticides in tbe Aquatic Environment, Advances in Chemistry Series, #111, American Chemical Society (1972), 159—172.) Exposure Time, t (days) [Pidoram] (mol L_1) 0 4.14 X 10-6 7 3.70 X 10-6 14 3.31 X 10-6 21 2.94 X 10~6 28 2.61 X 10~6 35 2.30 X 10-6 42 2.05 X 10-6 49 1.82 X 10"6 56 1.65 X 10-6 Determine the order of reaction, the rate constant, and the half-life for the photodecomposition of picloram.

The thermal decomposition of diacetylene, C4H2, was studied at 950 C. Use the following data (K. C. Hou and H. B. Palmer, Journal of Physical Chemistry. Vol. 60, p. 858, 1965) to determine the order of the reaction.

In a first-order reaction, suppose that a quantity X of a reactant is added at regular intervals of time, t. At first the amount of reactant in the system builds up; eventually, however, it levels off at a saturation value given by the expression a saturation value saturationvalue= x110a where a=0.30tt1/2 This analysis applies to prescription drugs, of which you take a certain amount each day. Suppose that you take 0.100 g of a drug three times a day and that the half-life for elimination is 2.0 days. Using this equation, calculate the mass of the drug in the body at saturation. Suppose further that side effects show up when 0.500 g of the drug accumulates in the body. As a pharmacist, what is the maximum dosage you could assign to a patient for an 8-h period without causing side effects?

11.48 The following data were collected for the decomposition of NT),-: Time, f (min) [N2Os] (mol L-1) 0 0.200 5 0.171 10 0.146 15 0.125 20 0.106 25 0.0909 30 0.0777 35 0.0664 40 0.0570 Use appropriate graphs to determine the rate constant for this reaction. Find the half-life of the reaction.

Explain why half-lives are not normally used to describe reactions other than first order.

Derive an expression for the half-life of a a third order reaction;b a reaction whose order is =1; c a reaction whose order is 12. In these last two cases, examples are rare but known.