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- The decomposition of azomethane, (CH3)2N2, to nitrogen and ethane gases is a first-order reaction, (CH3)2N2(g)N2(g)+C2H6(g). At a certain temperature, a 29-mg sample of azomethane is reduced to 12 mg in 1.4 s. (a) What is the rate constant k for the decomposition at that temperature? (b) What is the half-life of the decomposition? (c) How long will it take to decompose 78% of the azomethane?For the past 10 years, the unsaturated hydrocarbon 1, 3-butadiene (CH2 = CH - CH = CH2) has ranked 38th among the top 50 industrial Chemicals. It is used primarily for the manufacture of synthetic rubber. An isomer exists also as cyclobutene: The isomerization of cyclobutene to butadiene is first-order and the rate constant has been measured as 2.0104s1 at 150 C in a 0.53-L ?ask. Determine the partial pressure of cyclobutene and its concentration after 30.0 minutes if an isomerization reaction is carried out at 150 C with an initial pressure of 55 torr.A drug decomposes in the blood by a first-order process. A pill containing 0.500 g of the active ingredient reaches its maximum concentration of 2.5 mg/ 100 mL of blood. If the half-life of the active ingredient is 75 min, what is its concentration in the blood 2.0 h after the maximum concentration has been reached?
- The hydrolysis of the sugar sucrose to the sugars glucose and fructose, C12H22O11+H2OC6H12O6+C6H12O6 follows a first-order rate equation for the disappearance of sucrose: Rate =k[C12H22O11] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.) (a) In neutral solution, k=2.11011s1 at 27 C and 8.51011s1 at 37 C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature). (b) When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is 1.65107M . How long will it take the solution to reach equilibrium at 27 C in the absence of a catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible. (c) Why does assuming that the reaction is irreversible simplify the calculation in pan (b)?Regular ?ights of supersonic aircraft in the stratosphere ale of concern because such aircraft produce nitric oxide, NO, as a byproduct in the exhaust of their engines. Nitric oxide reacts with ozone, and it has been suggested that this could contribute to depletion of the ozone layer. The reaction NO+O3NO2+O2 is first order with respect to both NO and O3 with a rate constant of 2.20107 L/mol/s. What is the instantaneous rate of disappearance of NO when [NO]=3.3106 M and [O3]=5.9107M?The reaction of compound A to give compounds C and D was found to be second-order in A . The rate constant for the reaction was determined to be 2.42 L/mol/s. If the initial concentration is 0.500 mol/L, what is the value of t1/2?
- The first-order rate constant for the decomposition of a certain hormone in water at 25C is 3.42104day1. (a) If a 0.0200 M solution of the hormone is stored at 25C for two months, what will its concentration be at the end of that period? (b) How long will it take for the concentration of the solution to drop from 0.0200 M to 0.00350 M? (c) What is the half-life of the hormone?One possible mechanism for the decomposition of nitryl chloride, NO2CI, is What is the overall reaction? What rate law would be derived from this mechanism? What effect does increasing the concentration of the product NO2 have on the reaction rate?The initial concentration of the reactant in a tirst-order reaction A —» products is 0.64 rnol/L and the half-life is 30.0 s. Calculate the concentration of the reactant exactly 60 s after initiation of the reaction. How long would it take for the concentration of the reactant to drop to one-eighth its initial value? How long would it take for the concentration of the reactant to drop to 0.040 mol/L?
- When formic acid is heated, it decomposes to hydrogen and carbon dioxide in a first-order decay. HCOOH(g) CO2(g) + H2(g) At 550 C, the half-life of formic acid is 24.5 minutes. (a) What is the rate constant, and what are its units? (b) How many seconds are needed for formic acid, initially 0.15 M, to decrease to 0.015 M?The decomposition of sulfuryl chlorideSO2Cl2fur dioxide and chlorine gases is a first-order reaction. It is found that at a certain temperature, it takes 1.43 hours to decompose 0.0714 M to 0.0681 M. (a) What is the rate constant for the decomposition? (b) What is the rate of decompostion [ SO2Cl2 ]=0.0462M? (c) How long will it take to decompose SO2Cl2 so that 45% remains?11.64 HBr is oxidized in the following reaction: 4 HBr(g) + O2(g) —• 2 H2O(g) + 2 Br,(g) A proposed mechanism is HBr + O2 -* HOOBr (slow) HOOBr + HBr — 2 HOBr (fast) HOBr + HBr — H2O + Bn (fast) Show that this mechanism can account for the correct stoichiometry. Identify all intermediates in this mechanism. What is the molecularity of each elementary’ step? Write the rate expression for each elementary' step. Identify the rate-determining step.