Assuming that first-order kinetics occur, calculate the half-life of Drug B, which is eliminated from the body at a rate constant of 25% per hour.
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Assuming that first-order kinetics occur, calculate the half-life of Drug B, which is eliminated from the body at a rate constant of 25% per hour.
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- Iodine-131 is used to treat tumors in the thyroid. Its decomposition is first-order with a half-life of 8.1 days. If a patient is given a sample containing 5.00 mg of I-131, how long will it take for 32% of the isotope to remain in her system?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)?When enzymes are present at very low concentration, their effect on reaction rate can be described by first-order kinetics. Calculate by what factor the rate of an enzyme-catalyzed reaction changes when the enzyme concentration is changed from 1.5 107 M to 4.5 106 M.
- As with any drug, aspirin (acetylsalicylic acid) must remain in the bloodstream long enough to be effective. Assume that the removal of aspirin from the bloodstream into the urine is a lirst-order reaction, with a half-life of about 3 hours. The instructions on an aspirin bottle say to take 1 or 2 tablets every 4 hours. If a person takes 2 aspirin tablets, how much aspirin remains in the bloodstream when it is time for the second dose? (A standard tablet contains 325 mg of aspirin.)When formic acid is heated, it decomposes to hydrogen and carbon dioxide in a first-order decay: HCOOH(g)CO2(g)+H2(g) The rate of reaction is monitored by measuring the total pressure in the reaction container. Time (s) Pressure (torr) 0 220 50 324 100 379 150 408 200 423 250 431 300 435 Calculate the rate constant and half-life in seconds for the reaction. At the start of the reaction (time = 0), only formic acid is present. (HINT: Find the partial pressure of formic acid using Dalton's law of partial pressure and the reaction stoichiometry to find PHCOOH at each time.)The half-life of tritium, 3H, is 12.26 years. Tritium is the radioactive isotope of hydrogen. (a) What is the rate constant for the radioactive decay of tritium, in y1 and s1? (b) What percentage of the original tritium is left after 61.3 years?
- Sucrose decomposes to fructose and glucose in acid solution. A plot of the concentration of sucrose as a function of time is given in the margin. What is the rate of change of the sucrose concentration over the first 2 hours? What is the rate of change over the last 2 hours? Concentration versus time for the decomposition of sucrose.The hydrolysis of the sugar sucrose to the sugars glucose and fructose follows a first-order rate equation for the disappearance of sucrose. C12H22O11(aq)+H2O(l)C6H12O6(aq)+C6H12O6(aq) Rate =k[C12H22O11] In neutral solution, k=2.11011 at 27 C. (As indicated by the rate constant, this is a very slow reaction. In the human body, the rate of this reaction is sped up by a type of catalyst called an enzyme.) (Note: That is not a mistake in the equation—the products of the reaction, glucose and fructose, have the same molecular formulas, C6H12O6, but differ in the arrangement of the atoms in their molecules). The equilibrium constant for the reaction is 1.36105 at 27 C. What are the concentrations of glucose, fructose, and sucrose after a 0.150 M aqueous solution of sucrose has reached equilibrium? Remember that the activity of a solvent (the effective concentration) is 1.If a reaction has the same rate constant, what time does it take for a reactant to decrease by 5 that is, still near the beginning of the reaction process if the kinetics are zeroth-order, first-order, and second-order with respect to that reactant?
- Sucrose decomposes to fructose and glucose in acid solution. A plot of the concentration of sucrose as a function of time is given in the margin. What is the rate of change of the sucrose concentration over the first 2 hours? What is the rate of change over the last 2 hours? Concentration versus time for the decomposition of sucrose.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?
