To determine how much of a drug is absorbed into the body, researchers measure the difference between the dosage D and the amount of the drug excreted from the body. The total amount excreted is found by integrating the excretion rate r(t) from 0 to ∞. Therefore, the amount of the drug absorbed by the body is D − ∞ 0r(t) dt. If the initial dose is D = 350 milligrams (mg), and the excretion rate is r(t) = 30e−0.5t mg per hour, find the amount of the drug absorbed by the body.

To determine how much of a drug is absorbed into the body, researchers measure the difference between the dosage D and the amount of the drug excreted from the body. The total amount excreted is found by integrating the excretion rate r(t) from 0 to ∞. Therefore, the amount of the drug absorbed by the body is D − ∞ 0r(t) dt. If the initial dose is D = 350 milligrams (mg), and the excretion rate is r(t) = 30e−0.5t mg per hour, find the amount of the drug absorbed by the body.

Chemical Principles in the Laboratory

11th Edition

ISBN:9781305264434

Author:Emil Slowinski, Wayne C. Wolsey, Robert Rossi

Publisher:Emil Slowinski, Wayne C. Wolsey, Robert Rossi

Chapter42: Rate Studies On The Decomposition Of Aspirin

Section: Chapter Questions

Problem 1ASA

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To determine how much of a drug is absorbed into the body, researchers measure the difference between the dosage D and the amount of the drug excreted from the body. The total amount excreted is found by integrating the excretion rate r(t) from 0 to ∞. Therefore, the amount of the drug absorbed by the body is D − ∞ 0 r(t) dt. If the initial dose is D = 300 milligrams (mg), and the excretion rate is r(t) = 35e−0.5t mg per hour, find the amount of the drug absorbed by the body.
Peroxynitric acid (HOONO2) is an unstable molecule that decomposes to nitric acid and oxygen: 2HOONO2(aq) → 2HNO3(aq) + O2(g)When the concentration of peroxynitic acid is graphed against time, the resulting plot is curved, but if the logarithm of this concentration is plotted, we instead get a straight line. Based on this, which statement is true? a) This decay is a second order in peroxynitric acid. b) The slope of the straight-line graph is the rate constant. c) One needs the concentration of peroxynitric acid to calculate its half-life. d) The rate law appears to be of the form -Δ[HOONO2]/Δt = k[HOONO2].
Consider the reaction a A(aq) → bB(aq) (1) Where a and b are stoichiometric coefficients for the balanced chemical reaction The average reaction rate r can be measured if the concentration change of the reagents or products is known: 1 ΔΙΑ 1 Δ r = and r = At b At a where A and B notate the concentration of A and B in solution, and A is always defined as the difference between "final" and "initial": A[4] = [A],2 - [4],1 and At = t2 – t . - A particular case of eq. (1) could be A(aq) → 2 B(aq) If the initial concentration of B is 0.2569 mol L1, and after 415.6 s it increases to 0.4633 mol L1, what is the rate of the reaction in mol L1s? mol L-1 s1. (Use scientific notation)
A bimolecular chemical reaction is one in which two chemicals react to form another substance. Suppose that one molecule of each of the two chemicals reacts to form two molecules of a new substance. If x represents the number of molecules of the new substance at time t, then the rate of change of x is proportional to the square of the numbers of molecules of the original chemicals available to be converted. That is, if each of the chemicals initially contained A molecules, then dx dt = k(A − x)2 where k is a constant. If 40% of the initial amount A is converted after 1 hour, how long will it be before 50% is converted? (Give an exact answer. Do not round.)
In a study of the formation of HI from its elements, H2(g) + 12(g) == 2HI(g) equal amounts of H2 and 12 were placed in a container, which was then sealed and heated. (a) On one set of axes, sketch concentration vs. time curves for H and HI, and explain how Q changes as a function of time. (b) Is the value of Q different if [12] is plotted instead of [H2]?
In a study of the decomposition of ammonia on a tungsten surface at 1100 °C NH3- →1/2 N2 + 3/2 H, the concentration of NH3 was followed as a function of time. It was found that a graph of [NH3] versus time in seconds gave a straight line with a slope of -4.52x10-6 M s1 and a y-intercept of 5.82×10-3 M. Based on this plot, the reaction is order in NH, and the rate constant for the reaction is Ms!.
In a study of the decomposition of hydrogen iodide on a gold surface at 150 °C HI(g)% H2(g) + ½ I½(g) the concentration of HI was followed as a function of time. It was found that a graph of [HI] versus time in seconds gave a straight line with a slope of -1.91×10-4 Ms and a y-intercept of 0.235 M. Based on this plot, the reaction is reaction is order in HI and the rate constant for the Ms!
Sucrose (C₁2H₂2O₁1), which is commonly known as table sugar, reacts in dilute acid solutions to form two simple sugars, glucose and fructose, both of which have the formula C6H₁2O6. C₁2H₂2O11 + H₂O 2 C6H₁2O6 Time (min) [C₁₂H₂2O₁] (M) 0.316 0.274 0.238 0.190 0.146 a) Is the reaction first or second order? b) What is the value of the rate constant? c) What is the first half-life? 0 39 80 140 210
The rate at which crickets chirp depends on the ambient temperature, because crickets are cold-blooded insects whose body temperature follows the temperature of their environment. It has been found that the Celsius temperature can be estimated by counting the number of chirps in 8 seconds and then adding 4. In other words, te - (number of chirps in 8 seconds) + 4. (a) Calculate the number of chirps in 8 seconds for the temperature 25°C. chirps eTextbook and Media (b) The number of chirps per unit of time is directly proportional to the rate constant for a biochemical reaction involved in the cricket's chirp. On the basis of this assumption, make a graph of In(# of chirps) versus (1/7). Calculate the activation energy for the biochemical reaction involved using the values of temperature 20°C and 35°C. E, - i J/mol (c) How many chirps would a cricket make in 8 seconds at a temperature of 45°C? chirps
In a study of the decomposition of hydrogen iodide on a gold surface at 150 °C HI(g)% H,(g) + % I»(g) the concentration of HI was followed as a function of time. It was found that a graph of [HI] versus time in seconds gave a straight line with a slope of -1.61×10-4 M s and a y-intercept of 0.103 M. Based on this plot, the reaction is |order in HI and the rate constant for the reaction is Ms!
Consider the reaction A(aq) →→ B(aq) (1) The average reaction rate r can be measured if the concentration of the reagent or the product is known at two different times: r=−Δ[A]/Δt for the reagent, and r=Δ[B]/Δt for the product, where [A] and [B] notate the concentration of A and B in solution, and Δ is always defined as the difference between "final" and "initial": Δ[A]=[A]t2−[A]t1 (t2 and t1 are subscripts) and Δt=t2−t1 (2 and 1 are subscript) A reaction proceeds according to the chemical equation (1). If the initial concentration of B is 0.1053 mol L-1, and after 194.5 s it increases to 0.4275 mol L-1, what is the rate of the reaction in mol L-1 s-1? r=? mol L-1 s-1. (Use scientific notation)
A bimolecular chemical reaction is one in which two chemicals react to form another substance. Suppose that one molecule of each of the two chemicals reacts to form two molecules of a new substance. If x represents the number of molecules of the new substance at time t, then the rate of change of x is proportional to the square of the numbers of molecules of the original chemicals available to be converted. That is, if each of the chemicals initially contained A molecules, then dx - = k(A – x)2 dt where k is a constant. If 10% of the initial amount A is converted after 1 hour, how long will it be before 80% is converted? (Give an exact answer. Do not round.) hr