The initial rate for a reaction is equal to the slope of the tangent line at t ≈ 0 in a plot of [A] versus time. From calculus, initial rate =
Assuming you have some calculus in your background, derive the zero-, first-, and second-order integrated rate laws using the differential rate law.
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Chemistry: An Atoms First Approach
- At 500 K in the presence of a copper surface, ethanol decomposes according to the equation C2H5OH(g)CH3CHO(g)+H2(g) The pressure of C2H5OH was measured as a function of time and the following data were obtained: Time(s) PC2H5OH(torr) 0 250. 100. 237 200. 224 300. 211 400. 198 500. 185 Since the pressure of a gas is directly proportional to the concentration of gas, we can express the rate law for a gaseous reaction in terms of partial pressures. Using the above data, deduce the rate law, the integrated rate law, and the value of the rate constant, all in terms of pressure units in atm and time in seconds. Predict the pressure of C2H5OH after 900. s from the start of the reaction. (Hint: To determine the order of the reaction with respect to C2H5OH, compare how the pressure of C2H5OH decreases with each time listing.)arrow_forwardAt 573 K, gaseous NO2(g) decomposes, forming NO(g) and O2(g). If a vessel containing NO2(g) has an initial concentration of 1.9 102 mol/L, how long will it take for 75% of the NO2(g) to decompose? The decomposition of NO2(g) is second-order in the reactant and the rate constant for this reaction, at 573 K, is 1.1 L/mol s.arrow_forwardOne experimental procedure that can be used to determine the rate law of a reaction is the method of initial rates. What data are gathered in the method of initial rates, and how are these data manipulated to determine k and the orders of the species in the rate law? Are the units for k. the rate constant, the same for all rate laws? Explain. If a reaction is first order in A, what happens to the rate if [A] is tripled? If the initial rate for a reaction increases by a factor of 16 when [A] is quadrupled, what is the order of n? If a reaction is third order in A and [A] is doubled, what happens to the initial rate? If a reaction is zero order, what effect does [A] have on the initial rate of a reaction?arrow_forward
- Hydrogen peroxide, H2O2(aq), decomposes to H2O() and O2(g) in a reaction that is first-order in H2O2 and has a rate constant k = 1.06 103 min1 at a given temperature. (a) How long will it take for 15% of a sample of H2O2 to decompose? (b) How long will it take for 85% of the sample to decompose?arrow_forwardMany biochemical reactions are catalyzed by acids. A typical mechanism consistent with the experimental results (in which HA is the acid and X is the reactant) is Step 1: Step 2: Step 3: Derive the rate law from this mechanism. Determine the order of reaction with respect to HA. Determine how doubling the concentration of HA would affect the rate of the reaction.arrow_forwardThe Raschig reaction produces the industrially important reducing agent hydrazine, N2H4, from ammonia, NH3, and hypochlorite ion, OCl−, in basic aqueous solution. A proposed mechanism is Step 1: Step 2: Step 3: What is the overall stoichiometric equation? Which step is rate-limiting? What reaction intermediates are involved? What rate law is predicted by this mechanism?arrow_forward
- Isomerization of CH3NC occurs slowly when CH3NC is heated. CH3NC(g) CH3CN(g) To study the rate of this reaction at 488 K, data on [CH3NC] were collected at various times. Analysis led to the following graph. (a) What is the rate law for this reaction? (b) What is the equation for the straight line in this graph? (c) Calculate the rate constant for this reaction. (d) How long does it take for half of the sample to isomerize? (e) What is the concentration of CH3NC after 1.0 104 s?arrow_forwardAmmonia decomposes when heated according to the equation NH3(g) NH2(g) + H(g) The data in the table for this reaction were collected at a high temperature. Plot In [NH3] versus time and 1/[NH3] versus time. What is the order of this reaction with respect to NH3? Find the rate constant for the reaction from the slope.arrow_forwardIn Exercise 11.39, if the initial concentration of N2Oj is 0.100 .\1. how long will it take for the concentration to drop to 0.0100 times its original value? The decomposition of N2O5 in solution in carbon tetrachloride is a first-order reaction: 2N2O5—»4NO2 + O2 The rate constant at a given temperature is found to be 5.25 X 10-4 s-’. If the initial concentration of N2O5 is 0.200 M, what is its concentration after exactly 10 minutes have passed?arrow_forward
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: An Atoms First ApproachChemistryISBN:9781305079243Author:Steven S. Zumdahl, Susan A. ZumdahlPublisher:Cengage Learning
- Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning