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.
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EBK CHEMISTRY: AN ATOMS FIRST APPROACH
- At 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_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_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_forwardNitryl fluoride is an explosive compound that can be made by oxidizing nitrogen dioxide with fluorine: 2 NO2(g) + F2(g) → 2 NO2F(g) Several kinetics experiments, all done at the same temperature and involving formation of nitryl fluoride, are summarized in this table: Write the rate law for the reaction. Determine what the order of the reaction is with respect to each reactant and each product. Calculate the rate constant k and express it in appropriate units.arrow_forward
- The reaction 2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g) was studied at 904 C, and the data in the table were collected. (a) Determine the order of the reaction for each reactant. (b) Write the rate equation for the reaction. (c) Calculate the rate constant for the reaction. (d) Find the rate of appearance of N2 at the instant when [NO] = 0.350 mol/L and [H] = 0.205 mol/L.arrow_forwardThe decomposition of SO2Cl2 is a first-order reaction: SO2Cl2(g) SO2(g) + Cl2(g) The rate constant for the reaction is 2.8 103 min1 at 600 K. If the initial concentration of SO2Cl2 is 1.24 103 mol/L, how long will it take for the concentration to drop to 0.31 103 mol/L?arrow_forwardThe decomposition of many substances on the surface of a heterogeneous catalyst shows the following behavior: How do you account for the rate law changing from first order to zero order in the concentration of reactant?arrow_forward
- Kinetics II You and a friend are working together in order to obtain as much kinetic information as possible about the reaction A(g)B(g)+C(g). One thing you know before performing the experiments is that the reaction is zero order, first order, or second order with respect to A. Your friend goes off, runs the experiment, and brings back the following graph. a After studying the curve of the graph, she declares that the reaction is second order, with a corresponding rate law of Rate = k[A]2. Judging solely on the basis of the information presented in this plot, is she correct in her statement that the reaction must be second order? Here are some data collected from her experiment: Time (s) [A] 0.0 1.0 1.0 0.14 3.0 2.5 103 5.0 4.5 105 7.0 8.3 107 b The half-life of the reaction is 0.35 s. Do these data support the reaction being second order, or is it something else? Try to reach a conclusive answer without graphing the data. c What is the rate constant for the reaction? d The mechanism for this reaction is found to be a two-step process, with intermediates X and Y. The first step of the reaction is the rate-determining step. Write a possible mechanism for the reaction. e You perform additional experiments and find that the rate constant doubles in value when you increase the temperature by 10oC. Your lab partner doesnt understand why the rate constant changes in this manner. What could you say to your partner to help her understand? Feel free to use figures and pictures as part of your explanation.arrow_forwardThe 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)?arrow_forwardChlorine dioxide, ClO2, is a reddish-yellow gas that is soluble in water. In basic solution it gives ClO3 and ClO2 ions. 2ClO2(aq)+2OH(aq)ClO3(aq)+ClO2(aq)+H2O To obtain the rate law for this reaction, the following experiments were run and, for each, the initial rate of reaction of ClO2 was determined. Obtain the rate law and the value of the rate constant.arrow_forward
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