Integrated Rate Law

Multiple Choice

For the reaction A → B, the rate constant is 0.0837 M^–1•sec^–1. How long would it take for [A] to decrease by 85%?

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Multiple Choice

The following reaction has a rate constant of 3.7 × 10^–3 M•s^–1 at 25°C:

A → B + C

Calculate the concentration of C after 2.7 × 10^–3 sec where [A]₀ was 0.750 M at 25°C; assume [C]₀ = 0 M.

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Multiple Choice

For the decomposition of urea, NH₂CONH₂ (aq) + H⁺(aq) + 2 H₂O (l) → 2 NH₄⁺ (aq) + HCO₃^– (aq), the rate constant is 3.24 × 10^–4 s^–1 at 35°C. The initial concentration of urea is 2.89 mol/L. What fraction of urea has decomposed after 3.5 minutes?

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Multiple Choice

Iodine-123 is used to study thyroid gland function. As this radioactive isotope breaks down, after 5.7 hrs the concentration of iodine-123 is 56.3% complete. Find the rate constant of this reaction.

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Textbook Question

The gas phase decomposition of HI has the following rate law: 2 HI1g2¡H21g2 + I21g2 Rate = k3HI42 At 443 °C, k = 30.1 M-1 min-1. If the initial concentration of HI is 0.010 M, what is the concentration after 1.5 hours? (LO 14.8) (a) 6.9 * 10-3 M (b) 1.8 * 10-3 M (c) 3.6 * 10-4 M (d) 8.9 * 10-4 M

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Textbook Question

Which of the following linear plots do you expect for a reaction A¡products if the kinetics are (a) zero order, [Section 14.4]

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Textbook Question

Chlorine monoxide (ClO) decomposes at room temperature according to the reaction 2 ClO1g2¡Cl21g2 + O21g2 The concentration of ClO was monitored over time, and three graphs were made:

What is the rate law for the reaction? (LO 14.9) (a) Rate = k (b) Rate = k3ClO4 (c) Rate = k3ClO42 (d) Rate = k3ClO43 M14_MCMU6230_

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Textbook Question

(a) For the generic reaction A S B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?

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Textbook Question

As described in Exercise 14.41, the decomposition of sulfuryl chloride 1SO2Cl22 is a first-order process. The rate constant for the decomposition at 660 K is 4.5 * 10-2 s-1. (b) At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?

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Textbook Question

The first-order rate constant for the decomposition of N2O5, 2 N2O51g2¡4 NO21g2 + O21g2, a t 70 C i s 6.82 * 10-3 s-1. Suppose we start with 0.0250 mol of N2O51g2 in a volume of 2.0 L. (a) How many moles of N2O5 will remain after 5.0 min?

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Textbook Question

Indicate the order of reaction consistent with each observation c. The half-life of the reaction gets longer as the initial concentration is increased.

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Textbook Question

Indicate the order of reaction consistent with each observation. a. The half-life of the reaction gets shorter as the initial concentration is increased.

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Textbook Question

The gas-phase decomposition of NO2, 2 NO21g2¡ 2 NO1g2 + O21g2, is studied at 383 C, giving the following data: Time (s) 3no2 4 (M) 0.0 0.100 5.0 0.017 10.0 0.0090 15.0 0.0062 20.0 0.0047 (c) Predict the reaction rates at the beginning of the reaction for initial concentrations of 0.200 M, 0.100 M, and 0.050 M NO2.

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Textbook Question

The tabulated data show the concentration of AB versus time for this reaction: AB( g)¡A( g) + B( g) Time (s) [AB] (M) 0 0.950 50 0.459 100 0.302 150 0.225 200 0.180 250 0.149 300 0.128 350 0.112 400 0.0994 450 0.0894 500 0.0812 Determine the order of the reaction and the value of the rate constant. Predict the concentration of AB at 25 s.

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Textbook Question

Sucrose 1C12H22O112, commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 C and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose: Time (min) 3C12H22o11 4 1M2 0 0.316 39 0.274 80 0.238 140 0.190 210 0.146 (a) Is the reaction first order or second order with respect to 3C12H22O114?

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Textbook Question

The reaction A¡products was monitored as a function of time. The results are shown here. Time (s) [A] (M) 0 1.000 25 0.914 50 0.829 75 0.744 100 0.659 125 0.573 150 0.488 175 0.403 200 0.318 Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [A] = 0.10 M?

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Textbook Question

This reaction was monitored as a function of time: A → B + C A plot of ln[A] versus time yields a straight line with slope -0.0045/s. a. What is the value of the rate constant (k) for this reaction at this temperature?

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Textbook Question

This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms. b. Write the rate law for the reaction.

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Textbook Question

The decomposition of N2O5 is a first-order reaction. At 25 °C, it takes 5.2 h for the concentration to drop from 0.120 M to 0.060 M. How many hours does it take for the concentration to drop from 0.030 M to 0.015 M? From 0.480 M to 0.015 M?

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Textbook Question

You wish to determine the reaction order and rate constant for the following thermal decomposition reaction: AB2 S 1>2 A2 + B2 (c) Describe how you would determine the value of the rate constant.

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Textbook Question

Nitrosyl bromide decomposes at 10 °C. NOBr1g2S NO1g2 + 1>2 Br21g2 Use the following kinetic data to determine the order of the reaction and the value of the rate constant for consumption of NOBr.

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Textbook Question

Consider the following concentration–time data for the decomposition reaction AB S A + B.

(a) Determine the order of the reaction and the value of the rate constant.

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Textbook Question

Consider the following concentration–time data for the decomposition reaction AB S A + B.

(b) What is the molarity of AB after a reaction time of 192 min?

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Textbook Question

The tabulated data were collected for this reaction at 500 °C: CH3CN(g)¡CH3NC( g) Time (h) [Ch3Cn] (M) 0.0 1.000 5.0 0.794 10.0 0.631 15.0 0.501 20.0 0.398 25.0 0.316 a. Determine the order of the reaction and the value of the rate constant at this temperature.

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Textbook Question

The tabulated data were collected for this reaction at a certain temperature: X2Y¡2 X + Y Time (h) [X2y] (M) 0.0 0.100 1.0 0.0856 2.0 0.0748 3.0 0.0664 4.0 0.0598 5.0 0.0543 a. Determine the order of the reaction and the value of the rate constant at this temperature.

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Textbook Question

The tabulated data were collected for this reaction at a certain temperature: X2Y¡2 X + Y Time (h) [X2y] (M) 0.0 0.100 1.0 0.0856 2.0 0.0748 3.0 0.0664 4.0 0.0598 5.0 0.0543 c. What is the concentration of X after 10.0 hours?

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Textbook Question

Dinitrogen pentoxide decomposes in the gas phase to form nitrogen dioxide and oxygen gas. The reaction is first order in dinitrogen pentoxide and has a half-life of 2.81 h at 25 °C. If a 1.5-L reaction vessel initially contains 745 torr of N2O5 at 25 °C, what partial pressure of O2 is present in the vessel after 215 minutes?

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Textbook Question

Iodine atoms combine to form I2 in liquid hexane solvent with a rate constant of 1.5 * 1010 L>mol # s. The reaction is second order in I. Since the reaction occurs so quickly, the only way to study the reaction is to create iodine atoms almost instantaneously, usually by photochemical decomposition of I2. Suppose a flash of light creates an initial [I] concentration of 0.0100 M. How long will it take for 95% of the newly created iodine atoms to recombine to form I2?

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Textbook Question

The reaction 2 NO2¡2 NO + O2 has the rate constant k = 0.63 M- 1s - 1. (b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

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Textbook Question

You wish to determine the activation energy for the following first-order reaction: AS B + C (b) How would you use these data to determine the activation energy?

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Textbook Question

The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 * 103 M-1 cm-1 at 520 nm. (d) How long does it take for the absorbance to fall to 0.100?

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Textbook Question

A certain substance X decomposes. Fifty percent of X remains after 100 minutes. How much X remains after 200 minutes if the reaction order with respect to X is (c) second order?

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Textbook Question

Assume that you are studying the first-order conversion of a reactant X to products in a reaction vessel with a constant volume of 1.000 L. At 1 p.m., you start the reaction at 25 °C with 1.000 mol of X. At 2 p.m., you find that 0.600 mol of X remains, and you immediately increase the temperature of the reaction mixture to 35 °C. At 3 p.m., you discover that 0.200 mol of X is still present. You want to finish the reaction by 4 p.m. but need to continue it until only 0.010 mol of X remains, so you decide to increase the temperature once again. What is the minimum temperature required to convert all but 0.010 mol of X to products by 4 p.m.?

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Textbook Question

Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H3O+ by OH-, which has a second-order rate constant of 1.3 * 1011 M-1 s-1 at 25 °C. (b) Under normal laboratory conditions, would you expect the rate of the acid–base neutralization to be limited by the rate of the reaction or by the speed of mixing?

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Textbook Question

Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H3O+ by OH-, which has a second-order rate constant of 1.3 * 1011 M-1 s-1 at 25 °C. (a) If equal volumes of 2.0 M HCl and 2.0 M NaOH are mixed instantaneously, how much time is required for 99.999% of the acid to be neutralized?

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Textbook Question

The reaction 2 NO1g2 + O21g2S 2 NO21g2 has the thirdorder rate law rate = k3NO423O24, where k = 25 M-2 s-1. Under the condition that 3NO4 = 2 3O24, the integrated rate law is 13O242 = 8 kt +113O24022 What are the concentrations of NO, O2, and NO2 after 100.0 s if the initial concentrations are 3NO4 = 0.0200 M and 3O24 = 0.0100 M?

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Textbook Question

The rate constant for the decomposition of gaseous NO2 to NO and O2 is 4.7>1M ~ s2 at 383 °C. Consider the decomposition of a sample of pure NO2 having an initial pressure of 746 mm Hg in a 5.00 L reaction vessel at 383 °C. (c) What is the mass of O2 in the vessel after a reaction time of 1.00 min?

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Textbook Question

The rate constant for the first-order decomposition of gaseous N2O5 to NO2 and O2 is 1.7 * 10-3 s-1 at 55 °C. (a) If 2.70 g of gaseous N2O5 is introduced into an evacuated 2.00 L container maintained at a constant temperature of 55 °C, what is the total pressure in the container after a reaction time of 13.0 minutes?

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Textbook Question

For the thermal decomposition of nitrous oxide, 2 N2O1g2S 2 N21g2 + O21g2, values of the parameters in the Arrhenius equation are A = 4.2 * 109 s-1 and Ea = 222 kJ>mol. If a stream of N2O is passed through a tube 25 mm in diameter and 20 cm long at a flow rate of 0.75 L/min at what temperature should the tube be maintained to have a partial pressure of 1.0 mm of O2 in the exit gas? Assume that the total pressure of the gas in the tube is 1.50 atm.

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Textbook Question

A 0.500 L reaction vessel equipped with a movable piston is filled completely with a 3.00% aqueous solution of hydrogen peroxide. The H2O2 decomposes to water and O2 gas in a first-order reaction that has a half-life of 10.7 h. As the reaction proceeds, the gas formed pushes the piston against a constant external atmospheric pressure of 738 mm Hg. Calculate the PV work done (in joules) after a reaction time of 4.02 h. (You may assume that the density of the solution is 1.00 g/mL and that the temperature of the system is maintained at 20 °C.)

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Open Question

For the reaction x ⟶ y identify what the graphs of [x] versus time and [y] versus time would look like for various orders. in each graph, [?] represents either [x] or [y].

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Open Question

Consider the following general reaction and data: 2a + 2 b + c → d + 3 e

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