15. Chemical Kinetics

Practice this topic

Multiple Choice

The rate constant of a reaction at 32°C is 0.060/s. If the frequency factor is 3.1 × 10¹⁵ s^–1, what is the activation barrier?

Multiple Choice

A reaction with an activation energy E_a = 55.00 kJ/mol is run at temperature of 30ºC. Determine the temperature required to increase the rate constant 3 times.

Multiple Choice

The following data shows the rate constant of a reaction measured at numerous temperatures. Use the Arrhenius plot to determine the frequency factor for the reaction.

3697

(a) Based on the following energy profile, predict whether kf > kr or kf < kr. [Section 15.1]

333

The accompanying graph shows plots of ln k versus 1>T for two different reactions. The plots have been extrapolated to the y-intercepts. Which reaction (red or blue) has (b) the larger value for the frequency factor, A? [Section 14.5]

545

The accompanying graph shows plots of ln k versus 1>T for two different reactions. The plots have been extrapolated to the y-intercepts. Which reaction (red or blue) has (a) the larger value for Ea,

371

Calculate the fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater.

1379

(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.6) is 160 kJ>mol. Calculate the fraction of methyl isonitrile molecules that has an energy equal to or greater than the activation energy at 500 K. (b) Calculate this fraction for a temperature of 520 K. What is the ratio of the fraction at 520 K to that at 500 K?

1079

The activation energy of a reaction is 56.8 kJ>mol and the frequency factor is 1.5 * 1011> s. Calculate the rate constant of the reaction at 25 °C.

2510

The rate constant (k) for a reaction was measured as a function of temperature. A plot of ln k versus 1>T (in K) is linear and has a slope of -7445 K. Calculate the activation energy for the reaction.

5803

The temperature dependence of the rate constant for a reaction is tabulated as follows: Temperature (K) k 1M 1 s1 2 600 0.028 650 0.22 700 1.3 750 6.0 800 23 Calculate Ea and A.

1783

The data shown here were collected for the first-order reaction: N2O( g)¡N2( g) + O( g) Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction. Temperature (K) Rate Constant (1 , s) 800 3.24 * 10- 5 900 0.00214 1000 0.0614 1100 0.955

1307

The tabulated data show the rate constant of a reaction measured at several different temperatures. Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction. Temperature (K) Rate Constant (1 , s) 300 0.0134 310 0.0407 320 0.114 330 0.303 340 0.757

2170

A reaction has a rate constant of 0.0117>s at 400.0 K and 0.689>s at 450.0 K. a. Determine the activation barrier for the reaction.

2180

A reaction has a rate constant of 0.000122>s at 27 °C and 0.228>s at 77 °C. b. What is the value of the rate constant at 17 °C?

1816

Consider these two gas-phase reactions: a. AA( g) + BB( g)¡2 AB( g) b. AB( g) + CD( g)¡AC( g) + BD( g) If the reactions have identical activation barriers and are carried out under the same conditions, which one would you expect to have the faster rate?

1321

Which of these two reactions would you expect to have the smaller orientation factor? Explain. a. O( g) + N2( g)¡NO( g) + N(g) b. NO( g) + Cl2( g)¡NOCl( g) + Cl( g)

942

The activation barrier for the hydrolysis of sucrose into glucose and fructose is 108 kJ>mol. If an enzyme increases the rate of the hydrolysis reaction by a factor of 1 million, how much lower must the activation barrier be when sucrose is in the active site of the enzyme? (Assume that the frequency factors for the catalyzed and uncatalyzed reactions are identical and a temperature of 25 °C.)

1477

The enzyme urease catalyzes the reaction of urea, 1NH2CONH22, with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 * 10-5 s-1 at 100 C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 * 104 s-1 at 21 C. (c) In actuality, what would you expect for the rate of the catalyzed reaction at 100 C as compared to that at 21 C?

1798

The activation energy of an uncatalyzed reaction is 95 kJ>mol. The addition of a catalyst lowers the activation energy to 55 kJ>mol. Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (b) 125 C?

864

A certain first-order reaction has a rate constant of 1.0 * 10-3 s-1 at 25 °C. (b) What is the Ea (in kJ/mol) if the same temperature change causes the rate to triple?

1080

If the rate of a reaction increases by a factor of 2.5 when the temperature is raised from 20 °C to 30 °C, what is the value of the activation energy in kJ/mol? By what factor does the rate of this reaction increase when the temperature is raised from 120 °C to 130 °C?

769

The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.) C2H5Br(aq) + OH- (aq)¡C2H5OH(l ) + Br - (aq) Temperature (°C) k (L,mol # s) 25 8.81 * 10- 5 35 0.000285 45 0.000854 55 0.00239 65 0.00633 b. Determine the rate constant at 15 °C.

803

The reaction 2 N2O5¡2 N2O4 + O2 takes place at around room temperature in solvents such as CCl4. The rate constant at 293 K is found to be 2.35 * 10 - 4 s - 1, and at 303 K the rate constant is found to be 9.15 * 10 - 4 s - 1. Calculate the frequency factor for the reaction.

988

At 28 C, raw milk sours in 4.0 h but takes 48 h to sour in a refrigerator at 5 C. Estimate the activation energy in kJ>mol for the reaction that leads to the souring of milk.

1767

Ethyl chloride vapor decomposes by the first-order reaction: C2H5Cl¡C2H4 + HCl The activation energy is 249 kJ>mol, and the frequency factor is 1.6 * 1014 s - 1. Find the value of the rate constant at 710 K.

183

In a hydrocarbon solution, the gold compound 1CH323AuPH3 decomposes into ethane 1C2H62 and a different gold compound, 1CH32AuPH3. The following mechanism has been proposed for the decomposition of 1CH323AuPH3: Step 1: 1CH323 AuPH3 Δ k1 k -1 1CH323Au + PH3 1fast2 Step 2: 1CH323 Au ¡k2 C2H6 + 1CH32Au 1slow2 Step 3: 1CH32Au + PH3 ¡k3 1CH32AuPH3 1fast2 (f) What would be the effect on the reaction rate of adding PH3 to the solution of 1CH323AuPH3?

248

Ethyl chloride vapor decomposes by the first-order reaction: C2H5Cl¡C2H4 + HCl The activation energy is 249 kJ>mol, and the frequency factor is 1.6 * 1014 s - 1. What fraction of the ethyl chloride decomposes in 15 minutes at this temperature?

The reaction between ethyl iodide and hydroxide ion in ethanol 1C2H5OH2 solution, C2H5I1alc2 + OH- 1alc2 ¡ C2H5OH1l2 + I - 1alc2, has an activation energy of 86.8 kJ>mol and a frequency factor of 2.10 * 1011 M-1 s-1. (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 C.

392

Values of Ea = 6.3 kJ>mol and A = 6.0 * 108>1M # s2 have been measured for the bimolecular reaction: NO1g2 + F21g2S NOF1g2 + F1g2 (a) Calculate the rate constant at 25 °C.

368

Open Question

The rate of a certain reaction was studied at various temperatures. The table shows temperature (𝑇) and rate constant (𝑘) data collected during the experiments. Plot the data to answer the questions. What is the value of the activation energy, 𝐸_a, for this reaction?