Deck 6: Chemical Kinetics

Question 1

The transmittance of a sample is the ratio of the intensity of radiation transmitted to the intensity of the incident radiation. The molar absorption coefficient of the [Cu(NH₃)₄]²⁺ complex ion in aqueous solution is 50 dm³ mol^-1 cm^-1 at a wavelength of 590 nm. Determine the transmittance when light of this wavelength passes through an aqueous solution of the ion of molar concentration 0.100 mol dm^-3 and path length 1.00 cm.

A) 10^-5
B) 10^-2
C) 10^-6
D) 10^-4

Answer 1

A

Question 2

The rate constant for the reaction
2 N₂O₅(g) ⇌ 4 NO₂(g) + O₂(g)
Is reported in units of s^-1. What is the overall order of the reaction?

A) Zeroth order
B) First order
C) Second order
D) Third order

Answer 2

B

Question 3

The rate constant for the gas-phase reaction
H₂(g) + I₂(g)  2 HI(g)
Has the value 4.45  10^-5 mol^-1 dm³ s^-1. What is the equivalent rate constant in units of molecule^-1 cm³ s^-1?

A) 7.39  10^-28 molecule^-1 cm³ s^-1
B) 7.39  10^-29 molecule^-1 cm³ s^-1
C) 4.45  10^-2 molecule^-1 cm³ s^-1
D) 7.39  10^-26 molecule^-1 cm³ s^-1

Answer 3

D

Question 4

The mechanism for the gas-phase reaction that converts nitrogen dioxide, NO₂, into nitric oxide, NO, and oxygen, O₂ was explored by measuring the initial rate of the reaction for different pressures of reactant. The data below shows how the initial rate of reaction varied with the partial pressure of nitrogen dioxide at a temperature of 300 °C. An inert buffer gas was used so that the overall initial pressure was the same for each experiment. Use the method of initial rates to determine the order of the reaction.
$\begin{array}{lllll}\mathrm{p} / \mathrm{Pa} & 2000 & 4000 & 6000 & 8000 \\\mathrm{v}_{0} /\left(\mathrm{Pa} \mathrm{s}^{-1}\right) & 0.36 & 0.65 & 0.94 & 1.21\end{array}$

A) Zeroth order
B) First order
C) Second order
D) Third order

Question 5

The kinetics of the hydrolysis of methyl methanoate, CH₃COOCH₃, in aqueous solution were investigated by measuring the concentration of the ester after different time intervals. The reaction was found to be first order in the concentration of the ester. Use the data below to determine the rate constant for the reaction.
$\begin{array}{lllllll}\text { time, } & 0 & 1800 & 3600 & 5400 & 7200 & 9000 \\t / \mathrm{s} & & & & & & \\\text { concentration, } & 0.300 & 0.191 & 0.135 & 0.081 & 0.055 & 0.035 \\c /\left(\mathrm{mol} d \mathrm{~m}^{-3}\right) & & & & &\end{array}$

A) 2.38 ? 10^-4 s^-1
B) 7.87 ? 10^-4 s^-1
C) 1.01 ? 10^-4 s^-1
D) 9.54 ? 10^-4 s^-1

Question 6

The rate constant for the pseudo first-order acid-catalysed hydrolysis of glucose is 4.07  10^-4 s^-1. Calculate the half-life for the reaction.

A) 1700 s
B) 2460 s
C) 740 s
D) 339 s

Question 7

The rate constant for the reaction
2 N₂O(g) ? 2N₂(g) + O₂(g)
Has been found to vary with temperature according to the following data. Determine the activation energy for the reaction.
$\begin{array}{lllll}\theta /{ }^{\circ} \mathrm{C} & 565 & 728 & 757 & 780 \\k_{r} / \mathrm{s}^{-1} & 1.10 \times 10^{-3} & 0.380 & 0.871 & 1.67\end{array}$

A) 190 kJ mol^-1
B) 22.8 kJ mol^-1
C) 30.6 kJ mol^-1
D) 254 kJ mol^-1

Question 8

For the second-order reaction between methyl iodide, CH₃I, and thiosulfate ions, S₂O₃^2-, ions in water, the Arrhenius pre-exponential factor is 2.19  10¹² dm³ mol^-1 s^-1 and the activation energy is 78.7 kJ mol^-1. Calculate the rate constant for the reaction at a temperature of 25°C.

A) 1.59  10^-3 dm³ mol^-1 s^-1
B) 2.19  10¹² dm³ mol^-1 s^-1
C) 2.12  10¹² dm³ mol^-1 s^-1
D) 0.035 dm³ mol^-1 s^-1

Question 9

The rate constant for the enzyme-catalysed decomposition of hydrogen peroxide, H₂O₂, increases by a factor of 3.8 when the temperature is increased from 298 K to 348 K. Determine the activation energy.

A) 23 kJ mol^-1
B) 75 kJ mol^-1
C) 48.9 kJ mol^-1
D) 16 kJ mol^-1

Question 10

Use collision theory to calculate an estimate of the Arrhenius pre-exponential factor for the reaction of two chlorine, ³⁵Cl, atoms at a temperature of 298 K. The collisional cross section of a chlorine atom is estimated to be 0.064 nm².

A) 33 10⁶ mol^-1 m³ s^-1
B) 23 10⁶ mol^-1 m³ s^-1
C) 11 10⁶ mol^-1 m³ s^-1
D) 17 10⁶ mol^-1 m³ s^-1

Question 11

For a solution-phase dimerization reaction, the rate constants for the second-order forward reaction is 2  10⁷ dm³ mol^-1 s^-1 and for the first-order backward reaction is 4  10⁵ s^-1. Determine the equilibrium constant.

A) 0.2  10^-2
B) 50
C) 1  10⁹
D) 1  10^-4

Question 12

For the isomerization of cyclopropane into propene
Cyclo-C₃H₆ ∏ CH₃CH=CH₂
The rate constants of the forward and backward reactions are 1.47  10¹³ s^-1 and 5.19  10¹² s^-1 respectively at a temperature of 1500 K. Determine the partial pressure of cyclopropane at equilibrium if the initial partial pressure is 0.100 bar.

A) 13.5 bar
B) 0.283 bar
C) 0.074 bar
D) 0.353 bar

Question 13

In a temperature-jump experiment to investigate the kinetics of protein folding, the relaxation time following perturbation of the equilibrated system was measured to be 240 ns. Both the forward and backward transformations were found to be first order, with the rate constant for the forward transformation known to be 1.1  10⁶ s^-1. Determine the rate constant for the backward transformation.

A) 2.2  10^-18 s^-1
B) 4.6  10¹² s^-1
C) 4.2  10⁶ s^-1
D) 3.1  10⁶ s^-1

Question 14

For a large excess of oxygen, O₂, the rate of production of nitrogen dioxide, NO₂, by the gas-phase oxidation of nitric oxide, NO
2 NO(g) + O₂  2 NO₂(g) is found to be independent of the partial pressure of oxygen present. Under these conditions, the rate of formation of nitrogen dioxide was measured to be 8.34  10^-13 s^-1 for a concentration of nitric oxide of 5.38  10^-6 mol dm^-3. Use the description of the mechanism of the reaction given in section 11.5 to determine the rate constant for the dimerization of nitric oxide
2 NO(g)  N₂O₂(g).

A) 14.4  10^-3 dm⁶ mol^-2 s^-1
B) 1.55  10^-7 dm⁶ mol^-2 s^-1
C) 28.8  10^-3 dm⁶ mol^-2 s^-1
D) 7.8  10^-8 dm⁶ mol^-2 s^-1

Question 15

Calculate the diffusion coefficient for the diffusion of a haemoglobin molecule through water at a temperature of 25°C. The effective cross sectional area of a haemoglobin macromolecule is 3.6  10^-9 m² and the viscosity of water is 8.90  10^-4 kg m^-1 s^-1 at this temperature.

A) 5.78  10^-12 m² s^-1
B) 5.78  10^-12 m² s^-1
C) 0.69  10^-10 m² s^-1
D) 2.26  10^-9 m² s^-1

Question 16

The root-mean-square distance travelled by a molecule undergoing a one-dimensional random walk in a liquid or gas in a time interval is . The diffusion coefficient for the diffusion of sucrose through water at a temperature of 20°C is 4.59  10^-10 m² s^-1. Calculate the distance through which a sucrose molecule moves in 1.00 ms.

A) 9.18 m
B) 3.03 m
C) 1.74 mm
D) 95.8 m

Question 17

Calculate the rate constant for the rate-determining step of a diffusion-controlled reaction that takes place in toluene, C₆H₅CH₃, at 20 °C. The viscosity of toluene at this temperature is  = 5.85  10^-4 kg m^-1 s^-1.

A) 253  10³ mol^-1 m³ s^-1
B) 3.70  10⁶ mol^-1 m³ s^-1
C) 758  10³ mol^-1 m³ s^-1
D) 11.1  10⁶ mol^-1 m³ s^-1

Question 18

In an experiment to investigate the inhibition of the enzyme-glucosidase the following data for the rates of reaction with glucopyranoside for various substrate concentrations was obtained. By constructing a Leaver-Burk plot, determine the value of the Michaelis constant.
$\begin{array}{lllll} [S]/\left(10^{-8} \mathrm{~mol} \mathrm{dm}^{-3}\right) & 1.00 & 2.00 & 3.00 & 4.00 \\V/\left(10^{-3} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\right) & 16.7 & 33.3 & 41.1 & 49.8\end{array}$

A) 8.46 ? 10^-6 mol dm^-3
B) 8.46 mol dm^-3
C) 8.46 ? 10³ mol dm^-3
D) 8.46 ? 10⁶ mol dm^-3

Question 19

Analysis of the kinetics of the enzyme-catalysed hydrolysis of an ester by -chymotrypsin show that for an initial enzyme concentration of 4.5  10^-9 mol dm^-3, the maximum rate was 5.9  10^-13 mol dm^-3 s^-1 and the Michaelis constant was 5.6  10^-7 dm³ mol^-1. Calculate the efficiency of the enzyme.

A) 230 dm³ mol^-1 s^-1
B) 4.27  10^-3 dm³ mol^-1 s^-1
C) 1.36  10¹⁰ dm³ mol^-1 s^-1
D) 7.63  10³ dm³ mol^-1 s^-1

Question 20

The pyrolysis of ethane, C₂H₆
C₂H₆  C₂H₄ + H₂
Proceeds through a multistep chain mechanism involving radicals, which are highly reactive species with one or more unpaired electrons. Radicals are formed in initiation steps, transferred in propagation steps and lost in termination steps. Retardation steps maintain the concentration of radical species but regenerate the reactant. One of the steps in the reaction mechanism is
H + C₂H₆  H₂ + C₂H₅
What is the best description of this step?

A) Initiation
B) Propagation
C) Retardation
D) Termination