Q1: A very unstable molecule, 'XYZ', decomposes via the following set of first order reactions, XY+Z XYZ K₁ K X + YZ X+Y+Z If the initial concentration of XYZ is [XYZ]o, show that the decomposition of XYZ follows, [XYZ] - [XYZ]o exp[-(k)+k₂+k3)t]
Q1: A very unstable molecule, 'XYZ', decomposes via the following set of first order reactions, XY+Z XYZ K₁ K X + YZ X+Y+Z If the initial concentration of XYZ is [XYZ]o, show that the decomposition of XYZ follows, [XYZ] - [XYZ]o exp[-(k)+k₂+k3)t]
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Chapter12: Kinetics
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![Q1: A very unstable molecule, 'XYZ', decomposes via the following set of first order reactions,
XY+Z
k₂
XYZ
k₁
«
k3
X + YZ
X+Y+Z
If the initial concentration of XYZ is [XYZ]o, show that the decomposition of XYZ follows,
[XYZ] = [XYZ]o exp[-(k)+k₂+ k3)t]
Q2: Radioactive decay is a first order kinetic process. A convenient source of gamma rays for
radiation chemistry research is 60Co, which decays to give a beta particle, gamma rays and Ni.
The half-life for the decay is 5.27 years. What is the rate constant for the decay process? How
many days will it take for a sample of 60Co to decay to 1/8th of its original amount?
Q3: Hydrogen peroxide, H₂O2, decomposes in water by a first order kinetic process. A solution
of 0.156 mol/L H₂O2 in water has an initial decomposition rate of 1.14 x 105 mol L´¹s¹.
Calculate the rate constant for the decomposition reaction and the half-life of the reaction.
Q 4: The equilibrium constant for the reaction H+ (aq) + OH(aq) = H₂O () at 25 °C is
5.49 x 10¹5 L mol-¹. The time-dependent conductivity of the solution following a temperature
jump to a final temperature of 25 °C shows a relaxation time of t = 3.7 x 10¹5 s. Determine the
values of the rate constant ki and k-1. The density of water at 25°C is 0.997 g/ml.
Q5: The water flea Daphnia performs a constant number of heartbeats and then dies. The flea
lives twice as long at 15 °C as at 25 °C. Calculate the activation energy for the reaction that
controls the rate of its heartbeat.
Q6: In a reaction vessel, reactant A forms two different products P₁ and P2 in two individual
first order reactions with activation energies of Eal and Ea2 (respectively) as follows,
A
P₁
Show that the total observed activation energy E, can be written as,
k₁. Ea1 + K₂.Eaz
k₁+ K₂
E₂ =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6ab806b-464c-4756-9d8f-72da0489465e%2Ff04b216a-5bf0-48ea-b180-e98a30cae97a%2Fsnh2g7f_processed.png&w=3840&q=75)
Transcribed Image Text:Q1: A very unstable molecule, 'XYZ', decomposes via the following set of first order reactions,
XY+Z
k₂
XYZ
k₁
«
k3
X + YZ
X+Y+Z
If the initial concentration of XYZ is [XYZ]o, show that the decomposition of XYZ follows,
[XYZ] = [XYZ]o exp[-(k)+k₂+ k3)t]
Q2: Radioactive decay is a first order kinetic process. A convenient source of gamma rays for
radiation chemistry research is 60Co, which decays to give a beta particle, gamma rays and Ni.
The half-life for the decay is 5.27 years. What is the rate constant for the decay process? How
many days will it take for a sample of 60Co to decay to 1/8th of its original amount?
Q3: Hydrogen peroxide, H₂O2, decomposes in water by a first order kinetic process. A solution
of 0.156 mol/L H₂O2 in water has an initial decomposition rate of 1.14 x 105 mol L´¹s¹.
Calculate the rate constant for the decomposition reaction and the half-life of the reaction.
Q 4: The equilibrium constant for the reaction H+ (aq) + OH(aq) = H₂O () at 25 °C is
5.49 x 10¹5 L mol-¹. The time-dependent conductivity of the solution following a temperature
jump to a final temperature of 25 °C shows a relaxation time of t = 3.7 x 10¹5 s. Determine the
values of the rate constant ki and k-1. The density of water at 25°C is 0.997 g/ml.
Q5: The water flea Daphnia performs a constant number of heartbeats and then dies. The flea
lives twice as long at 15 °C as at 25 °C. Calculate the activation energy for the reaction that
controls the rate of its heartbeat.
Q6: In a reaction vessel, reactant A forms two different products P₁ and P2 in two individual
first order reactions with activation energies of Eal and Ea2 (respectively) as follows,
A
P₁
Show that the total observed activation energy E, can be written as,
k₁. Ea1 + K₂.Eaz
k₁+ K₂
E₂ =
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