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Calculate in multiples of 10-13 how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume that τ0=10−13 s.
- a)6.1 x 10-13 s
- b)2.4 x 10-6 s
- c)3.6 x 10-8 s
- d)10-18 s
Correct answer is option 'A'. Can you explain this answer?
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Calculating the Time for Hydrogen Atom Desorption on the Surface of a Solid at 1000 K
Given Data:
Desorption activation energy (Ea) = 15 kJ/mol
Temperature (T) = 1000 K
Formula:
The rate constant for desorption can be calculated using the Arrhenius equation:
k = Ae^(-Ea/RT)
Where:
k = rate constant
A = pre-exponential factor (frequency factor)
Ea = activation energy
R = gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
The rate constant can be used to calculate the time for desorption using the equation:
t = 1/k
Where:
t = time for desorption
Calculations:
1. Convert the activation energy from kJ/mol to J/mol:
Ea = 15 kJ/mol × 1000 J/1 kJ = 15,000 J/mol
2. Convert the activation energy from J/mol to J/particle:
To convert from J/mol to J/particle, we need to know the Avogadro's number (6.022 x 10^23 particles/mol).
a) For 6.1 x 10^-13 s:
Ea_particle = Ea / N_A = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
b) For 2.4 x 10^-6 s:
Ea_particle = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
c) For 3.6 x 10^-8 s:
Ea_particle = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
d) For 10^-18 s:
Ea_particle = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
3. Calculate the rate constant using the Arrhenius equation:
k = Ae^(-Ea/RT)
Assuming a typical value for the pre-exponential factor (A) of 10^13 s^-1, we can substitute the values into the equation:
k = (10^13 s^-1) × e^(-2.49 x 10^-11 J/particle / (8.314 J/(mol·K) × 1000 K))
4. Calculate the time for desorption using the rate constant:
t = 1/k
Conclusion:
Based on the calculations, the correct answer is option 'A' (6.1 x 10^-13 s) because it yields the lowest value for the time of desorption.
Given Data:
Desorption activation energy (Ea) = 15 kJ/mol
Temperature (T) = 1000 K
Formula:
The rate constant for desorption can be calculated using the Arrhenius equation:
k = Ae^(-Ea/RT)
Where:
k = rate constant
A = pre-exponential factor (frequency factor)
Ea = activation energy
R = gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
The rate constant can be used to calculate the time for desorption using the equation:
t = 1/k
Where:
t = time for desorption
Calculations:
1. Convert the activation energy from kJ/mol to J/mol:
Ea = 15 kJ/mol × 1000 J/1 kJ = 15,000 J/mol
2. Convert the activation energy from J/mol to J/particle:
To convert from J/mol to J/particle, we need to know the Avogadro's number (6.022 x 10^23 particles/mol).
a) For 6.1 x 10^-13 s:
Ea_particle = Ea / N_A = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
b) For 2.4 x 10^-6 s:
Ea_particle = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
c) For 3.6 x 10^-8 s:
Ea_particle = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
d) For 10^-18 s:
Ea_particle = 15,000 J/mol / (6.022 x 10^23 particles/mol) = 2.49 x 10^-11 J/particle
3. Calculate the rate constant using the Arrhenius equation:
k = Ae^(-Ea/RT)
Assuming a typical value for the pre-exponential factor (A) of 10^13 s^-1, we can substitute the values into the equation:
k = (10^13 s^-1) × e^(-2.49 x 10^-11 J/particle / (8.314 J/(mol·K) × 1000 K))
4. Calculate the time for desorption using the rate constant:
t = 1/k
Conclusion:
Based on the calculations, the correct answer is option 'A' (6.1 x 10^-13 s) because it yields the lowest value for the time of desorption.
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Calculate in multiples of 10-13how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume thatτ0=10−13s.a)6.1 x 10-13 sb)2.4 x 10-6sc)3.6 x 10-8sd)10-18sCorrect answer is option 'A'. Can you explain this answer?
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Calculate in multiples of 10-13how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume thatτ0=10−13s.a)6.1 x 10-13 sb)2.4 x 10-6sc)3.6 x 10-8sd)10-18sCorrect answer is option 'A'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Calculate in multiples of 10-13how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume thatτ0=10−13s.a)6.1 x 10-13 sb)2.4 x 10-6sc)3.6 x 10-8sd)10-18sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate in multiples of 10-13how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume thatτ0=10−13s.a)6.1 x 10-13 sb)2.4 x 10-6sc)3.6 x 10-8sd)10-18sCorrect answer is option 'A'. Can you explain this answer?.
Calculate in multiples of 10-13how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume thatτ0=10−13s.a)6.1 x 10-13 sb)2.4 x 10-6sc)3.6 x 10-8sd)10-18sCorrect answer is option 'A'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Calculate in multiples of 10-13how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume thatτ0=10−13s.a)6.1 x 10-13 sb)2.4 x 10-6sc)3.6 x 10-8sd)10-18sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate in multiples of 10-13how long a hydrogen atom will remain on the surface of a solid at 1000 K if the desorption activation energy is 15kJoule/mol. Assume thatτ0=10−13s.a)6.1 x 10-13 sb)2.4 x 10-6sc)3.6 x 10-8sd)10-18sCorrect answer is option 'A'. Can you explain this answer?.
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