Collision & Transition State Theory Homework

Question

Assuming ideal gas: a)  Calculate the average velocity of a nitrogen molecule at 298K and compare to the velocity of a helium molecule at the same conditions.

b)      Calculate the temperature where the velocity of a nitrogen molecule will be the same as that of a helium molecule at 298K.

2. Assuming 1 mol of ideal gas at 100 °C and 1 atm. total pressure and a collision time of 10^-13 seconds:

a)      Calculate the total collision number for O2 molecules.  Estimate the molecular diameter for O2 using ChemSketch.

b)      Calculate the total collision number for a mixture of O2 and O4 molecules.  Use a molecular diameter of 4 Å for O4 complexes and assume that all O2-O2 collisions result in the formation of one O4 complex.

a)      What can be concluded regarding the relative likelihood of 2-body interactions (O2-O2) as compared to 3-body interactions (O2-O4)?

 

3. The decomposition of HI:

 

2HI - > I₂ + H₂

has an experimentally-determined rate constant at 321.4 °C and 1.0 atm of k = 2.0x10^-6 l/gmol-s

From collision theory, estimate the rate constant for this reaction and compare to the experimental value.  Assume the steric factor (p) is equal to unity and the activation energy for the reaction is Ea=44 Kcal/gmol. Estimate σ_AA using ChemSketch.

 

4.  The reaction between atomic and molecular hydrogen proceeds via a linear symmetrical transition state (H₃):

H + H₂ < -> (H₃ ) -> H₂+H

Compute the frequency factor (pre-exponential) for this reaction at 300K using transition state theory.

Data:

Moment of inertia (H3) = 3.34x10^-40 g-cm²

Moment of inertia (H2) = estimate using ChemSketch

Fundamental vibrational frequency (H2) @ 4395.2 cm^-1

Fundamental Frequencies, H3

                Stretching @ 3650 cm^-1

                Doubly degenerate bending @ 670 cm^-1 

  σ (O₂) = 2.636 Å

 σ_AA = 3.47 Å

 I (H₂) = 4.2X10^-41 g-cm²