Tutorial 3: Reaction Dynamics
1)
Calculate the collision frequency, z, and the collision density, Z, in ammonia,
R = 190pm, at 25C and 100 kPa.
2)
Collision theory demands knowing the fraction of molecular collisions having at
least the kinetic energy Ea along the line of flight. What is the fraction when
Ea = 10kJ mol-1 at 300 K? Calculate the percentage increase in the fraction
when the temperature is raised by 10 K.
3)
Use the collision theory of gas-phase reactions to calculate the theoretical value
of the second-order rate constant for the reaction H2(g) + I2(g)  2HI(g) at
650 K, assuming that it is elementary bimolecular. The collision cross-section is
0.36 nm2, the reduced mass is 3.3210-27 kg, and the activation energy is 171
kJ mol-1.
4)
In a certain collision an energy equivalent to 400 kJ mol-1 is delivered; the
energy needed to break a bond is 250 kJ mol-1; there are 5 relevant molecular
modes. What is the value of the P-factor for the reactive encounter?
5)
A typical diffusion coefficient for small molecules in aqueous solution at 25C is
4.210-9 m2 s-1. If the critical reaction distance is 0.40 nm, what value is
expected for the second-order rate constant for a diffusion-controlled reaction?
6)
Calclulate the magnitude of the diffusion-controlled rate constant at 298 K for a
species in water. The viscosity of water is 1.0010-3 kg m-1 s-1.
7)
Two neutral species, A and B, with diameters 588 pm and 1650 pm,
respectively, undergo the diffusion-controlled reaction A + B  P in a solvent of
viscosity 2.3710-3 kg m-1 s-1 at 40C. Calculate the initial rate d[P]/dt if the
initial concentrations of A and B are 0.150 mol dm-3 and 0.330 mol dm-3,
respectively.
8)
In the dimerization of methyl radicals at 25C, the experimental pre-exponential
factor is 2.41010 dm3 mol-1 s-1. What are (a) the reactive cross-section and (b)
the P-factor for the reaction if the C-H bond is 154 pm?
9)
Nitrogen dioxide reacts bimolecularly in the gas phase to give 2NO + O 2. The
temperature dependence of the second-order rate constant for the rate law
d[P]/dt = kr[NO2]2 is given below. What are the reactive cross-section and the
P factor for the reaction at 750 K. Take  = 0.60 nm2.
T/K
600
700
800
1000
3
-1
-1
2
3
5
kr /cm mol s
4.610
9.710
1.310
3.1106