Question

For the elementary gas phase reaction H+C₂H₄ ®C₂H₅, the second-order rate constant

varies with temperature in the following way:

T / K                                       198      298      400      511      604

10¹² k/(cm³molecule^-1s^-1)       0.20     1.13     2.83     4.27     7.69

a) Use the data to calculate the activation energy, Ea, and the pre-exponential factor, A, for the reaction.

b) The simple collision theory of bimolecular reactions yields the following expression for the rate constant:

k = (8kT/p m)^1/2 sexp^(-Ea/RT)

where mis the reduced mass of the reactants and s is the reaction cross section.

i) Interpret the role of the three factors in this expression.

ii) Use the answer to part a) to estimate s for the reaction at 400K.

iii) Compare the value obtained with an estimate of 4.0x10^-19 m² for the collision cross section.

[Take the atomic masses of H and C to be 1.0 amu and 12 amu, respectively.]

Answer 1

(a) By Arrhenius Law, the rate constant is given as:

where:

: rate constant

: Pre-exponential factor

: Activation energy

: Universal Gas constant (R = 8.314 J/mol.K)

: Temperature (in K)

Taking log on both sides:

If we plot ln(k) vs 1/RT , we get a straing line (y = c + mx) with slope = -Ea and y-intercept = ln(A)

Data Table:

T (K)	k	1/RT	ln(k)
198	0.2	0.000607	-1.60944
298	1.13	0.000404	0.122218
400	2.83	0.000301	1.040277
511	4.27	0.000235	1.451614
604	7.69	0.000199	2.039921

Plot:

From the plot,

slope = -8661.2 = -Ea   Ea = 8661.2 J

y-intercept = 3.6339 = ln(A) A = exp(3.6339) = 37.86

: Pre-exponential factor = 37.86

: Activation energy = 8661.2 J