First-order isomerization of cyclopropane

To calculate the first-order rate constant for the isomerization of cyclopropane in the vapour phase. 

The vapour of cyclopropane on heating to about 500 C undergoes a quantitative homogeneous isomerization to propylene 

The reaction was studied at 500 °C by Comer and Pease (J. Amer. Chem. Soc. 1945, 67, 2607). In each experiment cyclopropane at a pressure Pwas allowed to react for a time t, after which the fraction x converted to propylene was determined by a selective cataljdic hydrogenation technique which permits the estimation of both cyclopropane and propylene. Experimental results are given in table 1. 

INTRODUCTION The first-order rate constant k is given by 

We note that there is a tendency for the rate constant to decrease with decreasing pressure (see problem 148). Further study of this reaction has confirmed that the first-order rate constant corresponds to a single unimolecular rearrangement (Pritchard, Sowden, and Trotman-Dickenson, Proc. Roy. Soc. A. 1953, 217, 563). 

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