92 CHEMICAL REACTIONS IN THE GAS PHASE 



gives the temperature t at a distance r from the point of absorption of 

 the energy after a lapse of time t. Here k, the diffusivity, is the thermal 

 conductivity, k, divided by the heat capacity per cubic centimeter of 

 substance, p and c are the density and the heat capacity per gram, 

 respectively. For a hydrocarbon such as pentane k = 0.00032 while 

 pc ^ I. For water k = 0.00143 and pc « 1. Thus the rate at which 

 temperature drops off is approximately the same for different substances. 

 If we substitute the constants for water into expression 19, it becomes 

 immediately obvious that for periods of 10""^^ sec or greater and for 

 molecular distances of r = 3.3 X 10~^ or less the exponential factor is 

 unity. If it be further assumed that 100,000 cal per mole is delivered by 

 the radiation, one finds that after 10~^^ sec the temperature of the struck 

 molecule is 6900° C above its original temperature. After 10~^° sec it 

 has dropped to 7° above the original temperature. A C — C bond 

 oscillates about 3 X 10^^ times per second, while a CH bond oscillates 

 about 9 X 10^^ times per second. Thus, in the very unusual circum- 

 stances that enough energy is delivered to a bond to break it, dissociation 

 will ensue. The earlier considerations of the mass spectrographic data 

 indicate that 10~^ sec is a more probable half life for molecules. These 

 processes with half lives of 10~^ sec are completely quenched in the 

 liquid state. Even if the molecule should decompose, it still must escape 

 the Franck-Rabinowitch cage before recombination or there will be no 

 reaction. Thus the viscosities of pure liquids are given with some 

 accuracy by the equation 



V Vk' 



where 77, A^, h, V, AH^^p, R, T, and k' are the viscosity, Avogadro's 

 number, Planck's constant, molal volume, heat of vaporization, gas 

 constant, temperature, and rate of jumping out of the cage, respectively. 

 The constant 2.5 in this equation is the ratio of the heat of vaporization 

 of the liquid to the free energy of activation of the flow process (30). 

 Remembering that pure liquids have a viscosity at these melting points 

 of about 0.02 poise, one finds that a molecule has a half life inside the 

 Franck-Rabinowitch cage of about 2 X 10~^^ sec at room temperature. 

 Hot molecules or molecules dissociating with large kinetic energies can 

 escape from the cage even more quickly. Thus the rapid chilling of 

 molecules has much more to do with preventing decomposition than 

 does the entrapment in a cage of their neighbors. 



The main source of destruction of large molecules by direct hits will 

 be by the ejection of an electron and the reaction of the positive ion 



