Quantifying Hinshelwoods theory

Energy is accumulated in s vibrational modes, i.e. in 2s squared terms, and the 

Maxwell-Boltzmann distribution gives to a first approximation 

It is important to be aware of the difference in algebraic form between the Maxwell-Boltzmann distribution for two squared terms (Section 4.1.2) and that for 2s squared terms. Also note well that 2s squared terms are used. This is because one vibrational mode has two squared terms associated with it, and so if activation energy is accumulated in s vibrational modes then it will be associated with 2s squared terms. Physically, it may be easier to visualise energy going into normal modes of vibration than to think of its going into squared terms (Section 4.1.2). 

A calculated value of k can be found from Equation (4.51), which when rearranged gives 

A first approximate value of k2 can be found from the pressure at which the observed first order rate constant has fallen to half the constant high pressure value (Problem 4.19), and this first approximate value can be used to obtain a first approximate value for k. Thereafter k2, e0 and s are found by successive iterations and best fit of experiment with theory. 

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