Gaussian Form of the Plate Theory Elution Equation

10 Gaussian Form of the Plate Theory Elution Equation 

However, the elution equation in Poisson form has its zero point at the injection point (v = 0 in Equation [3.11]), whereas a Gaussian form as usually expressed is centred at the peak maximum. Thus conversion of Equation [3.11] to its Gaussian equivalent involves changing the origin in addition to considering the limit for large values of N. Recall that v is defined as the number of plate volumes of mobile phase that have passed through the column, and in the conversion it is convenient to work with dimensionless numbers, so a new quantity w is defined as the number of plate volumes eluted measured relative to the number required to reach the peak maximum of solute A  

More details of the conversion are given in Appendix 3.2. The final result is  

Equation [3.31 a] is the elution equation written in Gaussian form in terms of the continuous variable V and centered at the peak maximum where V =. This is 

The proposed analogy to the possible co-elution of analytes in a complex mixture is that of coincident birthdays among a group of people. The days of the year are the analogs of the discrete retention time windows considered in the calculation of peak capacity. The problem to be considered is the calculation of the probabUity that two or more people (analytes) in a group (complex mixture) will have birthdays (retention times) on the same day (retention time window). It is further assumed that in both cases the distribution of analytes (people) among the windows (days of the year) is random. 

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