By definition the concentration of A is the flow rate of A over the volumetric flow rate :

Since we are dealing with a gas the volumeteric flow rate will change down the PFR according to the equation:

The total flow rate, F_T, is equal to the intial flow rate plus the change in flow rate as the reaction occurs :

Substituting in and simplifying :

We will assume that there is no pressure drop and that it is isothermal since no information is given to the contrary:

The flow rate of A at any length along the PFR is the entering flow rate minus the amount converted:

Substituting both equations into the original gives:

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