Final answer:
The formula for percent reaction (%R) based on free vortex and constant reaction velocity profiles are derived and compared. The pros and cons of each method are assessed.
Step-by-step explanation:
The formula for percent reaction (%R) based on free vortex can be derived using the equation:
%R = 100 - (Q/Q0) * 100
where Q is the reaction rate at a given time interval, and Q0 is the initial reaction rate.
The formula for percent reaction based on a constant reaction velocity profile can be derived as:
%R = ((Vf - V0) / Vf) * 100
where Vf is the final volume of the reaction mixture, and V0 is the initial volume.
The formula based on free vortex takes into account the change in reaction rate over time, while the formula based on a constant reaction velocity profile assumes a constant reaction rate throughout the reaction. The pros of the free vortex method is that it allows for more accurate measurement of reaction progress, while the constant reaction velocity profile method is simpler to use and interpret.