[titanium]

Hi,

I have the following rate data from a kinetics of aqueous decomposition of A -> products investigated in a mixed flow reactor:

-rA (M/sec)     CA (M)
0.0235           0.06
0.0391           0.1
0.075             0.2
0.132             0.5
0.124             1.2
0.089              2

I have to find a rate law which is likely to fit the data.

My working:
A plot of -rA vs. CA gives a parabola with a maxmimum point. (Plot is attached)This suggests that no simple rate expression will fit the data. So, I figured out that there is a positive slope at low concentration of A. This suggests that at low concentration of A, the reaction is first order. However, at high concentration of A from the plot, the slope is a straight line but with a negative gradient. Hence, I am not sure what order is the reaction at high concentration of A. Can anyone please enlighten me?

I am trying to figure out the reaction orders at both high and low concentration ends, so that I can propose something similar to the Michaelis-Menton kinetics where power law kinetics are approximations at the extreme ends of the concentration.

Thank you.

[eugenedakin]

Hi titanium,

You are correct in the assumption that the reaction rate is like a Michaelis-Menton kinetic.

Instead of working with the fluctuation in reaction rate, why not attempt to determine a substrate concentration? See the following graph at this link http://en.wikipedia.org/wiki/Michaelis-Menton.

I am curious, is this reaction rate for a batch or continuous?

I hope this helps.

Sincerely,

Eugene

[titanium]

Dear Eugene,

The plot which is attached with the first post is indeed a reaction rate (-rA) vs. concentration of A (substrate) graph.

The graph is similar to the M-M plot, as at low concentration of substrate, the reaction is first order. Ar high substrate concentration for the MM plot, the slope is zero which implies zero order. However, at high concentration for my plot which is attched, the slope has a negative gradient. Thus, I am not sure to what order is the reaction rate at high concentration of A.

Thank you for your help.

[naren.iitr]

Hello Titanium
Your problem seems to be of substrate inhibition. Consider the following rate equation.
A reaction may obey an equation of the following form

    (-rA) = V'*S/(K'm+S+S²/Ki)

in which the constants V', K'm and Ki are used for illustration without any implication of universal or standard definitions. If Ki is large compared with Km the behaviour predicted by Eqn will approximate to that predicted by Michaelis-Menten equation, with V and Km replaced by V' and K'm, in the lower range of substrate concentrations. However, with above Eqn the rate passes through a maximum as the concentration increases, and there is said to be inhibition by substrate, and the constant Ki, which has the dimensions of a concentration, is called the substrate inhibition constant.
 As far as solutin is concerned, it beatifully fits your data.
V' = 8.797334, K'm = 21.96526 and Ki = 0.023025
I hope it will be helpful to you.

[titanium]

Dear naren.iitr,

Thank you so much!

Best regards,

titanium