If you have experimental data you can fit the mass balance of A, B and AB to the experimental data to fit the unknown parameters. If I understand your system, the equations of the model would be something like:

dCA/dt = kLa *(CAx-CA) - kd*CA*CB + ki*CAB

dCB/dt =  - kd*CA*CB + ki*CAB

dCAB/dt =  kd*CA*CB - ki*CAB

Equilibrium constant is K = kd/ki

In the steady state CA will be equal to the saturation concentration CAx and then I agree you can calculate the equilibrium constant. If you want to know kd, ki and kLa you should fit the model to the experimental data modifying these parameters.

One warning: depending on the type of data the parameters may not be identifiable (multiple parameter values able to describe the experimental data.

There is no relation between equilibrium constant and reaction rate.

These are quantities related to chemical thermodynamics (equilibrium) and chemical kinetics (reaction rate), they are not related. You can calculate the rate of reaction by knowing the change in mass of the substance with time

Thank you Mr. Nadirov and Abbas.

But how to determine the change in mass of the substance with time in case of very fast reactions? 

You have to use Insitu detection  technique whose response is much faster than the mass change rate. 

If you have experimental data you can fit the mass balance of A, B and AB to the experimental data to fit the unknown parameters. If I understand your system, the equations of the model would be something like:

dCA/dt = kLa *(CAx-CA) - kd*CA*CB + ki*CAB

dCB/dt =  - kd*CA*CB + ki*CAB

dCAB/dt =  kd*CA*CB - ki*CAB

Equilibrium constant is K = kd/ki

In the steady state CA will be equal to the saturation concentration CAx and then I agree you can calculate the equilibrium constant. If you want to know kd, ki and kLa you should fit the model to the experimental data modifying these parameters.

One warning: depending on the type of data the parameters may not be identifiable (multiple parameter values able to describe the experimental data.

For relating equilibrium constant with rate of reaction, the following can be done:

Write the balanced equation for the reaction taking place. Now, relate equilibrium constant with conversion data (like, after time = 't' seconds, the conc./ p.p. of the reactants). Depending on reaction stoichiometry, you might get a polynomial expression in X (conversion). Solve for this X.

Next, use this value of obtained X, and using the design equation for the agitated vessel, and knowing other parameters, such as molar flow rate and volume of the vessel, you can determine the rate of the reaction.

You can also determine the reaction rate constant from here.

Experts let me know, if what I'm suggesting is right or wrong.

If you cannot easily measure the mass change of each species, you can try to measure the heat flow from the reaction. This may give you more correct information on the reaction rate change from the commencement to the equilibrium.

Atul, I don't understand exactly the procedure you propose, I think that there is no need to fit any polynomial. In any case, with this procedure you are not taking into account mass transfer as in the problem proposed by B. Chandrashekhar. The mass balances I proposed in the previous post are the general unsteady state equations considering kinetics as an elementary reaction. If the kinetics is different it should be modified accordingly. The kinetics that provides best model fit should be the one selected.

I am sorry but the experiment was described not understandable. Is the gas pressure constant during all time of reaction or decreasing takes place? . In the first case you must use the analysis of [B] by using anyone method.  Second case is more easier- put anyone pressure sensor in your tank and measure decreasing of [A] pressure during time and calculate derivative.dP/dt

 Best regards

Dr. Mnatsakanyan

Thank you for you the response. I am sorry you could not understand the system. Actually, I want to use a CSTR (agitated tank) for gas liquid absorption. The volume of the liquid in the tank is constant with constant reactant [B]. I can continuously pass the gas having constant [A] into the tank. So, there is continuous inlet and outlet of the gas, and the liquid is in batch bode. Please note that neither A nor B gets destroyed during the reaction. The reaction between A and B is an equimolar coupling reaction and is reversible, so

A + B AB 

The analysis of [B] or [AB] at different time intervals is difficult in my system.  What I can analyze, is the outlet gas concentration [A] with respect to time using a sensor. As the liquid gets saturated with [AB], the outlet [A] increases with time till it becomes constant (i.e equilibrium state). 

Using the outlet [A] vs time curve, I can calculate the following-

1. the total  amount of A passed during the reaction time (F x [A] x t]

2. the amount of 'A' reacted with 'B' i.e [AB] (total A passed minus area under the curve)

3. the amount of unreacted [B] (difference between total [B] and [AB]).

The amount of unreacted A present in the liquid phase can be obtained from its solubility data. 

Using the above terms, we can calculate the equilibrium constant. 

As suggested by you, I cannot use pressure sensor as the pp of A in the gas phase is very small and the change in pressure of the head space is too small to be monitored accurately. 

Can I calculate the rate of reaction using this data ? 

Thank you for your time. 

HI

You can carry out experiments under static conditions. First, put a pressure manometer  into the reactor. Let the gas above the liquid at an initial pressure of A (0), then wait for the system to come to equilibrium and measure the residual pressure of A (t). If you know your stochiometry of your  complex, there is no problem to calculate the constants. On a reaction constant. firstly you must to show that interaction of A and B is the limited step but not diffusion of A from gas to the surface of liquid  or  in liquid to B

 Best regards

Dr. Mnatsakanyan

Thankyou for the help. 

Best Regards.

Further to this question, how do we calculate the individual mass transfer coefficients when the system is reactive in nature ? Especially I want to know about the gas-side mass transfer coefficient.  

Hi

Can you please find the attached image that shows the equation I used during the calculation of reaction rate of conversion of butene

Have a very good day and best of luck