I am studying the removal of So2 using CaCO3. My SO2 analyzer configuration is such that I can take SO2 readings at my reactor outlet once in 1 hr interval. So I ran my adsorption experiment for 5 hrs. At the end of 5 hrs the outlet concentration of SO2 was ~ equal to inlet concentration. I have readings of SO2 concentration at the outlet for every 1 hr. The caco3 in the reactor was not changed for the entire duration of 5 hrs.
So can someone explain how do I calculate qe and qt so as to draw a plot of ln(qe-qt)vs t. to check for PFO
AS the experiment reveals the concentration after five hours is equal for inlet and outlet it suggests that adsorbent is saturated and not capable of adsorbing further. The qt can be considered as the adsorption capacity calculated for the concentrations observed at 1, 2, 3, .... hours until you get the constant outlet concentration (Ce)(Obviously it should be less than the inlet concentration). the adsorption capacity estimated by using Ce is termed as qe and you can easily estimate the values for X and y axes. The above equation can also be modified in terms of concentrations to simplify the calculations.
I hope this is helpful to you.
Thanking you
Thanks sumit,
One thing is still not clear to me. The value of qt and qe will be same at the end of 5 hrs. so the value of ln(qe-qt) at 5 hrs is ln(0) which is undefined. so I am unable to fit a plot. Can you explain a bit more?
Dear Karthik,
You are correct, but I think there is an error in your experiments as you have to note down the time at which your adsorbent is saturated. If there is no provision to measure the concentration for lesser interval then you can consider the concentration measured at 4 hours to calculate the qe, if you can estimate the correct equilibrium concentration then that will give you the more accurate results from the plot.
Thanking you
Dear Karthik,
perhaps I misunderstand your question, but to check whether (or for how long) you have (pseudo) first-order kinetic removal of SO2, please plot the SO2 concentration as a function of time. First-order kinetics (or pseudo-first-order kinetics) should give a exponential decrease of the SO2 level with time. A simple way to see whether you have indeed a first-order decrease is to plot log[SO2] against time. This should give a straight line. If you do not see a linear decrease of log[SO2] with time the kinetics are not first-order.
In my answer I assumed you have a closed system. Is it closed, or do you have a supply of SO2 to the reactor?
best wishes
-pr
Dear Peter,
I have a continuous supply of SO2 to the reactor for the entire duration of 5 hrs.
Dear Karthik,
your system will go to a steady state. If inflow rate is k1 (or j1 and constant) and your pseudo-first-order removal rate constant is k2, your steady state concentration in SO2 is [SO2]ss=j1/k2=k1/k2.
The concentration of SO2 with time (under first-order removal conditions) should be:
[SO2]t-[SO2]ss=C*exp(-k2*t), where C is a constant. Taking the log of this equation gives
log ( [SO2]t-[SO2]ss ) = log ( C ) - k2*t
If you plot this and have a linear slope you have first-order removal with respect to SO2, but when t becomes large then [SO2]t -> [SO2]ss and you can't do the log-plot, because, as you wrote, you get log ( [SO2]t-[SO2]ss ) ≈ 0.
best wishes
-peter
You use the term “pseudo”, then, I guess, you assume the impact of mass transport phenomena on the overall process rate.
You also use correctly, the term “first-order” with respect to the reaction.
On the basis of the area under the line cin - cout (t) and constant, I assume, (molar mass or volume) flow rate you can, of course, determine the amount of adsorbed SO2.
But this is not enough information to determine whether you are dealing with the kinetic equation in the form r = k c, which corresponds to the reaction of the first order (pseudo first order). To see this, you should perform experiment for several concentrations of SO2 in the inlet and establish that the measurement points (X, t) form one line described by the equation X = 1 - exp (-kt). You should also shorten the time of sampling.
X - the current amount of adsorbed SO2/the total amount of adsorbed SO2, cin - constant concentration of SO2 in the inlet cout (t) time-dependent concentration of SO2 in the outlet, k – rate constant.
Asif Ayub, I wonder if you got acquainted with these two demos of commercial software. If so, you should be aware of the biased selection of kinetic data for the only “true” thesis that “PSO is the best”. It is the same situation as in the case of the works by Ho and McKay from 1998 and 1999, on which the authors of the software were probably based. The trash can seems to be the best place for both demos.
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