I tend to assume everything is first order until proven otherwise by an overwhelming amount of data.  Then I also consider multiple first order kinetics that make the overall system appear to be greater than 1st order.

It is unusual to see the rate constant decrease with increase in temperature unless you are seeing an equilibrium effect or an anomaly caused by a poor data fit. 

The fact that temperature response is changing as you increase temperature probably means your model is incorrect or at least incomplete.  I would start by considering equilibrium limits and would try to  repeat some of the data points that show unusual behavior.

I guess your observations may be of poor quality and therefore your data fits are suggesting this counter-intuitive behaviour. In that respect I follow Rick.

Also, Ricks suggestion of determining the maximum sorption of the dye onto the wool will be helpful, especially since the rate of adsorption should be proportional to the amount of vacant sorption sites as well as the desorption rate being proportional to the covered sorptions sites.

In what way did you measure the kinetics exactly. Are you sure, that your experiments are conducted isothermally with respect to space and not only time? What model and fitting method did you use to find your parameters?

There are three possible approaches to this problem: (1) attempt to build the relatively

primitive model which is able to reflect basic features of the system; (2) try to construct a model

that is as similar as possible to the real material carefully studied by means of modern

experimental techniques; (3) in the simulation procedure, attempt to mimic the manufacturing

process used to produce the real adsorbent

read this book

with regards

Andre,

I measured the adsorption kinetics of cochineal dye onto wool fabric by first mordanting the fabric with 3 different mordants- Alum, Copper and Tin to see whether they produce statistically different parameters. After I had mordanted the fabrics I carried out the kinetic experiment for each mordanted fabric seperately at different temperatures. First I did at room temperature, for that I filled up a 600 mL beaker with 300 mL cochineal dye solution and placed it on the magnetic stirrer and then I started the stopwatch simultaneously while adding the mordanted wool fabric and measured the absorbance of the solution after every 30 seconds for 10 minutes in the spectrophotometer using cuvettes then I repeated the same procedure for higher temperatures using a water bath by placing the solution in the water bath, set at the appropriate temperature and manually stirring the solution.

To find the parameters, I used the Pseudo first-order rate quation which is:

ln(qe-qt)= -kt + ln(qe), where qe and qt are the adsorption capacities at equilibrium and time t and k is the pseudo firat order rate constant for the kinetic model. qt was calculated as (Co-Ct)*V/W, where V was the volume of the dye solution and W was the weight of the mordanted wool fabric and Co concentration at t=0 and Ct concentration at time=t, in order to calculate Co and Ct I had to convert absorbance into concentration. qe was found out by plotting a graph of qt versus t and was the maximum absorption capacity or the last data point where the graph flattens out. Then using the value of qe and qt I plotted the graph of ln(qe-qt) vs t to determine the rate constant. I repeated the same method for different temperatures. 

For Pseudo- second oder rate equation I used:

t/qt= 1/Vo + 1/qe (t) where Vo is calculated as Vo= k qe^2, so by plotting a graph of t/qt versus t I was able to determine the second order rate constant.

The fact that the 2nd order rate constant decreases with increasing temperature is a red flag that something is wrong with the model.  Does the apparent 2nd order rate constant decrease with temperature for all of your data points  or just  a few of them?

If all you want is a curve fit of the data that the second order model could be adequate for your use.  But it seems unlikely to me .that  a two molecule collision is required for adsorption and that the rate decreases with increasing temperature. 

You might also want to try 1.5 order kinetics to see if it is better than 1st or 2nd order. Another possibility is that you have 2 or more distinct types of adsorption sites.one that adsorbs quickly and another that adsorbs more slowly.  You have a few more variables to play with (relative amount of fast and slow site and ratio of kinetic rate constants and activation energies) to fit this data. 

Rick,

The second order rate constant decrease for most of the data points and increase for some. I also used one of the variable to fit the data which was activation energy. I plotted the graph of ln k versus 1/T, for the first order it gives me a nice linear line with a very high R^2 value but for the second order it gives me a very low R^2 value because if I conducted the kinetic experiment at room temperature, 55, 75 and 85 degree Celcius the rate constant will decrease for T=55, then slightly increase for 75 and then decrease for 85, which I really don't understand?

Aleeza,   Thanks for the clarification.  It looks to me like you have data that demonstrates that 1st order kinetics works well and that 2nd order kinetics has some hard to explain problems.  That is not surprising to me because it seems unlikely to me that adsorption of die onto wool is a second order reaction.  You probably should accept 1st order kinetics as the better model and move on - unless you want to explore other possible kinetic models. 

Aleeza

First and second order fitting are just simple correlations which may result some inconsistencies due to some simple things that you might have done in your calculations like adding or removing a data point. In order to make a better comparison you may take a look at literature related with this issue (what type of relations were used and how they changed with T). You may also plot your data against time and observe whether adsorption takes place faster or slower as you increase T. You also need to do a precision check ( calculate standard deviation for the numbers you are getting); you might obtain increasing numbers or decreasing numbers but when you take experimental error in to account they might turn out to be the same result.