[garry123]

Hello forum members,

I have a doubt with the following question:

The surface tension of the non-ionic surfactant was measured at 25°C as a function of concentration with following results:

(concentration) 10^3 c/g dm^-3                Surface tension- mNm^-1


0.583                                                       61.1
1.77                                                         50.2
5.40                                                         43.2
13.8                                                         35.3
29.9                                                         32.1
54.4                                                         31.6
108.0                                                       31.7               
233.4                                                       31.6               
651.8                                                        32.1
1534                                                         31.6

Estimate the CMC.

As far as i know, the plot of surface tension versus ln c gives you the CMC.....i tried to plot it using excel, but since we also have negative log for the value 0.583 of concentration, i cannot get the answer.

I have this equation as well:

Γ = -c/RT (dγ/dc) at const temperature....please please please help me with this...this problem is eating my head...i ll be reALLY THANKFUL...

[Borek]

Please describe the procedure you should follow and explain why negative log value makes it impossible.

[garry123]

i am sorry, i didnt get you...this is the only data i have...i tried a lot, but i coudnt solve it....could you please guide me how to start on....i really apologise that i wont be able to answer any of your questions....i hope if you guide me, i can proceed with the solution and may be then understand....

[garry123]

Zero is an infinite distance way down past the bottom of
the chart, and negative numbers are "beyond infinity".

thats y negative log is not possible...i guess so...

[Borek]

Have you tried to simply make a plot of the surface tension vs log(c)?

Can't say I know anything about CNC, but just looking at the plot it is obvious it has a very characteristic point, easy to spot.

[garry123]

yes...i did plot it with the help of excel....then, when i add the trend lines choosing logarithmic plot, it says its impossible as i have a negative value on the x-axis...i am just asking you if you can give me an equation to solve CMC....its relationship with surface tension and concentration...

[garry123]

if any1 is reading then pls help me..

[Borek]

I can't give you an equation as I don't know one. Seems to me like your problem is that you don't understand the basic math behind the solution, which makes you hopelessly lost when Excel refuses to solve the problem for you.

when i add the trend lines choosing logarithmic plot, it says its impossible as i have a negative value on the x-axis...

Could be we are finally getting somewhere. Sounds like you are trying to calculate logarithm twice. You calculated logarithm of the concentration and THEN tried to calculate a logarithmic trend line. Don't. Once you have calculated logarithm you need a normal trend line, logarithmic trend line is what you need BEFORE you calculate logarithms, as first step in finding logarithmic trend line is calculation of a logarithm.

[garry123]

thanks...ok...wat i now did is that i plotted a graph of surface tension and ln c.....i get a curve which shows that initially surface tension decreases with increase in concentration...then we have CMC and then the surface tension remains constant....

fine...as u said, since i already have a log function on my graph, i tool linear for the trend line...
this is the equation i get:

y= -3.4643x+50.411...

but CMC= 3*10^-4 g dm^-3

[garry123]

what i mean is that the value of CMC that i wrote above is the actual answer...how do i get this value of CMC....as u said, i plotted surface tension and ln c...and used a normal trend line...

[Borek]

I am just guessing here, as I have never done this kind of experiment. You can't use all data for teh trend line, there are two distinct parts of the curve. CMC is where the relationship between concentration and tension changes from "no dependence" to "logarithmic dependence".

You were not told what is the correct procedure of determining CMC? There were no lecture on that? You have no book?

[DrCMS]

As far as i know, the plot of surface tension versus ln c gives you the CMC....

Yes it does but not in the way your are trying to do it.

What does the CMC mean?

What do surfactant molecules do below the CMC do and what do they do above the CMC? 

How will those two different situations effect the surface tension?

[garry123]

As far as i know, the plot of surface tension versus ln c gives you the CMC....

Yes it does but not in the way your are trying to do it.

What does the CMC mean?

What do surfactant molecules do below the CMC do and what do they do above the CMC? 

How will those two different situations effect the surface tension?

well, when we plot the graph of surface tension against ln c, we get to see three regions in the line...the 1st region which is linear, meaning that the surface tension decreases linearly with increase in concentration....then there is a point where micelle formation takes place and finally the line becomes straight which means that the surface tension more or less becomes constant on further increase in concentration...

[DrCMS]

As far as i know, the plot of surface tension versus ln c gives you the CMC....

Yes it does but not in the way your are trying to do it.

What does the CMC mean?

What do surfactant molecules do below the CMC do and what do they do above the CMC? 

How will those two different situations effect the surface tension?

well, when we plot the graph of surface tension against ln c, we get to see three regions in the line...the 1st region which is linear, meaning that the surface tension decreases linearly with increase in concentration....then there is a point where micelle formation takes place and finally the line becomes straight which means that the surface tension more or less becomes constant on further increase in concentration...

That doesn't quite answer the questions I gave up but is close.

Below the CMC some surfactant molecules will migrate to the surface and reduce the surface tension.

Once the surface has a single layer of surfactant the extra surfactant starts to form micelles. 

After that point any extra surfactant added will on longer reduce the surface tension.

The intercept of the first part of your graph with the final section is the CMC.