# Logarithmic Decay of Hypochlorite/Chlorine by UV light

1. Aug 18, 2012

### jaamae

Hi,

Does anyone know why the decay of hypochlorite/free chlorine in pool water due to UV light might show a logarithmic decay (natural log) as opposed to an exponential one?

I did a chemistry experiment with scaled up concentrations of chlorine and cyanuric acid (scaled up 25x). Even in the solution with no cyanuric acid it still shows logarithmic decay.

Analysis was by titration. Excess potassium iodide and sulpuric acid was added and then it was titrated with sodium thiosulphate.

I'm wondering because ALL secondary data I have found shows a logarithmic decay.

With thanks,

Jaamae.

2. Aug 19, 2012

### Staff: Mentor

Please elaborate on how did you get to the conclusion it is logarithmic.

3. Aug 19, 2012

### jaamae

I plotted the results as a graph in Excel and the logarithmic trendline option fits best.

Thanks,

Jaamae.

4. Aug 19, 2012

### Staff: Mentor

On how many points of data?

And what have you plotted against what? If $C=C_0e^{-kt}$ you will get a perfect linear plot for $\ln{C}=\ln{C_0}-kt$, but it doesn't mean trend is logarithmic.

5. Aug 19, 2012

### jaamae

Hi,

I plotted amount of thiosulfate added (which is directly proportional to concentration of chlorine left) (y axis) against time (x axis).

I have attached the data. Sheet 1 shows the data with a logarithmic trendline fitted to it. Sheet 2 shows the same data with exponential trendlines fitted to it.
As you can see the R^2 values for logarithmic are much better.

With thanks,

Jaamae.

6. Aug 19, 2012

### jaamae

Woops forgot to attach :)

#### Attached Files:

• ###### chem data2.xls
File size:
89.5 KB
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7. Aug 19, 2012

### Staff: Mentor

I have a feeling errors are way too large for any meaningful result.

8. Aug 19, 2012

### jaamae

OK, but can you think of any reason a logarithmic trendline fits better?

9. Aug 19, 2012

### Staff: Mentor

By pure chance.

10. Aug 19, 2012

### jaamae

But it fits noticably better on most of them. If we take out 1500 and 2500 (procedural anomalies) then its definitely fits better. I have a feeling there is a reason buried in the chemistry somewhere.

11. Aug 19, 2012

### morrobay

Since exponential and logarithmic curves are inverses of each other.
Is it possible that you have exponential decay but your titration would be a
logarithmic curve ?
You can check this with: dm/dt = - km
with solution y(t) = y0e-kt
Solve for k : 1/[Chlorine] = ekt
And data check decay curve

Last edited: Aug 20, 2012
12. Aug 20, 2012

### jaamae

Hi Morrobay,

Thanks for your reply. But could you please explain the bit about a logarithmic titration a bit more. Also what does 'm' represent in your equations?

Thanks very much,

Jaamae.

13. Aug 20, 2012

### morrobay

m = [chlorine]

see these pages : https://www.physicsforums.com/showthread.php?t=291766 [Broken]

note: I had a question mark on whether the titration curve could be logarithmic.
Maybe you should plot this experiment from a decay curve, see reference

Last edited by a moderator: May 6, 2017
14. Aug 21, 2012

### chemisttree

How did you expose your sample to UV radiation? Describe the reaction setup.
Did you calculate the quantum yield for Cl2 vs. concentration? The quantum yield can vary from 2 to 4.5 for concentrations of 500 ppm and 1500 ppm respectively. Quantum yield of concentrations less than 100 ppm are ~1.0

Last edited: Aug 21, 2012
15. Aug 21, 2012

### jaamae

Hi,

Firstly thanks very much for your reply. The setup was a commercial UV light mounted above a shelf. The beakers (with different trials in them) were placed under it for 3 hours. Ever 30 mins a 20mL sample was removed and titrated to find the hypochlorite content.

How does one calculate quantum yield? Keep in mind the varying ppm in the excel data is the Cyanuric Acid, which was a test variable. The original chlorine solution was made to be 100ppm. Please elaborate on how to calculate the quantum yield as I am very interested. Thanks very much for your help.

Jaamae.

16. Aug 21, 2012

### chemisttree

17. Aug 22, 2012

### morrobay

So is it correct to conclude that this photolysis is exponential decay:
-d[A]/dt = k[A] and as Borek said in post #4 it is linearized to :
ln [A]t = ln [A]0 -kt

18. Aug 23, 2012

### chemisttree

Yes, this is what the OP expected but it is usually written as d[A]/dt = -k[A]. OP found that when concentration is plotted vs -k*ln(t) + C there is a better fit than when remaining concentration is plotted vs C1e-kt+ C2.

I'm not going to analyze and replot the data so I won't comment as to why OP gets these results. I thought that perhaps a change in the quantum efficiency during the experiment might affect the best-fit curve enough to skew the results.