FC, Sunlight, CYA relationship

[sbcpool]

I did a little searching for something to quantify the relationship between CYA, sunlight, and FC loss. In my pool so far it seems to be loosely following something along the lines of:

FC² ÷ (10 x CYA) = PPM FC lost per hour direct sunlight

Do other people see a similar relationship, or better yet have a better equation?

 

[JVTrain]

One of my favorite chem geek posts to check out here: Pool Water Chemistry has a lot of description on the topic and some great graphs to put it in perspective. Not sure why it's not a sticky.

 

[chem geek]

If you maintain the pH, then that equation is not correct. For a constant CYA level, the loss in sunlight is proportional to the FC level. So you see a constant percentage FC loss. What you are seeing that has you think there is a power of 2 on the FC is that if you SLAM the pool or otherwise elevate the FC using a hypochlorite source of chlorine, then the pH rises and that produces much more hypochlorite ion compared to hypochlorous acid in the pool water. The half-life of hypochlorite ion in noontime sunlight is only 20 minutes while for hypochlorous acid it is 2 hours and 10 minutes. At a pH of 7.5 with a 50/50 mix of the two, the half-life is around 35 minutes (this is at the surface of the water and ignoring CYA shielding effects).

I've measured the FC drop in my pool after raising the FC to around 20% of the CYA level and then seeing it drop day to day. With 50 ppm Borates in the water, my pH didn't change very much from the addition or subsequent drop and I have noticed a consistent percentage loss day to day. However, this is with the pool covered most of the day except for an hour or so each day. Others on this forum seem to also report FC percentage drops except, as I wrote, when they elevate the FC a lot as with a SLAM in which case the pH rises significantly so an increased loss rate would be expected.

So I think the equation that should be used should be of the form where the d(FC)/dt = FC * f(CYA, pH, temp) so that the absolute FC loss is proportional to the FC level when CYA and pH and temperature are held constant. Another way to put this is that the percentage FC loss is a function of those factors so %FCloss/dt = f(CYA, pH, temp).

We know that the loss rate due to temperature is roughly doubled for every 13ºF of temperature. I can also calculate the pH effect for the loss from hypochlorite ion and hypochlorous acid. What I don't have good data for is the loss rate from CYA and its CYA (or CYA-Cl) shielding effect. The closest I have to that is an estimate for SWG pools in the table in this post. That table intentionally has the same FC/CYA ratio for most of its entries so the loss from unbound CYA should be constant for all of them. It shows the CYA shielding effect because any loss rate associated with chlorine bound to CYA (which is most of FC) should have loss rates increase but instead one sees them decrease at higher CYA levels even with proportionally higher FC levels. So the loss rate formula should have CYA in the denominator at some higher power.

At the 5% FC/CYA ratio in the table and at a pH of 7.5 the absolute FC loss rate of hypochlorous acid and hypochlorite ion with no CYA shielding effect would be 118% of the unbound FC per hour and the unbound FC is 0.041 so that is 0.048 ppm FC per hour or over 8 hours of noontime equivalent sun that would be 0.38 ppm FC per day. Clearly most of the FC loss is not coming from the unbound chlorine. The amount of bound chlorine is close to the FC level (around 99% of the FC level at FC 4 ppm with CYA 80 ppm). If I sum the 0.04 with a presumed bound chlorine loss (subtracting out 0.04 from the 0.15 total) and then divide by CYAⁿ, I get an "n" of 1.6 but remember that the table is a very rough approximation of what is seen and is not carefully measured from experiment.

So that table's FC loss/hr is very roughly close to (80*FC/CYA + 10*FC) / (CYA^1.6)

The formula is of the form (unbound chlorine loss + bound chlorine loss) / (CYA shielding effect). The "80" will be a function of pH and FC/CYA ratio (it can be calculated from my Pool Equations spreadsheet and knowing the relative loss rates in sunlight of hypochlorous acid and hypochlorite ion) and will be higher at higher pH while both the "80" and the "10" will depend on temperature and amount of sunlight. As described in this post the CYA shielding effect is more likely to be an exponential function of water depth rather than the simple power function shown above but the power function approximates the behavior for average pool depth. Note that the formula only works in the normal ranges of FC/CYA ratios and would not be correct at high FC/CYA ratios approaching a SLAM or a pool with little or no CYA.

How does this fit with your data? If you have pH data then we can calculate the fixed unbound chlorine loss factor.

 

[sbcpool]

If you maintain the pH, then that equation is not correct. For a constant CYA level, the loss in sunlight is proportional to the FC level. So you see a constant percentage FC loss.

I'm not seeing that. When my FC is around 8 I loose about 2.0 - 2.5 ppm during the day. When it's 20 ppm I loose about 8 - 9 ppm during the day. pH remains at ~7.4 and CYA at 40.

 

[chem geek]

How did you raise the FC from 8 to 20 ppm? Did you add chlorinating liquid or bleach (or Cal-Hypo or lithium hypochlorite)? If so, then with 80 ppm TA the pH would rise from 7.4 to 8.1 when adding the hypochlorite source of chlorine (if you had 50 ppm Borates then the pH would rise to 7.7). The pH would not stay the same. Chlorinating liquid or bleach is high in pH and it is only pH neutral AFTER the chlorine is used/consumed since that process is acidic. So did you test and see the pH being high and added acid to lower it? You can't usually reliably test pH when the FC is significantly above 10 ppm though usually it would read falsely high not low.

The amount of hypochlorite ion increases from 0.089 to 1.602 due to the additional chlorine and the pH rise. The amount of hypochlorous acid increases from 0.105 to 0.380. This is because CYA is a hypochlorous acid buffer resisting changes in its concentration so when CYA is present addition of hypochlorite has the pH rise more than when CYA is not present. If I ignore CYA shielding effects and only look at unbound chlorine the loss would go from 2.04*0.089 + 0.317*0.105 = 0.215 ppm FC/hour to 2.04*1.602 + 0.317*0.380 = 3.39 ppm FC/hour. CYA shielding would reduce these amounts but would add losses from FC bound to CYA. So the larger increase you saw would be readily explained if the pH were higher due to adding a hypochlorite source of chlorine.

 

[sbcpool]

How did you raise the FC from 8 to 20 ppm?

Liquid chlorine tested to be ~17%.

So did you test and see the pH being high and added acid to lower it? You can't usually reliably test pH when the FC is significantly above 10 ppm though usually it would read falsely high not low.

I neutralized the FC with H2O2 prior to testing pH.

 

[chem geek]

I neutralized the FC with H2O2 prior to testing pH.

That doesn't work to get you the correct pH. The neutralizing of chlorine with hydrogen peroxide lowers the pH. So while it gets rid of chlorine that could oxidize the pH indicator dye, it changes the pH you are trying to measure.

HOCl + H⁺ + 2e^- ---> Cl^- + H₂O
H₂O₂ ---> O₂(g) + 2H⁺ + 2e^-
------------------------------------------------
H₂O₂ + HOCl ---> O₂(g) + H⁺ + Cl^- + H₂O
Hydrogen Peroxide + Hypochlorous Acid ---> Oxygen Gas + Hydrogen Ion + Chloride Ion + Water

So with hydrogen peroxide, it ends up lowering the pH when it neutralizes chlorine. This is why you measured the same pH at the two FC levels because you just got back to where you started in pH.

This is why Taylor pH reagents contains a proprietary blend of chlorine neutralizers that in combination do not significantly alter the pH, at least up to an FC of 10 ppm. Your pH reading was completely bogus in terms of the original pH at the higher FC which was probably as high as I indicated. Why did you think you could use hydrogen peroxide to neutralize the chlorine before doing the pH test? We tell people that they can't use sodium thiosulfate (R-0007) for the same reason. The following shows why showing the most likely thiosulfate reaction to occur at pool pH (there are 4 different thiosulfate reactions that can occur):

2S₂O₃^2- + HOCl ---> S₄O₆^2- + OH^- + Cl^-

So with thiosulfate the most likely result is that it ends up raising the pH when it neutralizes chlorine.

 

[sbcpool]

Why did you think you could use hydrogen peroxide to neutralize the chlorine before doing the pH test?

NaClO + H₂O ---> HOCl + NaOH

H₂O₂ + HOCl + NaOH ---> NaCl + 2H₂O + O₂

 

[chem geek]

NaClO + H₂O ---> HOCl + NaOH

H₂O₂ + HOCl + NaOH ---> NaCl + 2H₂O + O₂

Yes but what you show just says you are getting back to the same pH you started with BEFORE you added chlorine. After you add chlorine in the first reaction above, you can see that it raises the pH (NaOH is lye, OH^- raises pH) though not all of the hypochlorite becomes hypochlorous acid. You want to measure the pH after the first reaction. The second reaction neutralizing the chlorine just gets you back where you started and you can see that it lowers pH because it consumes OH^- (in NaOH). The net of the two reactions you wrote above is the following:

NaClO + H₂O₂ ---> NaCl + H₂O + O₂

So neutralizing hypochlorite itself is pH neutral. The problem is that when you added the hypochlorite to the water the pH ROSE because some hypochorite became hypochorous acid which consumed hydrogen ions (or equivalently produced hydroxyl ions as you wrote). It is THAT pH that you want to measure -- the pH when chlorine is in the water. This is because the amount of hypochlorite ion vs. hypochlorous acid is dependent on the pH so you want to measure the pH in the water after chlorine has been added. You do not want to measure the pH after CHANGING the pH which is what adding hydrogen peroxide does because it lowers the pH when it neutralizes hypochlorous acid (it does not change pH when neutralizing hypochlorite ion).

 

[sbcpool]

It is THAT pH that you want to measure -- the pH when chlorine is in the water

Well, that's a conundrum for a dye-based test isn't it? I have an old Pinpoint pH probe, but the probe itself is long gone. I'm not sure I want to spend $60 for a new one just to find out Perhaps I can just dilute the sample and calculate the pH from the result. Diluting it by 50% will only have a small effect on a log scale.

 

[chem geek]

Yes, the safest way in a chemical pH test to measure pH when the FC is high is to dilute your water sample using distilled or deionized water. You can't use tap water or filtered water because the water must be unbuffered for the dilution to work properly.

The dilution with unbuffered water does not appreciably change the pH because the buffering of the original water sample prevents that. The amount of buffering is cut in half (if you do a 50/50 dilution) but that doesn't change the pH by any measurable amount. It's not the log scale that saves you because if you did in fact cut down the hydrogen ion concentration in half (i.e. if your original water sample did not have pH buffers in it) then that would change the pH by 0.3 units since log₁₀(1/2) = -0.3. For example, diluting full-strength Muriatic Acid (31.45% Hydrochloric Acid) 50/50 with distilled water changes its pH from -1.0 to -0.7. Diluting to 1/10th changes the pH from -1.0 to 0.0. You could dilute with tap water in the case of this strong acid because the tap water pH buffers will get exhausted with only a small amount of the acid used up.

 

[sbcpool]

Thanks

 

[chem geek]

pH = log₁₀( (10^-pH1 + 10^-pH2) / 2)

What you wrote only works for unbuffered water. It does not work for buffered water and pool water is significantly buffered with carbonates (and also cyanurates when CYA is present and borates when they are present). My Pool Equations spreadsheet does all of the calculations so if you use your hydrogen peroxide technique you can back-calculate what the original pH must have been by adding that chlorine in the spreadsheet and you'll see the pH rise. You need to have accurate values for TA, CYA and borates in order for this to calculate properly.

The reason the formula does not work with buffered water is that the hydrogen ions are largely stored in reserve in the pH buffer so changes from dilution or from acid or base addition are largely moderated where the pH buffer chemical absorbs or releases hydrogen ions in an attempt to keep the pH stable. This comes from equilibrium chemistry such as the following:

K = [HCO₃^-] * [H⁺] / [H₂CO₃]

where you can see that with large bicarbonate and carbonic acid (includes carbon dioxide) and a small hydrogen ion concentration (by comparison) means that additions or removal of hydrogen ion result in replenishment via the following equilibrium:

H₂CO₃ <---> HCO₃^- + H⁺

So to keep the equilibrium ratio constant, the H⁺ doesn't move much and instead most of the H⁺ added/removed/diluted is added or removed from carbonic acid / bicarbonate. Water dilution may cut down carbonic acid and bicarbonate concentrations each in half, but they are still much larger than the hydrogen ion concentration so still perform their pH buffering. This post and this post show the effects of some chemical addition on the pH buffer system though I didn't show any example of straight water dilution, but you can see from the above formula that if I cut down both carbonic acid and bicarbonate in half then their ratio is unchanged. The hydrogen ion gets cut in half, but that is then changed as follows where I use water with a TA of 80 ppm and no CYA for simplicity and pH 7.5.

.......................................... /2 ............. re-equilibrate
[H₂CO₃] 103.16 µM -------> 51.58 ---------> 51.734
[HCO₃^-] . 15.926 µM -------> 7.963 ---------> 7.9616
[CO₃^2-] ... 2.8142 µM ------> 1.4071 --------> 1.3877
[H⁺] ....... 0.033027 µM ----> 0.0165135 ---> 0.032795 (pH 7.50096)

So you can see that to get back to equilibrium it only takes very small changes in carbonic acid, bicarbonate, and carbonate to bring the pH back to almost where it was before. If you calculate the equilibrium constant from the above, you'll notice it changes slightly and that is due to changes in ionic strength but has nothing to do with the main point of pH buffering.

 

[sbcpool]

Sorry. I edited my post before you replied to it.

 

[hokiemo]

My head hurts now!