Urinating in the swimming pool - how bad is it? Putting concentration in context

[Image credit: Vecteezy]

A few years ago there was a bit of an uproar when the Olympic champion swimmer Michael Phelps confessed that he urinated in the swimming pool.  (I say 'confessed', although it wasn't like he was in police custody or anything).  Phelps's response was similar to mine at the time, which was that I reckon most people do this from time to time.  However, what is the reality of this in terms of risks to public health, or simply in the context of being an unsavoury thing to do?  Can we use some simple science and maths to help us decide whether it's socially acceptable or not?

This is the basis of a context-based activity related to the concept of the concentration of solutions.  Concentration can be a tricky concept for children to understand.  Partly, I'd suggest, this can be because it is abstract and as with most abstract concepts, we all need something concrete or familiar to relate it to.  Perhaps if urine had a much darker colour, such that the gradual darkening of swimming pool water might be measurable, it would be easier to conceptualise concentration.  But equally, were this the case, perhaps people wouldn't do it.  

What follows is a calculation of the concentration of urea, the main urine component (other than water) in swimming pool water, and a comparison to UK limits on the presence of pollutants in drinking water.  Actually you could dispense with the calculation if you are just teaching the qualitative aspects of the concept, and simply use this as an interesting context for introducing concentration.  What it also raises is the inherent difficulty in answering scientific questions because of uncertainty and variability.  

The context in more detail

Urine is a solution, and in terms of its composition the vast majority of it is just water.  The main purpose of urination is to remove the metabolite urea, formed when the body breaks down amino acids in proteins.  Urine can be regarded as a solution of urea, but it does contain other substances too, some of which are simply passed through the body from food and drink, unchanged.  One such substance is the artificial sweetener, Acesulfame K.  This substance would not normally be found in swimming pool water, and hence its presence is a sure indication someone who has ingested this substance has urinated in the pool.  It can, as such, be used as a 'marker' for urination.  (See cen.acs.org/articles/95/i11/Sweetener-track-pee-pool.html)

When someone urinates in a swimming pool it is essentially a process of diluting a solution.  Before the urine mixes with the swimming pool water it has a certain concentration with respect to the various dissolved substances it contains.  After it has mixed with the swimming pool water we now have the same solution but much less concentrated.  (This is somewhat simplified; swimming pool water is itself a solution of various things so we are really mixing two solutions, but for the purposes of clarity we'll just imagine we have a pristine tank of pure water to begin with, into which we are mixing urine).

While we are considering the detail, there is actually some chemistry to take account of in all of this, which is that urinating in the pool does not just produce a more dilute urine solution - there are reactions which occur between substances in urine and substances added to swimming pool water for hygiene purposes, and these lead to by-products which would not otherwise be there.  We're not considering this in the following calculation. 

Data to use in the calculation

As in most calculations like this, we have to make some assumptions and generalisations.  This is so we  can use some actual figures to arrive at an answer.  The answer will, inevitably, be an approximation.  This does not diminish its worth.  It is just that we're dealing with things that vary, like the size of swimming pools and the amount of urine passed by different people.

In the calculation we'll use the unit g/L for concentration, as this is the predominant unit found when public data on concentrations are made available (as opposed to mol/L which chemists tend to favour). 

Nominal volume of urine released during urination = 0.2 litres (L)

Nominal concentration of urine with respect to urea = 9.3g/L

Size of an Olympic swimming pool = 2,500,000 L

Calculation

Mass of urea passed each urination  = 9.3 g/L x 0.2 L = 1.86 g

Concentration urea solution after mixing in pool = Mass / Volume

 = 1.86 / 2,500,000

= 7.44 x 10^-7 g/L

= 0.744 ug/L

This figure is a bit meaningless by itself, but if we compare it to the acceptable limits on substances in drinking water, we get some standard of comparison.

Discussion

What we do have to take into account is that our calculation, above, was for one person urinating once in the pool.  How many people would realistically urinate in the pool over the duration that the water is kept in it?  This is a difficult figure to estimate and will have a high degree of uncertainty because there are so many variables.  However, it is possible to perform a rough calculation to get a ball-park figure.  

According to www.ehow.co.uk/info_8660665_do-change-water-pools.html   swimming pool water is changed every 3-5 years.  How many visitors might it have over this time?  This will obviously vary enormously from place to place, but a figure of 21,700 visitors to Barnsley's newly re-furbished pool over the Easter holiday fortnight in 2012 (www.wearebarnsley.com/news/707/calypso-cove-records-record-results) would suggest for a busy pool it will definitely be in the hundreds of thousands.  How many of them would urinate in the pool?  That's anyone's guess, but even if it's just 1% of visitors (a  guess and probably much too low) the potential is for the concentration of urine-derived substances in the water to increase considerably.  This puts a slightly different complexion on the initial low-seeming figure calculated when one person urinates in a pool.  

Does it matter?  The irritant properties of some of the by-products formed when urine reacts with pool cleansing additives (like chlorine) suggest it could lead to noticeable outcomes for swimmers.  If 100,000 swimmers urinated in an Olympic size swimming pool, the concentration of urea would be in the region of 74 mg/L, although as just stated it is likely the urea would form some by-products with substances that are already in the water.  The conclusion is we probably shouldn't do it.    

Comparing the concentration of urea calculated above with some accepted safe limits on substances in drinking water gives further scope for discussion, which I'll not go into here, but it's certainly something to consider with students so they can put the calculation into some context.  It might be surprising that the allowable concentration for cyanide (which I reckon most people know as a deadly poison) is higher than for several other substances, including vinyl chloride, the monomer used for making PVC, present in so many plastic items.  The following data are from Thames Water (for simplicity ionic charges are not shown):

Solute	Standard limit	Formula of solute
Aluminium	200 μg/l	Al
Ammonium	0.5 mg/l	NH4
Antimony	5 μg/l	Sb
Arsenic	10 μg/l	As
Benzene	1 μg/l	C6H6
Boron	1 mg/l	B
Cadmium	5 μg/l	Cd
Chloride	250 mg/l	Cl
Chromium	50 μg/l	Cr

Cyanide	50 μg/l	CN
Fluoride	1.5 mg/l	F
Iron	200 μg/l	Fe
Lead	25 μg/l	Pb
Mercury	1 μg/l	Hg
Nitrate	50 mg/l	NO3
Sodium	200 mg/l	Na
Tetrachloromethane	3 μg/l	CCl4
Vinyl chloride	0.5 μg/l	C2H3Cl