Problem of the Day
2015.Jul.03
Problem of the Day
A plant used 175 pounds of chlorine yesterday to disinfect a flow of 840,000 gallons per day.
Calculate the chlorine dose in mg/L.
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Introduction
The impact that chlorination in drinking water and wastewater treatment has had improving public health
is, in a word, miraculous. With this in mind, I looked up chlorine on Wikipedia from which I have extracted
the following (https://en.wikipedia.org/wiki/Chlorine):
Essentially no chlorine was created in the Big Bang. Chlorine in the universe is created and
distributed through the interstellar medium from creation in supernovae, via the r-process. This
chlorine provides the supply found in the Solar System.
In meteorites and on Earth, chlorine is found primarily as the chloride ion which occurs in minerals. In
the Earth's crust, chlorine is present at average concentrations of about 126 parts per million,
predominantly in such minerals as halite (sodium chloride), sylvite (potassium chloride), and carnallite
(potassium magnesium chloride hexahydrate.
Chloride is a component of the salt that is deposited in the earth or dissolved in the oceans—about
1.9% of the mass of seawater is chloride ions. Even higher concentrations of chloride are found in the
Dead Sea and in underground brine deposits. Most chloride salts are soluble in water, thus, chloridecontaining minerals are usually only found in abundance in dry climates or deep underground.
Over 2,000 naturally occurring organic chlorine compounds are known.
Who knew?
Solution
This is what I call a reverse pounds equation: we are given pounds and flow from which we are to calculate
concentration. The question asks the answer to be in mg/L of chlorine (Cl2) so these units, as always, are
entered between heavy vertical lines followed by an equals sign and the blank solution bridge.
Problem of the Day: A plant used 175 pounds of chlorine yesterday to disinfect a flow of 840,000
gallons. Calculate the chlorine dose in mg/L.
mg Cl2
L
=
The following list summarizes the information given in the problem statement expressed in the
appropriate units:
1. Chlorine use = 175 lb Cl2/d
2. Flow rate = 840,000 gal/d
As stated in previous Problems of the Day, whenever a question asks to calculate concentration, mg/L or
ppM, the solution bridge is always started with M∙mg/L. Doing so puts the units mg and L needed in the
answer on the solution bridge as shown in bold.
mg Cl2
L
M∙mg
=
L
mg/L of what? The unit Cl2 is entered next. It only appears in one place in the list of information.
mg Cl2
L
M∙mg 175 lb Cl2
=
L
d
The solution bridge has the units needed in the answer but it as unwanted units as well: M, lb and d. The M
reminds us that we need an Mgal in the pounds and reverse pounds calculations, but we don’t have an
Mgal in our list. On this account, we use a conversion factor, canceling the Ms.
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M∙mg 175 lb Cl2 106 gal
mg Cl2
L
=
L
d
Mgal
We can now cancel d and gal by entering the flow in the denominator.
M∙mg 175 lb Cl2 106 gal
mg Cl2
L
=
L
d
Mgal
d
840,000 gal
We still have a gal and lb to cancel. We do so by entering the density of water in the denominator.
M∙mg 175 lb Cl2 106 gal
mg Cl2
L
=
L
d
Mgal
d
gal
840,000 gal
8.34 lb
Since all of the units have canceled except those needed in the answer, we know the solution bridge is
complete. The arithmetic gives the answer.
Problem of the Day: A plant used 175 pounds of chlorine yesterday to disinfect a flow of 840,000
gallons. Calculate the chlorine dose in mg/L.
M∙mg 175 lb Cl2 106 gal
mg Cl2
L
=
L
d
Mgal
d
gal
840,000 gal
8.34 lb
175 x 1,000,000 ÷ 840,000 ÷ 8.34 = 25 mg Cl2/L.
Discussion
While disinfection with chlorine has had an amazing impact in our business, it is not without problems.
Chlorine gas, for example, is very dangerous and the formation of disinfection by-products, DBPs, in the
water is becoming more and more a concern. Stay tuned: there’s more to learn.
Happy calculating! Let us know, by leaving a comment, if you want us to do a specific problem, if
you see a mistake, or if you have a question on any of the Problems of the Day you are looking at.
18030 Brookhurst Street, PMB 573 · Fountain Valley, California 92708 · 866-773-WWTT ·
www.wastewatertechnologytrainers.com