# Definition of alkalinity

Hi,

My question is about the definition of alkalinity, I found this one:

Dickson (DOE, 1994; compare also Dickson, 1981): "The total alkalinity
of a natural water is thus defined as the number of moles of hydrogen ion
equivalent to the excess of proton acceptors (bases formed from weak acids
with a dissociation constant K < 10 -4.5, at 25°C and zero ionic strength)
over proton donors (acids with K > 10 -4.5) in one kilogram of sample. ''

Total Alkalinity = [HCO3-]+ 2[CO3-2] + [B(OH)4-] + [OH-]
+[HPO4-2] + 2[PO4-3] + [H3SiO4]- +[NH3] + [HS-]- [H+] -[HS04-] - [HF] - [H3P04]......(1)

So when u start adding a strong acid and eating the alkalinity away u get to a point where TA (total alkalinity) is zero (equivalent point). Then u get the proton condition:

[H+] +[HS04-] + [HF] + [H3P04]
=[HCO3-]+ 2[CO3-2] + [B(OH)4-] + [OH-]
+[HPO4-2] + 2[PO4-3] + [H3SiO4]- +[NH3] + [HS-]...................................................(2)

You can compare the state of the equivalent point with a solution u made from pure water and where u add H2CO3, NaH2PO4, B(OH)3, NH4Cl, NaF, Na2SO4 and H4SiO4 in all the equivalent amounts. You cant find these subtances in the proton condition because they are by definition the zero proton levels.

My first question is, why is H2SO4 not in (1) and consequently (2)? Seeing that SO4- is considered zero proton level, H2SO4 should be in the left side of (2), seeing as it is considered a proton acceptor.

My second question is concerning the fact that NaH2PO4, NaF and NaSO4 are the zero proton levels and not H3PO4, HF and H2SO4. When H2PO4- is formed it can still absorb an equivalent amount of H+ by forming H3PO4, so actually there is more alkalinity then (1) says. The same for F-, it can take H+ to form HF. So my definition would be:

Total Alkalinity = [HCO3-]+ 2[CO3-2] + [B(OH)4-] + [OH-]
+[HPO4-2] + 2[PO4-3] + [H3SiO4]- +[NH3] + [HS-] + [F-] + [H2PO4-] + [HSO4-] +
2[SO4-] - [H+] ...............................................................................................(3)

So (3) doesnt look at pKa values of all the acid-base systems like (1) does, but just gives all neutral substances zero proton level, and the alkalinity of (3) will be higher than (1). Now your proton condition at the equivalence point after adding a strong acid is:

[H+] = [HCO3-]+ 2[CO3-2] + [B(OH)4-] + [OH-]
+[HPO4-2] + 2[PO4-3] + [H3SiO4]- +[NH3] + [HS-] + [F-] + [H2PO4-] + [HSO4-] +
2[SO4-] ........................................................................................................(4)

and this will be the same as a solution starting from pure water and adding equivalent amounts of H2SO4, H2CO3, H3PO4, B(OH)3, NH4Cl, HF and H4SiO4

And my last question is, how can u determine the total alkalinity according to (1) experimentally of an unknown sample, when do u know when to stop, is there some pH jump?

Last edited:

symbolipoint
Homework Helper
Gold Member

Vulgar,
You are taking an extremely intricate viewpoint about alkalinity. Think of alkalinity as the opposite of acidity. You choose whatever kind of equivalence you find necessary or practical. You can titrate alkalinity to whatever standard or agreed-upon endpoint you want. Just a titration using a standard acid titrant. Your equivalents can be percent of some named alkaline material whether real or theoretical, or moles of alkaline unit per gram of sample; to whatever kind of endpoint is needed such as to a pH indicator endpoint or to pH-meter endpoint.

This is just the definition of alkalinity as I found it, and I wanted to know the reason why they chose acids with a pKa smaller than 4,5 as proton acceptors and bigger than 4,5 as proton donors, instead of any other pKa values or the way how I defined it. There has to be some advantage or reason.

Say u chose the definition:

Total Alkalinity = [HCO3-]+ 2[CO3-2] + [B(OH)4-] + [OH-]
+[HPO4-2] + 2[PO4-3] + [H3SiO4]- +[NH3] + [HS-]- [H+] -[HS04-] - [HF] - [H3P04]......(1)

and u have an unknown sample, how do u go about finding TA as this definition prescribes?

Last edited:
Borek
Mentor

Let's assume that alkalinity is the ability of a solution to neutralize acids to the equivalence point of bicarbonate - this is just one of possible definitions. Equivalence point of bicarbonate is around pH 8.3. Everything that gets protonated up to this pH will consume H+ and will increase alkalinity.

$$K_a = \frac {[A^-][H^+]}{[HA]}$$

can be rewritten as

$$\frac {[A^-]}{[HA]} = \frac {K_a}{[H^+]}$$

or

$$\frac {[A^-]}{[HA]} = 10^{pH-pK_a}$$

Using this approach you can easily check which substance increases alkalinity - if it gets protonated before assumed end point of titration, its presence increases alkalinity, as it will consume acid. Note that for a given pH ratio of concentrations of forms of a given acid/base is not a function of its concentration.

For example let's look at phosphoric acid. At pH 8.31 solution contains

H3PO4 - 0.0%
H2PO4- - 7.0%
HPO42- - 93.0%
PO43- - 0.0%

Do you see which one gets where and why?

Ok,

So suppose u have a solution which only contains carbonate species, than the equivalence point called carbonate alkalinity is described by the proton condition:

[H+] + [H2CO3]=[CO3-2]+[OH-]........................................(1)

The alkalinity for this solution is:

Alk = [CO3-2] + [OH-] - [H+] - [H2CO3]..............................(2)

So when u start adding acid u will reach the equivalence point at about pH 8.3 and u can calculate the exact pH with (1).

Now u take a solution which has carbonate and phosphate species in it, u cant really speak about carbonate alkalinity anymore because u have several acid-base systems. But if u titrate with acid untill u reach 8.3, u can make the following maybe:

acid u need to add untill pH 8.3= [CO3-2] + 0,93*[total phosphate] + 2*0,07*[total phosphate] - [H+]

This is considering if at your start pH only PO4-2 and CO3-2 are present and assuming that all carbonate is present as HCO- at end pH

Something which makes more sense to me is to titrate untill u reach this proton condition for instance:

[H+] + 2*[H3PO4] + [H2PO4-] = [CO3-] + 2*[PO4-2]

or

alk= [CO3-] + 2*[PO4-2] - 2*[H3PO4] - [H2PO4-] - [H+]

This definition is a lot less random than specifying an end pH

symbolipoint
Homework Helper
Gold Member

Vulgar,
Study the theory of neutralization titrations for acids and bases, including the equilibiria of weak acids and weak bases. Also, if you have the opportunity (like you are in school), pay close attention to actual titrations you do on acids and bases. The practical experience will make the explanations easier to understand. Using the academic viewpoint, you can choose millimoles of equivalents per gram of sample, or moles per gram of sample, or whichever is most practical. You will take your endpoints either with chemical pH indicators, or with pH meter.

Borek
Mentor

Something which makes more sense to me is to titrate untill u reach this proton condition for instance:

[H+] + 2*[H3PO4] + [H2PO4-] = [CO3-] + 2*[PO4-2]

How are you going to do it? You can't measure concentrations of all ions separately. The only property of the solution that is related and that you an easily measure is pH.

Every time u do a simple acid-base titration, u titrate until a certain proton condition which is the equivalent point and it usually accomponies a big pH jump which is the endpoint, which is not exactly equal usually to the equivalent point.

I think the point of alkalinity is:

u got seawater for instance and u know all the components in it but not the separate concentrations, so u measure alkalinity where u only need a strong acid. Then u record the pH during this titration and then try to curve fit it to your definition of alkalinity. And from here u can get the seperate concentrations. But the definitions are still confusing to me and how exactly u proceed with this

Borek
Mentor

u u u u u u u u u

u got seawater for instance and u know all the components in it but not the separate concentrations, so u measure alkalinity where u only need a strong acid. Then u record the pH during this titration and then try to curve fit it to your definition of alkalinity. And from here u can get the seperate concentrations. But the definitions are still confusing to me and how exactly u proceed with this

How is it different from titrating till the predefined pH?

Vulgar,
Study the theory of neutralization titrations for acids and bases, including the equilibiria of weak acids and weak bases. Also, if you have the opportunity (like you are in school), pay close attention to actual titrations you do on acids and bases. The practical experience will make the explanations easier to understand. Using the academic viewpoint, you can choose millimoles of equivalents per gram of sample, or moles per gram of sample, or whichever is most practical. You will take your endpoints either with chemical pH indicators, or with pH meter.

Unfortunately, I left school some time ago, but i do have some experience with normal titrations, but almost forgotten

How is it different from titrating till the predefined pH?

Sorry, old habits die hard

I dont know really, the first time I read about alkalinity, I thought it was similar to a normal acid-base titration where you keep seeing pH jumps at different pH's, and you just take the volume of strong acid where the last pH jump occurs and that's your alkalinity, so I didn't expect to see so many definitions. But I think you can only speak of equivalent amounts when u reach a proton condition.

Last edited:
Borek
Mentor

There can't be a large jump when you have several substances, each buffering the solution in different pH range.

symbolipoint
Homework Helper
Gold Member

Sorry, old habits die hard

I dont know really, the first time I read about alkalinity, I thought it was similar to a normal acid-base titration where you keep seeing pH jumps at different pH's, and you just take the volume of strong acid where the last pH jump occurs and that's your alkalinity, so I didn't expect to see so many definitions. But I think you can only speak of equivalent amounts when u reach a proton condition.

Recall someone said, "... to a predefined pH".

Forget the different components in the solution! You have a sample, as you suggested, sea water; if pH is greater than 7, then you may have an alkaline sample of sea water. Other components may or may not contribute to alkalinity, but you do not need this information. Just you have a water sample with pH greater than 7. TITRATE to a predetermined pH. Now you can compute moles of H+ and you should have measured how much sample you titrated. From those, you calculate your alkalinity. What is your unit of alkalinity? That is up to you or the institution for whom you work.

The way I use "equivalents" here, it is for moles of H+.

It depends on what you need it for I guess. If you want to find out concentrations of seawater components you need a definition of alkalinity, which includes these components.

Borek
Mentor

Alkalinity won't let you determine components, it characterizes sample on the whole.

There seems to be a difference between operational alkalinity and the mathematical definition. For instance the practical alkalinity of seawater is:

PA = [HCO3-] + 2[C03-2] + [B(OH)4-] + [OH-] - [H+]

So I guess you need to titrate until you reach a pre-defined pH, where only these components contribute and no others,although they don't mention what pH (I think it is pH 4 to 5). The mathematical definition is the one i first posted and curve fitting is used there with a thermodynamical model.

I have found articles where alkalinity is used to determine the new pH-value after addition of for instance ammonia. You know for instance the practical alkalinity and the components which are responsible for it and then you can calculate the new pH.

Edit: at pH-values above 8 PA seems to be a good approximation for seawater: so when your initial pH is above 8, and you titrate until pH 4 to 5, you can use the PA expression.

Last edited:
symbolipoint
Homework Helper
Gold Member

There seems to be a difference between operational alkalinity and the mathematical definition. For instance the practical alkalinity of seawater is:

PA = [HCO3-] + 2[C03-2] + [B(OH)4-] + [OH-] - [H+]

So I guess you need to titrate until you reach a pre-defined pH, where only these components contribute and no others,although they don't mention what pH (I think it is pH 4 to 5). The mathematical definition is the one i first posted and curve fitting is used there with a thermodynamical model.

I have found articles where alkalinity is used to determine the new pH-value after addition of for instance ammonia. You know for instance the practical alkalinity and the components which are responsible for it and then you can calculate the new pH.

Edit: at pH-values above 8 PA seems to be a good approximation for seawater: so when your initial pH is above 8, and you titrate until pH 4 to 5, you can use the PA expression.

My thoughts here are not yet cleanly formulated into what to say, but I try:

Some equilibrium situations are analyzed with charge balance and mass balance, but the use of [H+] in your "PA" expression does not seem to have a reason if your interest is in alkalinity.

Some materials can interact with water to hydrolyze, yielding hydroxide. You have focused some of your attention to carbonate and bicarbonate. Maybe you know what the source is for the carbonate or bicarbonate. Maybe CO2 from the atmosphere? But not clear if that be enough to go all the way to CO3-2.

This may be helpful as reminder...
H2O + CO3-2 <------> HCO3-1 + OH-
That reaction shows the production of hydroxide, therefore alkaline, raising the pH.

The PA I posted:

PA = [HCO3-] + 2[C03-2] + [B(OH)4-] + [OH-] - [H+]

is right though, I didn't make it myself, I got it from a book concerning CO2 in seawater. The [H+] in PA actually has a minus sign . When you start titrating with a strong acid not all the acid is used to neutralize the alkalinity, but part of it is used to lower pH, so that's why it is in there with a minus sign I think.

When you reach the equivalence point when you add acid, the PA will be reduced to zero and you can say:

[H+] = [HCO3-] + 2[C03-2] + [B(OH)4-] + [OH-]

and this is the proton condition for the equivalence point. So your titration for the alkalinity will be exact if you stop the titration at the pH where:

[H+] = [HCO3-] + 2[C03-2] + [B(OH)4-] + [OH-]

This is the exact equivalence point and not the endpoint of titration which can be a bit of.