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Offline Lauren52891

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Calculating exact pH of a buffer
« on: January 23, 2013, 10:13:57 PM »
How do you calculate the exact pH of a potassium buffer? Known buffer info: -0.5 g/L KH2PO4, +0.5 g/L K2HPO4 in a 1 L solution at a pH of 7.00.

Experimentally, I took four pH readings. One of just the buffer and three of increased dilutions. I started with 5 mL of buffer to 45mL of water, then diluted each concentration by one tenth from there.

I tried the Henderson-Hasselbach equation. It is not giving me an accurate enough pH.

Offline Arkcon

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Re: Calculating exact pH of a buffer
« Reply #1 on: January 23, 2013, 11:29:12 PM »
What pH were you able to calculate?  Its not too surprising that the observed pH is different, there are many possible sources of error.  But how far off you were is needed to pin down what happened.  If everything was done properly, the numbers should be at least close.
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Offline Lauren52891

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Re: Calculating exact pH of a buffer
« Reply #2 on: January 23, 2013, 11:46:28 PM »
1 L x .5g/L x 1 mol/136.09 g = .00367 mol acid

1 L x .5g/L x 1 mol/174.2 g = .00287 mol base

pKa of potassium phosphate (monobasic) = 6.82

pH = pKa +log [ b]/[a]
pH = 6.82 +log (174.2/136.09)
pH = 6.91

The calculations are fine until I start calculating the dilutions. They are all coming out to be the same with the Henderson-Hasselbach equation. I know there is a more exact way to calculate the pH...that's where I'm having problems.
« Last Edit: January 24, 2013, 03:57:19 AM by Borek »

Offline Borek

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Re: Calculating exact pH of a buffer
« Reply #3 on: January 24, 2013, 04:00:59 AM »
Where did you got pKa of 6.82 from? Correct value (not corrected for ionic strength) is 7.2.
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Offline Lauren52891

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Re: Calculating exact pH of a buffer
« Reply #4 on: January 24, 2013, 09:45:11 AM »
Can you give me a credible source to reference that pKa? I used the Aldrich catalogue, but couldn't decide which entry I was right for my purposes.

Also, I think the help I'm looking for to calculate a more exact pH has to do with calculating relative concentrations of the conjugates then [h+].

Here are my ideas:
KH2PO4 dissociates into K+ and H2PO4-
The equilibrium expression for the acid is then
H2PO4- + H2O --> H3O+ + HPO4--

[H+]= [H2PO4-] (Ka)/[HPO4--]
Ka= 6.2 x 10^-8

And this is where I'm getting confused. How do you calculate those concentrations?

Offline Babcock_Hall

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Re: Calculating exact pH of a buffer
« Reply #5 on: January 24, 2013, 09:47:29 AM »
If the ionic strength is changing from dilution, then does this explain qualitatively changes in pH (are they in the expected direction)?  Assuming that the answer is yes, I suppose that one could use apparent pKa values, but I cannot be of any help beyond that observation.

Offline Lauren52891

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Re: Calculating exact pH of a buffer
« Reply #6 on: January 24, 2013, 09:50:10 AM »
log fz = (-.51z2sqrtI) / (1 + sqrt(I))

aion = fz x Cion
What do I use for the concentration of ions?

And where exactly do I relate this activity coefficient after I have calculated it?
« Last Edit: January 24, 2013, 10:37:41 AM by Lauren52891 »

Offline Babcock_Hall

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Re: Calculating exact pH of a buffer
« Reply #7 on: January 24, 2013, 10:16:44 AM »
The thermodynamic pKa value is tabulated at an ionic strength of zero, IIUC.  I seem to recall that it is about 7.20 for potassium phosphate.  However, as ionic strength increases, the pKa seems to go down (that is what I meant by apparent pKa values).  See this link for some examples:
http://lclane.net/text/ionicstrength.html

My memory and experience is that the effect(s?) on pKa is (are) very large when one gets above 1 M in phosphate concentration.  Also, there may be some additional effects or problems.  Suppose that there is some carbon dioxide in the water...

Offline Borek

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Re: Calculating exact pH of a buffer
« Reply #8 on: January 24, 2013, 10:18:26 AM »
Apparent - corrected for ionic strength.

In Handbook of Chemical Equilibria in Analytical Chemistry (Kotrly and Sucha, Ellis Horwood Ltd. 1985), pKa2 is given as 7.199 for IS=0, plus apparent values of 6.72 for I=0.1 and 6.46 for IS=1.0. Apparently 6.82 that you used is an apparent value for IS somewhere between 0 and 0.1.
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Offline Big-Daddy

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Re: Calculating exact pH of a buffer
« Reply #9 on: January 25, 2013, 02:25:01 PM »
log fz = (-.51z2sqrtI) / (1 + sqrt(I))

aion = fz x Cion
What do I use for the concentration of ions?

And where exactly do I relate this activity coefficient after I have calculated it?

If you're using the Henderson-Hasselbalch approximation then activity coefficients are unlikely to be relevant - using the approximation will already take you 0.1-0.4 pH points away from a true value. On the other hand calculating buffer composition with exact accuracy is something I'm unclear on as well (all I know is that the Henderson-Hasselbalch approximation is doubly approximated and even the exact expression is phrased in terms of concentrations, so you can expect these answers to be far away from the truth).

Offline Borek

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Re: Calculating exact pH of a buffer
« Reply #10 on: January 25, 2013, 03:43:23 PM »
If you're using the Henderson-Hasselbalch approximation then activity coefficients are unlikely to be relevant - using the approximation will already take you 0.1-0.4 pH points away from a true value.

Care to elaborate? HH equation is not an approximation, it is just a rearranged acid dissociation constant. Problems start when it is used blindly and without understanding limitations of the typical approach.
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Offline Arkcon

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Re: Calculating exact pH of a buffer
« Reply #11 on: January 25, 2013, 03:48:17 PM »
Likewise  Big-Daddy:, I've also used Henderson-Hasselbach to prepare a buffer.  With the correct pKa, and careful measurement of masses to produce the correct concentration, I don't recall being more than 0.2 pH units off (and having to correct that with strong acid or base).  And that's without taking the thermodynamic and neutral ionic concentrations into account.  You say you can be off by 0.1 pH unit, which is fine.  But you seem also to be sure of 0.4, which is (kinda) a big error.
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Offline Lauren52891

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Re: Calculating exact pH of a buffer
« Reply #12 on: January 25, 2013, 06:17:34 PM »
I am doing something wrong because I am still getting almost the exact same pH for the dilutions, even after using the water activity coefficient.

For the HH pH calculation, I got 7.092 for all of the solutions (using the corrected pKa value), which I think I am supposed to expect because the ratio of acid to conjugate base stays the same even though the concentration of the solution is changing.

Then for the activity coefficient I get a number like .0012, which, if subtracted from my HH pH calculation, still isn't going to make a large enough difference to match what I got experimentally.         

Offline Big-Daddy

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Re: Calculating exact pH of a buffer
« Reply #13 on: January 26, 2013, 07:26:43 PM »
If you're using the Henderson-Hasselbalch approximation then activity coefficients are unlikely to be relevant - using the approximation will already take you 0.1-0.4 pH points away from a true value.

Care to elaborate? HH equation is not an approximation, it is just a rearranged acid dissociation constant. Problems start when it is used blindly and without understanding limitations of the typical approach.

The HH equation as I know it is of the form:

[H+]=Ka*(Ca/Cs) where Cs is the initial concentration of your salt = concentration of the cation B+ present from salt BA, where you also have some HA present (initial concentration Ca) in the mixture

This is heavily approximated. An exact solution is first obtaining

[H+]=Ka*((Ca-[H+]+(Kw/[H+]))/(Cs+[H+]-(Kw/[H+])))

After two approximations follows [H+]=Ka*(Ca/Cs).

I have also seen the equation Ka=([H+]*[salt])/[weak acid], but am unclear what this means - presumably [salt]=Cs as all salts are assumed to dissociate 100% in solution, or for salt BbAa, [salt]=Cs*b. Thus in calculating buffer composition you would work to find out what mass of salt would produce this concentration [salt] for your desired pH. But what does [weak acid] refer to and how could you calculate it exactly? My issue with that is the reason I don't see this so far as an exact method.

Offline AWK

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Re: Calculating exact pH of a buffer
« Reply #14 on: January 27, 2013, 02:34:32 AM »
How do you calculate the exact pH of a potassium buffer? Known buffer info: -0.5 g/L KH2PO4, +0.5 g/L K2HPO4 in a 1 L solution at a pH of 7.00.

Experimentally, I took four pH readings. One of just the buffer and three of increased dilutions. I started with 5 mL of buffer to 45mL of water, then diluted each concentration by one tenth from there.

I tried the Henderson-Hasselbach equation. It is not giving me an accurate enough pH.
This is a very bad example for testing changes of pH during dilutions. For pH very close to 7 all diluted solutions will show practically the same pH. And, of course, an unabbreviated HH equation given by Big-Daddy with activity corrections should be used. This equation still assumes that nor acid or base undergo protolysis (1000 times dilution of phosphate buffer with pH far from 7 can change pH even by 1, mainly because of protolysis of dihydrogen phosphate)

Moreover phosphates form hydrates and usually the hydrates are sold. Check if you used anhydrous salts.
« Last Edit: January 27, 2013, 02:45:45 AM by AWK »
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