why might measured and calculated pH differ

[Bill Tindall]

This post is in response to a question buried in a previous post on pH.

To paraphrase the question: When I make up a buffer according to calculated amounts of buffer components, the measured pH differs from the calculated pH. Why?

This question does not have a simple answer. I spend an hour of a Pittcon short course on pH providing enough background on the theory and practice of pH measurement to fully answer this question. Within the limits of my typing stamina here is a partial answer:

1. The internationally accepted definition of pH is defined as a result of a measurement process (an operational definition) and only in very limited cases is pH equal to –log (hydrogen ion activity). Hence, accuracy in most pH measurements is a meaningless concept; only precision is relevant. Unfortunately, few books and classes get beyond the outdated and limited definition, –log (hydrogen ion activity), so the rest of this discussion may be hard to accept.

2. The glass electrode response includes a junction potential response as well as the desired pH response. This junction potential component is dependent on the solution components including any charged species (ions, colloides, zwitter ions and polyelectrolytes) as well as nonaqueous solvent components. The magnitude of this response can be between zero and several pH unit equivalents.

3. If the buffer is dilute, aqueous and in the mid range of pH, and the glass electrode was calibrated with NIST pH standards, then the measured pH of the buffer in question will be very close to –log (hydrogen ion activity). Under these special conditions, the junction potential errors of the calibration standard and sample buffer essentially cancel. When these specific criteria are not met, then the measured pH response differs from –log (hydrogen ion activity).

4. If a pH is calculated using an accurate thermodynamic pKa (the value likely found in reference tables) and activity coefficients of all buffer components are properly accounted for, then the calculated pH will equal –log (hydrogen ion activity). These calculations are tedious. Fortunately, there is a buffer program available that does these calculations.

5. While a precision of better than 0.01 unit is possible, the typical precision of making a pH measurements is closer to 0.1 unit.

From the information in 3, 4 and 5 we see ample opportunity for a calculated pH to differ from a measured pH. Does it matter? Most pH measurements only need to be reproducible; accuracy is irrelevant or even meaningless in the context of these operational pH measurements.

Because measured pH values usually have no fundamental significance, when reporting pH values it is essential to describe how the values were obtained so that others can reproduce them. When this description is absent, others reproducing the work can (usually will) make differing assumptions or measuring operations, which can lead to different results. We have seen this problem many times on this Forum.

Suppose one reports that a reaction or separation is best accomplished by preparing a buffer by adding XX grams of component A and YY grams of component B. There is no ambiguity in reproducing this buffer and it can be reproduced with great precision. In many practical cases the true –log (hydrogen ion activity) of this buffer is unknown, can't be measured, nor does it matter. An operational pH of this buffer can be measured and reported, but is this value more useful than the buffer recipe?

[rc_12321]

Tindall ,for me , it seems that you are missing some thing .Your balance may be very accurate in weighing, but still there is some thing hidden there when you try to connect weight of the salt to Ph meter.Ph meter depends on the activity of hydrogen.But then how many? is the question.Even a small variation in weight may vary your hydrogen ion concentration if try to calculate it using avagadro s number.I thik this is what actually makes difference.

[HW Mueller]

rc, I think we can let you get away with this if you weigh on a seesaw.

[Victor]

Bill,

Thank you very much for this answer- I am still thinking about it. A solution of 0.1 (w/w) % TFA in water seems quite close to the ideal you refer to. It is dilute, almost 100% aqueous and I am using reputable standards. So my measured pH should be close to -log(hydrogen ion activity). It is still not close enough to the calculated value for my liking, but your comments on reproduciblity vs accuracy are useful and important.

[Bill Tindall]

It is dilute, aqueous but NOT in the midrange of pH. Hence, there will be a significant junction potential of a few mV. 60 mV equal 1 pH unit. Also how well is the pKa known and what is the impact of this uncertainty on calculation?. Well, as I think about it, at this dilution it will essentially all be dissociated. For some reason I can't find a book or I could give you a better estimate on the junction potential error. Also, do you have a pH calibration standard that brackets the TFA solution? I am not fond of extrapolating a pH calibration.

[Victor]

Bill,

Actually I think your point about knowing the pKa of the buffer components is very relevant. I have seen all sorts of values for the first pKa of phosphate in the literature (even apparently at the same temperature) and this substance has been studied much more intensely than some of the other buffer components regularly used in HPLC.

My conclusion from all this is that SOMETIMES, a careful and experienced worker can measure the pH of a buffer solution more accurately than it can be calculated from one of these commercial programs. However, when the weights required to prepare the required buffer have been established, then measuring the pH can be performed as a check but is not really required any more. In 99% of cases, as you say, there is no reason to know accurately the pH of the buffer.