I don't think this is worth belabouring too much more but a couple of things caught my eye. They may be more a matter if terminology that anything else.
Quote:
Originally Posted by Biobrewer
Offset error cannot be completely compensated by ATC on a meter.
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A pH electrode produces, when exposed to a solution at pH, a voltage
E = Ei - 58.167*slope*((T + 273.15)/293.15)*(pH - pHi)
'slope' is a number close to 1 and Ei, technically the isolelectric voltage, is a few millivolts at most and is the voltage the meter would produce if pH - pHi. Given that the meter
assumes that pHi - 7, it thinks Ei is the offset.
IOW, the meter thinks
E = Eo - 58.167*slope*((T + 273.15)/293.15)*(pH - 7)
and calculates Eo (the voltage at pH 7) and slope based on that assumptions from buffer readings. Presented a voltage E, after calibration, the meter calculates and displays
pH = pHi + (E - Eo)/( 58.167*slope*((T + 273.15)/293.15) )
If pHi is indeed 7 then Ei = Eo is not a function of temperature and ATC has no problem dealing with sample temperatures different from buffer temperatures. But if pHi != 7 then Eo is a function of temperature and the meter has no way of dealing with that because it assumes it is not a function of temperature. OTOH if you know the true value of pHi you can determine, from the calibration, what the actual value of Ei is and from that point on you are fine.
Quote:
Originally Posted by Biobrewer
However, the error will be around 1/10 of a pH unit at it's worst for a good pH meter.
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That's a lot of uncertainty. A whole pH unit of uncertainty in pHi and buffer temperatures separated from sample temperature by 32 °C would be required to induce that much pH reading uncertainty from ATC error. A more reasonable level of pHi uncertainty is probably 0.3 as I noted in a previous post (but I do own that rogue electrode) for which the ATC unceratainty is more like 0.03 with the 32 °C temperature spread. That's still enough to dominate the uncertainties associated with temperature and voltage readings and buffer pH uncertainty (± 0.02 in the technical buffers used by most home brewers).
Quote:
Originally Posted by Biobrewer
For a home brewer, that is not a big deal.
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I guess I agree for the average home brewer. But when trying to do things like figure out the titratable acidity of a malt, for example, that's much more error than I am willing to live with.
Quote:
Originally Posted by Biobrewer
However, that is with a good pH meter. I happen to have a laboratory-grade pH meter from an old job that is highly accurate over a fairly wide temperature range,
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I'm sure this one is semantics but I'll point out any way that it is not the meter that is in question here but the electrode. The meter simply dumbly plugs readings into the second equation above blissfully assuming that the offset is the isoelectric voltage and pHi = 7. It is the fact that the electrode's pHi != 7 that induces most of the error when ATC is being used. All the meter itself needs to be able to do is measure temperature with rms error less than 0.5 °C and voltage with rms error less than 0.5 mV neither of which are terribly demanding requirements. It is, of course, just good systems engineering that the meter itself produce uncertainties low enough that when rss'd with the uncertainties from buffers and electrode the latter are dominant.
Quote:
Originally Posted by Biobrewer
though I know that cheaper pH devices, like the ones readily available to home brewers for <$50-100, will not meet that same spec, and will likely vary more with temperature and have a larger error associated with temperature drift.
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I wonder about that (and I don't mean I'm challenging that statement but literally that I keep thinking about it). From what I have been able to deduce with a small sample size it is often not that cheap meters drift so much as it is that the calibration routines take readings before the results are stable enough. For a calibration I find 10 minutes is a better criterion that just waiting until the change is less than 3 mV/min or whatever the auto cal routines use. Put another way the cheap meters jump too soon and get bal cal parameter estimates so that in reading samples they display stable, but wrong, pH values. This is easily fixed. OTOH some cheap meters are just unstable. That's not fixable.
I will also assert that $ is not a defense against an unusually large pHi deviation. The electrode I have that is way off cost me over $250.
I'll close by noting again that if you know pHi you can (and I do) use ATC confidently at temperatures quite removed from the calibration buffer temperature. The problems with this are 2
1. Meter's won't let you set in a pHi value
2. Since it takes a rather large pHi error (0.3) to induce a fairly small error in pH even at a fairly high temperature excursion (0.03 pH at 32 °C differential) pHi isn't very 'observable'. It thus takes hundreds of buffer readings at various temperatures and some fairly advanced math to estimate pHi from those readings.