Well, I hate to be a bugger here, but spectrophotometric methods do actually exist for phenol red both in freshwater (~0 ionic strength, 10 < T < 30 C, P = 1atm) (Yao and Byrne, 2001) and sea water (33 < S < 37 ppt, 0 < T < 30 C, P = 1 atm) (Robert-Baldo et al., 1985).
However, pK1 of phenol red is a bit low if you're trying to measure high-pH, warm, saline water like would be coming out of a reef tank (or the warm, surface ocean), though it works. It's definitely useful for colder, lower pH sea water. The pKa of m-cresol purple makes it much better suited for most seawater pH measurments.
The available calibrations also express pH on the Free scale. That works fine in solutions of low ionic strength (freshwater) since Free-scale pH and NIST-scale pH (aquarists use the NIST scale) are pretty much the same. In sea water Free pH values are a bit lower than NIST values due to ion pairing effects (~0.03 units--e.g., 8.198 on NIST scale = 8.169 on Free scale). With a set composition of major ions in sea water one can usually convert with reasonable confidence. However, since artificial sea water we use is bound to vary from NSW at least a little in major ion composition at a given salinity, adding 0.03 units to Free pH may not be a solid conversion to go to NIST pH.
In any event, pK1 @ 20.0 C is 7.564 +/- 0.002, @ 25.1 C is 7.495 +/- 0.006, @ 30.1 is 7.451 +/- 0.006, all @ 35 ppt, 1 atm. There's a small salinity dependence too.
In any event, pK1 can be well estimated over a range of temperatures and within a modest range of salinities using and equation of the form,
pK1 = A/T - B + C*log(T)
and the experimental data give us (including a salinity correction)
pK1 = (4834.00/T) - 84.31 + 30.7580*log(T) + 0.004(35-S)
where T is temp. in Kelvins and S is salinity in ppt (Robert-Baldo et al., 1985).
Absorbances are measured @ 433 nm, 588 nm, and 700 nm. The 433 and 588 nm provide a ratio for max absorbance of the yellow and red forms of the dye and 700 nm is used to correct for baseline shifts in the spectrometer. pH is then calculated as,
pH = pK1 + log ((R-e1)/(e2-R*e3))
where R is the absorbance ratio of 433/588 nm, e1 = 0.0038, e2 = 2.6155, and e3 = 0.1234.
Clearly you'd want to do all of that with a spreadsheet so you can just plug in temp, salinity, and absorbance values in have it spit out pH for you.
BUT, and of course it's a big but, that only works if you have a decent spectrophotometer and can measure at those wavelengths.
The pK1 at 0 ionic strength @ 20 C is 8.071, @ 25 C is 8.032, and @ 30 C is 8.000. Due to the much lower ionic strength, the indicator is going to behave differently and have different absorbances at any given pH, even after taking ionic strength into account.
Suffice it to say that, without a spectrophotometer and working within the ranges for the behavior for phenol red is known (either freshwater, = very low ionic strength, OR sea water at salinity ~33-37) at a stable, known temperature, it becomes a very difficult proposition to try to extrapolate a reliable correction factor from freshwater absorbance values to seawater values.
The best options are either 1) a pH meter with decent combination electrode, or a decent spec., and I'd recommend m-cresol purple for spectrophotometric pH (pKa of m-cresol purple is ~8.20 @ 25 C, 1 atm, 35 ppt on NIST pH scale--the mean pH of sea water).
Hope that makes sense of why a simple correction factor here just isn't prudent (or likely to work) and why a pH meter probably is the best option in this case
cj
