# How do spectrophotometric pH measurements work?

Spectrophotometric pH measurements are based on the addition of a pH-sensitive indicator dye to a water sample. One routinely used dye is m-Cresol purple (mCP), which we also investigated and used within PINBAL. Within the pH-range of seawater the dye changes its color from yellow to purple.

As the second dissociation constant pK_{2} of the diprotic dye mCP is in the pH range typical for seawater, the pH of the solution can be expressed as:

(1) |

where [HI^{-}] and [I^{2-}] are the concentrations of the monoprotonated and deprotonated species of the indicator dye, respectively. The concentration ratio [HI^{-}] / [I^{2-}] is determined by absorbance (A) measurements, which in general relate the light intensity recorded for the blank (I_{0}) to the light intensities recorded for the sample solution (I):

(2) |

HI^{-} and I^{2-} have two clearly distinguishable absorbance maxima at wavelength λ_{1} = 434 nm and λ_{2} = 578 nm, respectively (Clayton and Byrne 1993). However, the absorbance spectra of both indicator species overlap. Therefore, at both wavelength λ_{1} and λ_{2} the absorbance A_{λ} needs to be expressed by the Lambert-Beer-law describing the additive absorbance contribution of both indicator species as:

(3) |

where ε_{λ}(X) are the molar extinction coefficients of the indicator species X at wavelength λ, and d is the cuvette length. Illustrative absorption spectra of mCP at a range of pH levels are illustrated below.

Combining the equations 1 and 3, and algebraic manipulation allow to express the pH of the solution as:

(4) |

where R = A_{578} / A_{434} is the ratio of the absorbance measured at the two peak wavelengths and e_{1 }= ε_{578}(HI^{‑}) / ε_{434}(HI^{‑}), e_{2 }= ε_{578}(I^{2‑}) / ε_{434}(HI^{‑}) and e_{3} = ε_{434}(I^{2‑}) / ε_{434}(HI^{‑}) are the molar absorptivity ratios (Clayton and Byrne 1993).

The coefficients in Eq. 4 were determined in several studies, for a range of salinity and temperature conditions (see Mosley et al. 2004; Liu 2011; Lai et al. 2016).

The pH measurement system developed within PINBAL is a continued development of the flow injection analysis (FIA) approach described by Aßmann et al. (2011). The overall measurement principle of the instrument is based on the injection of a mCP stock solution into a continuous sample flow. After the injection of the dye a concentration peak passes the cuvette and the backward flank of the dilution curve is continuously recorded resulting in more than 100 absorbance spectra per single pH measurement. The pH-perturbation caused by the dye addition can be corrected by extrapolating the pH values calculated from each spectrum to zero absorbance at the isosbestic wavelength, which is a directly related to the dye concentration. For the absorbance measurements the system is equipped with a VIS broadband LED as light source and a CCD spectrometer as detector (see Aßmann et al. 2011 for details).

**References**

Aßmann, S., C. Frank, and A. Körtzinger. 2011. Spectrophotometric high-precision seawater pH determination for use in underway measuring systems. Ocean Sci. 7: 597–607. doi:10.5194/os-7-597-2011

Clayton, T. D., and R. H. Byrne. 1993. Spectrophotometric seawater pH measurements : total hydrogen results. Deep Sea Res. Part I Oceanogr. Res. Pap. 40: 2115–2129.

Lai, C.-Z., M. D. DeGrandpre, B. D. Wasser, and others. 2016. Spectrophotometric measurement of freshwater pH with purified meta-cresol purple and phenol red. Limnol. Oceanogr. Methods. doi:10.1002/lom3.10137

Liu, X. 2011. Purification and characterization of meta-cresol purple for spectrophotometric seawater pH measurements. Environ. Sci. Technol. 45: 4862–8. doi:10.1021/es200665d

Mosley, L. M., S. L. G. Husheer, and K. a. Hunter. 2004. Spectrophotometric pH measurement in estuaries using thymol blue and m-cresol purple. Mar. Chem. 91: 175–186. doi:10.1016/j.marchem.2004.06.008