pH - simple temperature correction of pH

Let us consider the RBRconcerto³ C.T.D.pH with an integrated Idronaut pH sensor. Without temperature correction, the pH output from Channel-4 would be a simple linear function of the raw data:

$//<![CDATA[ \begin{array}{l}pHraw = c_0 + c_1 \cdot R\end{array} //]]>$

where R is the normalized voltage ratio from Channel-4 monitoring the pH sensor, c0, c1 are the core coefficients of the linear equation, and pHraw is the uncorrected output in pH units.

The parameter pH is well known to have a dependence on temperature, so a more accurate value is obtained if the compensated version of the equation is used. This is typically expressed in a form such as:

$//<![CDATA[ \begin{array}{l}pHcorr = pHraw + Kph \cdot (pHraw - pHcal) \cdot (T - Tcal)\end{array} //]]>$

Casting this into the form used by the logger, corr_ph, is simple:

$//<![CDATA[ \begin{array}{l}pHcorr = pHraw + x_0 \cdot (pHraw - x_1) \cdot (value(n_0) - x_2)\end{array} //]]>$

where

• pHraw is c0 + c1 * R as before, now an intermediate variable in the equation,
• x0 corresponds directly in value to the constant "Kph",
• x1 is the calibration pH "pHcal", generally 7.0,
• x2 is the calibration temperature 'Tcal' in °C,
• n0 is the index of the temperature channel (2 in this example),
• value(n0) is the final output value of the temperature channel in °C,
• pHcorr is the corrected output in pH units.