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Defining Acids and Bases - the pH scale

Solutions can be described as acidic, neutral or basic. These terms are indicative of the hydrogen ion concentration [H+] in the solution. In aqueous media each hydrogen ion is associated with a water molecule and so may be represented as H+(H2O) - which is always abbreviated to the conventional notation, H3O+.

Since the H3O+ concentration, represented by [H3O+] can vary by many orders of magnitude, chemists define the pH of a solution as the negative logarithm of [H3O+], or pH = -log10[H3O+]. When defined in this way, the common pH scale spans from 0 to 14. Technically, pH values can theoretically lie outside this range but that goes well beyond the scope of this simple discussion. Suffice it to say that a neutral pH is around 7, with acidic solutions having lower pH values, and basic solutions having higher pH values.

The additional adjectives “strong” and “weak” can be applied when describing acids and bases. A 0.1 molar (0.1M) solution of hydrochloric acid (HCl) would have a pH of 1, since the acid formula is HCl and each molecule of this acid is completely ionised (into 1xH+ and 1xCl-) in solution - HCl is considered a strong acid.

Many acids are only partially dissociated into ions in solution. For example an aqueous 0.1M solution of acetic acid CH3COOH (the component in common vinegar) has a pH of ~ 2.87. This is because only ~ 1 in every 103 CH3COOH molecules are present in solution as H+ = H3O+. For that reason acetic acid is classified as a weak acid.

An example of a strong base would be sodium hydroxide - NaOH. A 0.1M solution of NaOH has a pH of 13, on account of the well known relationship that the product [H+][OH-] = Kw = 10-14. The quantity Kw is known as the “ionic product” for water.

Anthropogenic production of CO2 from fossil fuel burning has resulted in measureable changes in the dissolved CO2 concentration in the earth’s oceans. Additional dissolved CO2 affects the pH of seawater; rising CO2 levels resulting in a lowering of seawater pH. For this reason there is keen interest in developing highly accurate pH measurements to track these changes. Many of the instruments now being developed by oceanographers now use optical methods to determine pH.

Measuring pH

pH can be measured in various ways but by far the most common laboratory approach is to use a pH electrode. When placed in solution a pH electrode develops a potential that varies by ~ 59 mV per pH unit. Typically the pH electrode is calibrated by immersing it into a buffer solution (a solution having a very stable and well defined pH) and taking a reading. A second reading is then taken in another buffer, now providing a different pH. These two readings establish a calibration function for that electrode in the form E = E0 + c(pH), with knowledge of the two constants E0 and c allowing an unknown pH to then be determined from a measurement of E by interpolation.

There are several issues with pH measurements. Firstly, the measurement system that determines the electrode potential must not draw any current from the electrode. Secondly, the calibration process just described is temperature dependent. This means that errors creep into pH measurements if the temperature of the environment varies during the measurements.

A one chip pH measurement solution that manages both of these issues is the Texas Instruments LM91200. Based on the evaluation board for this part (LMP91200EVAL), a project is currently underway to make a low cost pH measurement shield for the XMOS Startkit with a LabVIEWTM front end. The schematic diagram and a brief description of the proposed system are shown below.
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Technical Description

The above schematic shows the 3 chip solution for pH measurement that has been implemented as an XMOS Startkit shield - see the photo below. The potential of a pH electrode connected at pin 5 of the LMP91200 appears as a potential difference between output pins 12 and 11; these are connected to the + and - differential inputs of a 16 bit ADC (ADC161S626). An AD441 supplies a precision 2.500V reference for the ADC.

A Pt resistance sensing element can be connected at pin 3 of the LMP91200 to allow temperature compensation of the pH readings.

The ADC and pH sensor IC each have 3 wire, SPI-style interfaces to I/O pins on J7 of the XMOS Startkit. Two additional I/O pins provide support for an LCD display. Alternatively, the XMOS Startkit can take pH readings and transfer them back to a host PC running a LabVIEWTM

A pH Calibration/Measurement Using 3 Buffer Solutions

The screen capture opposite shows the LabVIEWTM front panel during a pH calibration experiment.

Here the potential of a pH electrode is being measured when it is immersed in a series of buffer solutions having pH values of 10.00, 7.00 and 4.00 and then finally in a sample : Coca-ColaTM.

The potential at each pH value is noted and then used to make a calibration graph of the pH electrode potential vs pH, as seen below.
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pH Calibration Curve and Coca-ColaTM pH Measurement

The graph opposite shows the linear regression result using the data obtained in the above experiment. The fit parameters provide us with the relationship

V(pH) = 1.04632-0.05925(pH)

Notice that the slope of the line (-59.25 mV/pH unit) is very close to what is expected theoretically from the Nernst equation (-59.16 mV/pH unit).

Measurement of the Coca-ColaTM solution gives V(pH) = 0.8947V, yielding a pH of 2.56.
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