User talk:Plumbago/Sandbox 1

Seawater
As part of its operational definition of the pH scale, the IUPAC define a series of buffer solutions across a range of pH values (often denoted with NBS or NIST designation). These solutions have a relatively low ionic strength (~0.1) compared to that of seawater (~0.7), and consequently are not recommended for use in characterising the pH of seawater (since the ionic strength differences cause changes in electrode potential). To resolve this problem an alternative series of buffers based on artificial seawater was developed. This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is the referred to as the total scale, often denoted as pHT.

The total scale was defined using a medium containing sulphate ions. These ions experience protonation, $$H^{+} + SO_{4}^{2-} \leftrightharpoons HSO_{4}^{-}$$, such that the total scale includes the effect of both protons ("free" hydrogen ions, $$H^{+}_{F}$$) and sulphate ions:


 * $$ [H^{+}_{T}] = [H^{+}_{F}] + [HSO_{4}^{-}] $$

An alternative scale, the free scale, often denoted pHF, omits this consideration and focuses solely on $$[H^{+}_{F}]$$, in principle making it a simpler representation of hydrogen ion concentration. Analytically, only $$[H^{+}_{T}]$$ can be determined, so $$[H^{+}_{F}]$$ must be estimated using the $$[SO_{4}^{2-}]$$ and the stability constant of $$HSO_{4}^{-}$$ (= $$K_{S}^{*}$$):


 * $$ [H^{+}_{F}] = [H^{+}_{T}] - [HSO_{4}^{-}] = [H^{+}_{T}] \left( 1 + [SO_{4}^{2-}] / K_{S}^{*} \right) ^{-1}$$

However, it is difficult to estimate $$K_{S}^{*}$$ in seawater, limiting the utility of the otherwise more straightforward free scale.

Another scale, known as the seawater scale, often denoted pHSWS, takes account of a further protonation relationship between hydrogen ions and fluoride ions, $$H^{+} + F^{-} \leftrightharpoons HF$$. Adding this subtlety changes the concentration of $$H^{+}_{T}$$ to:


 * $$ [H^{+}_{T}] = [H^{+}_{F}] + [HSO_{4}^{-}] + [HF] $$

However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulphate ions occur at much greater concentrations (> 400 times) than those of flouride. Consequently, for most practical purposes, the difference between the total and seawater scales is very small.

The following three equations summarise the three scales of pH commonly used in oceanography :


 * $$ \rm{pH}_{F} = - \log\left([H^{+}]_{F}\right)                                                $$
 * $$ \rm{pH}_{T} = - \log\left([H^{+}]_{F} + [HSO_{4}^{-}]\right) = - \log[H^{+}]_{T}            $$
 * $$ \rm{pH}_{SWS} = - \log\left([H^{+}]_{F} + [HSO_{4}^{-}] + [HF]\right) = - \log[H^{+}]_{SWS} $$


 * pHF = - log[H+]F
 * pHT = - log([H+]F + [HSO4-]) = - log[H+]T
 * pHSWS = - log([H+]F + [HF]) = - log[H+]SWS


 * $$H^{+} + SO_{4}^{2-} \leftrightharpoons HSO_{4}^{-}$$

Seawater (v2)
In chemical oceanography pH measurement is complicated by the chemical properties of seawater, and several distinct pH scales exist.

As part of its operational definition of the pH scale, the IUPAC define a series of buffer solutions across a range of pH values (often denoted with NBS or NIST designation). These solutions have a relatively low ionic strength (~0.1) compared to that of seawater (~0.7), and consequently are not recommended for use in characterising the pH of seawater (since the ionic strength differences cause changes in electrode potential). To resolve this problem an alternative series of buffers based on artificial seawater was developed. This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is the referred to as the total scale, often denoted as pHT.

The total scale was defined using a medium containing sulphate ions. These ions experience protonation, H+ + SO42- ⇌ HSO4-, such that the total scale includes the effect of both protons ("free" hydrogen ions) and hydrogen sulphate ions:


 * [H+]T = [H+]F + [HSO4-]

An alternative scale, the free scale, often denoted pHF, omits this consideration and focuses solely on [H+]F, in principle making it a simpler representation of hydrogen ion concentration. Analytically, only [H+]T can be determined, so [H+]F must be estimated using the [SO42-] and the stability constant of HSO4-, KS*:


 * [H+]F = [H+]T - [HSO4-] = [H+]T ( 1 + [SO42-] / KS* )-1

However, it is difficult to estimate KS* in seawater, limiting the utility of the otherwise more straightforward free scale.

Another scale, known as the seawater scale, often denoted pHSWS, takes account of a further protonation relationship between hydrogen ions and fluoride ions, H+ + F- ⇌ HF. Adding this subtlety changes the concentration of H+T to:


 * [H+]T = [H+]F + [HSO4-] + [HF]

However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulphate ions occur at much greater concentrations (> 400 times) than those of flouride. Consequently, for most practical purposes, the difference between the total and seawater scales is very small.

The following three equations summarise the three scales of pH:


 * pHF  = - log [H+]F
 * pHT  = - log ( [H+]F + [HSO4-] )        = - log [H+]T
 * pHSWS = - log ( [H+]F + [HSO4-] + [HF] ) = - log [H+]SWS

In practical terms, the three seawater pH scales differ in their values by up to 0.12 pH units, differences that are much larger that the accuracy of pH measurements typically required (particularly in relation to the ocean's carbonate system). Since it omits consideration of sulphate and fluoride ions, the free scale is significantly different from both the total and seawater scales. Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly.