# 1.3: The Hydrogen Ion

## 1.3.1: Hydrogen Ion in Solution

Bare protons (ie H+) do not exist in solution. Protons are associated and react with surrounding water molecules. This is sometimes represented as H3O+ (the hydronium ion) but this one-to-one relationship is also inaccurate. Stewart suggests that the most accurate representation is {H:(H2O)n}+ to illustrate the reaction or interaction of H+ with water molecules. This would be extremely inconvenient to use clinically so we continue to speak of the hydrogen ion (H+) simply out of convenience. This is an acceptable convention but remember that H+ is a symbol for a metaphor (Stewart) and does not exist in solutions in that form. This "metaphorical H+" is extensively used and this convention is continued here.

## 1.3.2: Hydrogen Ion Activity

Chemists speak of ideal solutions which have certain predictable physicochemical properties. However, real solutions exhibit various degrees of non-ideal behaviour. This deviation from ideal behaviour is due to interactions between the molecules in the solution and includes both solvent-solute interactions and solute-solute interactions. The magnitude of this interaction (and the deviation from ideal behaviour) is higher with higher particle concentration in the solution and with ions as compared to non-charged species.

The idea of 'effective concentration' or 'activity' was introduced by Lewis to deal with this problem. Activity indicates how many particles seem to be present in the solution and is different from how many actually are present. Activity can be thought of as applying a correction factor to the concentration. Activity is related to concentration by the activity coefficient:

### Definition of Activity

$a_{x} = g \cdot [x]$

where:
ax = activity of substance x in the solution
g = activity coefficient of x
[x] = concentration of substance x in the solution

The activity coefficient of a solute is constant in any particular given solution but its value can change if the properties of the solution are changed (eg by changing the ionic strength or the temperature). If the relationship between concentration and activity is plotted on a graph, it is not linear. It depends on the type of solvent and the type and concentration of the various solutes present in the solution. In an ideal solution, the activity coefficient is one. The activity coefficient also approaches unity as non-ideal solutions become more and more dilute.

It is usual in discussions of acid-base balance to assume the activity coefficient of solutes is equal to one and use concentrations nstead of activities. This is obviously not correct but the errors introduced are usually small and not clinically relevant. Some measurement techniques (such as ion selective electrodes) measure activities and others measure concentration.

## 1.3.3: pH

The glass electrode for H+ is an ion-selective electrode (ISE) widely used in clinical medicine. The potential that develops in this electrode is proportional to the log of the hydrogen ion activity in the test solution. The term used is pH which is now defined as:

### Definition of pH

$pH = - \log_{10} aH^{+}$

or

$aH^{+} = 10^{-pH}$

where aH+ is activity of H+

The term pH (in that exact form - lowercase p, uppercase H) was first used by WM Clark (inventor of the Clark oxygen electrode) in 1920. (see: Compact Oxford English Dictionary) However the concept was invented by the Danish chemist Soren Peter Sorensen in 1909 to refer to the negative log of hydrogen ion concentration; he used the term PH in his original paper. He called it the Wasserstoffionenexponent (German for hydrogen ion exponent as hydrogen is "wasserstoff" in German).

There are several versions of what the 'p' means. In the common version, the p refers to the German word potenz (power in the sense of being an exponent) so pH means 'power of hydrogen'. The power referred to is the power of 10 used as the base for the log and not to the acid strength of the solution. Recent research suggests the 'p' was used as a result of how he arbitrarily labeled the 2 electrodes used in his experiment as 'p' and 'q', and the measurements derived from these electrodes included the letters p and q.

Note that the symbol p is used in two contexts in acid-base discussions:

• p meaning the negative log of as in pH, pK, pOH
• p meaning partial pressure as in pCO2

pH is regarded as a 'dimensionless representation of the [H+]' (Kellum, 2000) and is not itself a concentration. Because of this, pH does not have any units: it is just a number. There is a loose use of the term pH units as a device to assist explanation of some concepts. For example, the maximal pH gradient across the gastric mucosa is 6 pH units ( ie 7.4 minus 1.4 ) representing a hydrogen ion concentration gradient of 106 (ie 1,000,000). By contrast, the hydrogen ion gradient across the renal collecting duct when maximally acidic urine (pH 4.5) is produced is about 3 pH units (ie gradient of 103 ). The term pH unit is considered to mean unit change in pH in most contexts. The term pH concentration is simply wrong and should never be used.

Theoretically, values of pH could range from -infinity to +infinity but the practical limits in aqueous solutions are from -1.2 to +15 reflecting [H+] varying from 15 to 10-15 moles/litre. Concentrated hydrochloric acid used by chemists has a pH of -1.1. Values in human fluids range from extremely acid (pH 0.87 for HCl secretion into the intracellular canaliculus of gastric parietal cells) to the alkaline values of bile and pancreatic juice. The reference range for arterial pH is 7.36 to 7.44 and the limits of survival cover a ten fold range of H+ ( from 160 to 16 nmoles/l which is pH 6.8 to 7.8).

## 1.3.4: Which is Best: pH or [H+] ?

There is a continuing discussion about the most appropriate symbol to represent the acidity of body fluids: pH or [H+]. In practical terms it is best to be most familiar with what is used in your local pathology laboratory. The current recommendation of the relevant international body (the IUCC) is to use pH.

The advantages of pH compared to [H+] are:

• It is the traditional symbol and remains in wide use
• It is related to the activity of H+ (rather than concentration) or more specifically the log of H+ activity and this is what physiological systems seem to respond to.
• It is what is measured by the pH electrode (ie activity of H+)
• The alternative [H+] is not correct because the activity coefficient is ignored
• Free H+ (ie bare protons) are not the form really present in solution anyway.

• It is a contrived symbol which represents a double non-linear transformation of [H+] (ie the log of a reciprocal)
• It is difficult to learn and understand
• It disguises the magnitude of changes in [H+]

## 1.3.5: A Simple Way to Convert between pH and [H+]

Changes in the [H+] by a factor of 2 cause a pH change of 0.3 -this provides us with a simple way to determine various pH-[H+] pairs of values if we know that pH 7.4 is 40 nmoles/l. For example: a [H+] of 80 nmoles/l is a pH of 7.1 - inspection of the table above shows a value of 79 so this simple method is pretty accurate. This useful relationship holds because log 2 is 0.3 so a doubling or a halving of [H+] means a change in pH by 0.3 either up or down.

## Relationship between pH & [H+]

pH

[H+]
(nanomoles/l)

6.8

158

6.9

125

7.0

100

7.1

79

7.2

63

7.3

50

7.4

40

7.5

31

7.6

25

7.7

20

7.8

15

This doesn't allow you to mentally calculate every pH and [H+] value but the 4 basic pairs which are useful and easy to memorise are:

• pH 7.4 is 40 nM
• pH 7.0 is 100 nM
• pH 7.36 is 44 nM
• pH 7.44 is 36 nM

The last two values above are the normal range of pH values which is easy to remember because the relationship between the [H+] and the decimal part of the pH (ie the normal range of 7.36 to 7.44 is a [H+] range of 44 to 36 nM. Now you can work out that a pH of 7.06 has a [H+] value of 88nm as this is double that at 7.36 (ie 44nM) - and so on.

## References

1. Norby J. The origin and meaning of the little p in pH. Trends in Biochemical Sciences 2000; 25: 36-37.