Osmolarity, osmolality, tonicity, and the reflection coefficient

This chapter is relevant to Section I1(ii) of the 2017 CICM Primary Syllabus, which expects the exam candidates to "define osmosis, colloid osmotic pressure and reflection coefficients and explain the factors that determine them".  It also touches upon Section I3(ii), "Describe the measurement of osmolality". For the majority of these concepts, an in-depth understanding should be attractive to trainees, because the concepts are central and one cannot walk two steps in the ICU without tripping over one of them. On the other hand, it would be pointless to read extensively about any of this, as it has never come up in any of the written exam papers, and does not appear to be a common viva station. An inoffensively short summary of the important concepts is left here to resolve this conflict for the reader, who would not need to read any further. 

Still, if reading extensively about things is what one compulsively does, there are some good resources for this subject. Caon (2008) is probably the best, most comprehensive overview, written in an accessible language. Also, there is no way one could be exploring these topics without starting from or finishing with anaesthesiamcq.com

Osmolarity

Osmolarity is usually crudely defined as

 the measure of solute concentration per unit volume of solution

Or, from the Oxford dictionary, 

The concentration of a solution expressed as the total number of solute particles per litre.

The most important part of this concept to internalise is that

• it a measurement of something in a volume, and
• it specifically refers to the number of dissolved particles without regard for what kind of particles they are, i.e. this is a colligative property. 

For this reason, the term osmoles is used to measure this property, as it refers to the osmotic activity of a solute concentration. An osmole is the amount of substance that must be dissolved in order to produce an Avogadro's number of particles (6.0221 × 10²³). For substances which do not dissociate, the molarity and the osmolarity will be the same, whereas for substances that are ionised the osmolarity will be the molarity multiplied by the number of dissociated parts, eg. for sodium chloride the osmolarity will be doubled.

Osmolarity was "called "osmolarity" because "molarity" was formerly used for substance concentration" (Siggaard-Andersen et al, 1981).  IUPAC have been trying to kill this word since 1997, as they would prefer for us to use the term "osmotic concentration":

Osmotic concentration: Product of the osmolality and the mass density of water.
Formerly called osmolarity.

And theoretically for fundamental terms like this the IUPAC "Gold Book" Compendium of Chemical Terminology should be viewed as the definitive source, as it is literally their job to define such terms, but the word osmolarity still keeps showing up in textbooks, exams, scientific papers, in the published disagreements of professors and the casual plagiarism of textbook authors. Because CICM exams are written by people who are usually short on time, we can expect their research into the deep lore of chemical nomenclature to be limited and unenthusiastic. The definition they use for their marking rubric will likely be the one that comes up on the top results of a Google search, or the one made available by popular physiology authors. The Australian ICU trainee should therefore be prepared to memorise and regurgitate the Kerry Brandis definition of osmolarity, which is:

Osmolarity of a solution is the number of osmoles of solute per litre of solution

This is probably as good as you're going to get. Actual textbooks will frequently lead you far astray. Caon (2008)  identifies multiple other such errors in popular physiology resources.

Osmolality

Again, IUPAC have a definition for this, and again it is perfect for industrial chemistry and disappointing for a physiology teacher:

Osmolality: Quotient of the negative natural logarithm of the rational activity of water and the molar mass of water.

To unpack this would require a terrifying digression into other definitions (eg. a_w, the rational activity of water) , and so instead it is still better to turn to other well-known sources:

Osmolality of a solution is the number of osmoles of solute per kilogram of solvent

The main difference between this and the definition of osmolarity is that the definition uses the mass, rather than the volume, of the solvent. There are several reasons for this, of which the main is the dependence of solvent volume on things like temperature. Mass, in contrast, is dependably constant.

Measurement of osmolality

You don't usually measure osmolarity, owing to the meaninglessness and inconsistency of the volume metric, but osmolality can definitely be measured by a variety of instruments. For this, you would dust off the old automated osmometer. These devices usually measure the depression of the freezing point of the sample, which is another colligative property. Sweeney & Beauchat (1993) describe the technique and its limitations in more detail. For the casual browser, the central arguments of their excellent paper can be oversimplified as follows:

• Osmolality and osmotic pressure can be predicted from the concentrations of solutes added to a solution
• However, the van 't Hoff equation loses its predictive value unless the solution is extremely dilute.
• This is because solute particles in the solution will interact in a non-colligative way (i.e. the interaction will depend on their molecular shape, charge, size, etc)
  • For this reason, the calculation of osmolality can never replace the measurement of osmolality.  For example, the calculated osmolality of normal saline is 300 (150 mOsm of sodium and 150 mOsm of chloride), and yet its measured osmolality is 286, which resembles the measured plasma osmolality. The reason for this discrepancy is partly the interaction between the ionised sodium and ionised chloride, and partly the failure of some of the sodium chloride molecules to fully ionise (Williams et al, 1999, in their answer to Swank). For basically all solutions in clinical use, some discrepancy like this will exist.
• Fortunately, the addition of solute to a solvent changes its properties predictably: the freezing point and vapour pressure are lowered, and the boiling point and osmotic pressure are increased. 
• This change occurs for all colligative properties, which means from the measurement of the change of one colligative property, others can be extrapolated
• The relationship between the freezing point and the osmolality is complex and non-linear, but still predictable enough that the measurement of the freezing point of the sample can be used to approximate its osmolality. In its simplest form, 
  
  Osmolality = ΔT / -1.86
  
  where ΔT is the measured depression of the freezing point, and -1.86 is the cryoscopic constant for water, which is just another way of saying that one mole of solute added to 1kg of water will depress its freezing point by 1.86º K.

Incidentally, when one applies the common equation to human plasma in order to determine whether their patient has ingested a massive faceful of antifreeze or methylated spirits, the equation they use

([Na]× 2 ) + [Glucose] + [urea]

typically involves using lab-reported biochemistry values which are indexed to volume, rather than mass (i.e. that [Na] is reported as mmol/L). Thus, it is the osmolarity you are calculating here, not osmolality. But then,  to calculate the gap, you send a sample to the lab for a measured value, which will be returned to you as osmolality, i.e mOsm/kg. How can you subtract one from the other, and call the result an "osmolar" gap with a straight face? It boggles the mind. Fortunately, the difference between the calculated and measured osmolality values in human plasma is relatively small (Hooper et al, 2014, found one equation that was always within 2% of the measured value).

Tonicity

The standard definition of tonicity usually incorporates some mention of osmotic pressure or osmolality difference between solutions. 

Tonicity is the measure of the osmotic pressure gradient between two solutions.

Caon (2008) further elaborates by calling it "a semi-quantitative descriptor of the concentration of one solution compared to another".  It is also occasionally called "effective osmolality", which brings us to the next point: unlike osmolarity, tonicity is only influenced by solutes that cannot cross this semipermeable membrane, because these are the only solutes influencing the osmotic pressure gradient. This produces the distinction between "effective" and "ineffective" osmoles. Ineffective osmoles are those that are able to cross the semipermeable membrane and equilibrate in both solutions which are being compared, which means they cannot contribute to the osmotic pressure gradient.

Usually, when the discussion of tonicity comes up in textbooks, urea and glucose are offered as examples of such "ineffective" osmoles, as they are supposed to equilibrate effortlessly across body fluid compartments. This is partially true, in the sense that given enough time they will achieve an equilibrium. Time is the key factor here. Rapid changes in either of these molecules will give rise to major osmotic shifts, producing cerebral oedema in HHS, as one example.

The bottom line is that you can have solutions separated by a membrane that have equal osmolality on either side of the membrane, and there will be no osmotic pressure across that membrane, which makes these solutions isotonic, i.e. there is no osmotic pressure gradient between them. However, it is also possible to have iso-osmolar solutions which are not isotonic. For example, 5% dextrose, when infused, is iso-osmolar with the body fluid compartments. Its osmolality is the same as the osmolality of the cellular contents (about 300mOsm/L) However, because dextrose penetrates the cells so easily, it cannot contribute to tonicity. Thus, the infused dextrose is iso-osmolar but hypotonic.

Reflection coefficient, σ

They ask for this in the syllabus document, but not in the exam, making you wonder how much you really need to know about it. In short, from looking at the van 't Hoff equation, one immediately realises that it would not work properly as soon as the membrane separating the two solutions becomes even remotely imperfect, i.e. slightly permeable, allowing some of the solutes to leak through. On closer inspection, every membrane in biology is imperfect, which means that the van 't Hoff equation will (sometimes, massively) overestimate the osmotic pressure gradient between fluid compartments. The reflection coefficient is an empirically derived value which is a ratio of the measured and predicted osmotic pressures,  and which is different for every pair of solute and membrane. The usual equation to describe it is:

σ = (Π_eff) / (Π_RTC)

where Π_eff  is the effective osmotic pressure which is measured, and  Π_RTC is the theoretical osmotic pressure which would be expected from the system if the semipermeable membrane was ideally semipermeable. In this fashion, the reflection coefficient is a parameter that describes the departure of a membrane from perfect semipermeability. A reflection coefficient of 1.0 represents a perfectly solute-impermeable membrane, whereas a value of 0 represents a membrane that is perfectly leaky (i.e. as far as that solute is concerned, there may as well be no membrane).

What, might one ask, is the point of knowing this? One excellent paper which reflects on some of these uses of the reflection coefficient is Adamski & Anderson (1983).  The reflection coefficient value is useful for a number of practical and experimental purposes in medicine and physiology. For example, you could use it to calculate the expected flow of solvent across a membrane, if the σ values are known. Or, from the σ value, one could determine the porosity of a membrane, and from the change in σ values of solutes with different molecular mass you could determine the size of those pores.  In this fashion, the reflection coefficient factors into the calculation of the glomerular filtration rate or the fluid exchange in the microcirculation (as it slots into the Starling equation).