Solubility, Diffusion, and Osmosis
Henry’s law: (1803)
At constant temperature, the amount of gas dissolved in a liquid is proportional to the partial pressure of the gas with which it is in equilibrium. Solubility also depends on the specific vapor and the specific solvent.
With temperature and pressure, we need to define “amount” – as in Henry’s law. Although the “amount” of gas (and its activity) are directly proportional to pressure, this refers to the number of molecules; the higher the pressure, the greater the number of molecules, but they are compressed (Boyle’s law). Volume is a function only of temperature.
If temperature is not constant, the amount of gas or vapor dissolved is inversely proportional to the temperature.
At higher temperatures, gases are more active and have more energy with which to escape from solution. More O2 is dissolved in cool water, and aquatic life increases.
Gases diffuse through the plastic containers of fluids, and air bubbles can form in warmed intravenous lines because heating makes the gases less soluble. The only effective means of elimination is the use of a bubble trap. Blood is particularly affected, as it is stored at a low temperature, which increases the solubility of gases.
Consider ABGs. At high body temperatures, it is possible to get a PaCO2 which is lower than the end tidal PaCO2 recorded on the capnograph, unless the blood-gas technician temperature-corrects the sample.
Bunsen’s solubility coefficient.
Volume of gas, corrected to STP dissolved in unit volume of solvent.
Ostwald solubility coefficient.
Volume of gas dissolved in unit volume at ambient temperature and pressure. In anesthetic practice, these are quoted in tables, assuming a body temperature of 37°C. Note that the volume of gas dissolved is only dependent on temperature, and not pressure (though the number of molecules and the activity of these is pressure-dependent).
These relate the volume of gas or vapor in one phase to that in another phase, such as oil/gas, blood/gas, or oil/blood. The oil/gas solubility coefficient is relevant to anesthetic action because it relates the volume of agent in the gaseous phase (MAC), which determines the activity of the agent, to the volume dissolved in the lipid phase, which relates to the “amount” of anesthetic at the site of action, wherever that might be.
Anesthetic agents with a low blood/gas solubility coefficient act rapidly because the rate of fall in partial pressure is lower than that of a more soluble one, in which the volume of agent transferred from alveoli to blood may be initially greater, but at the expense of a lower partial pressure such that the partial pressure gradient drops. In reverse, at the termination of anesthesia, poorly soluble agents leave blood avidly, and provided ventilation is adequate, create a partial pressure gradient in favor of rapid transfer of agent out of the blood.
Solubilities of common gases in ml/100 ml of water at 40°C
Consider N2 dissolved in blood. If pressure is increased, enough N2 could be dissolved to result in general anesthesia, but if pressure decreases, N2 becomes less soluble, possibly resulting in the formation of gas bubbles within tissues.
Diffusion involves the random movement of molecules into an available space, rather than bulk flow, which is caused by convection currents (as with liquids, such as the movement of local anesthetics in CSF – liquids diffuse very slowly).
The rate if diffusion of a substance across unit area is proportional to the concentration gradient. For gases or vapors, this refers to the tension or partial pressure gradient.
The rate of diffusion of a gas is inversely proportional to the square root of the molecular weight.
(Note: fluids flow through an orifice not according to the molecular weight, as do gases but inversely as the square root of the density. Thus, water vapor flows through a dry orifice faster than does ether vapor, but liquid ether flows through an orifice faster than does water).
A limiting factor in determining the rate of transfer of a gas from one compartment to another is the rate at which it is removed from the compartment with the lower concentration or tension.
Thus, N2 diffuses faster across dry, porous membranes than does N2O. When there are fluid barriers or solutes, however, N2 diffuses more slowly than does N2O because of the former’s limited solubility in fluids, limiting the diffusion gradient.
Also consider CO2 and O2. Both diffuse across the alveolar membranes into the other phase. CO2 is a larger molecule than is O2, and would diffuse 20% more slowly through a dry porous membrane according to Graham’s law; O2 is poorly soluble in water and this limits the capacity of alveolar fluid to hold it. This creates a slight barrier to free diffusion, and means that although CO2 elimination is almost always complete, O2 uptake could be impaired under adverse conditions. Thus the diffusing capacity for CO2 is 20 times greater than that of O2.
The diffusing area of the lung is so vast and blood flow is sufficiently slow compared with normal diffusing capacity of gases or vapors that lung volume is usually not a significant factor in determining the rate of transfer of gases. Inequalities of V/Q are far more important. Pathological conditions, which impose diffusing barriers such as pulmonary edema, or rarely sarcoidosis or fibrosis, may increase the distance through which gases must pass between the gas and blood phases.
An application of diffusion and diffusion gradients is what is termed apneic oxygentation, or supply of oxygen in the absence of ventilation. The affinity of Hb for O2 creates a diffusion gradient in plasma, drawing in more O2 from the alveoli than the CO2 that it returns. This creates a negative pressure which draws gases from upstream, providing some degree of passive ventilation.
Diffusion of gases such as N2O can result in a concentrating effect or second gas effect. The requirements are:
· The gas be delivered in high enough concentration to make a significant difference
· The gas be sufficiently soluble in blood to diffuse relatively rapidly.
Although N2O is generally thought to be relatively insoluble in blood, this is only relative to other anesthetic agents, and not to N2O or O2.
The reverse, called diffusion hypoxia or the Fick effect results from sudden diffusion of N2O out of blood into alveoli diluting O2 and thus its partial pressure if supplementary oxygen is not given.
The nature of membranes may affect diffusing capacity of gases. Anesthetic agents and CO2 diffuse through plastic circuits relatively easily, but N2 does not, as it is poorly soluble in plastic.
Raising the FIO2 can be employed to relieve air accumulated in pneumothoraces or distended bowel. By eliminating N2 from the inspired gas, a diffusion gradient for N2 from cavity to blood is created, and this can help eliminate the volume of trapped air
Substances in dilute solution act as though they were gases. I mol of gas occupies 22.4 liters at STP, and I mole of anything dissolved in 22.4 liters of solute exerts an osmotic force of I atmosphere pressure.
The osmotic force relates to the number of particles in a solution rather than to their size or charge. If there is a barrier to diffusion to one type of particle with others all diffusing easily across a barrier, that particle effectively creates an osmotic force causing fluid to diffuse into that compartment, diluting the concentration of those particles which had flowed freely.
A 1 molar solution contains 1 mole dissolved in 1 liter of solute. However a 1 molar solution of glucose (180 gms/liter) has half the osmotic force of a 1 molar solution of NaCl (58gms/liter) because the latter ionizes into two sets of particles.
A 0.9% solution of NaCl contains 9 gms/liter or is 9/58 molar = 0.15.
This has the same osmotic force as 5%D which contains 50 grams/liter, which is 50/180 molar or about 0.3 molar, or about 300 mosmole/liter. Blood has an osmolarity of 290.
Because it is the number of particles rather than the concentration of electrolytes that determine osmotic pressure, it is common to list these as mmols/liter rather than meq/liter.
Subcutaneous injection of iso-osmolar substances are less likely to be painful than are those with very different osmolarities.
In most of the circulation, proteins constitute a small number of particles, but as they only cross through blood vessels under pathological conditions, they create an osmotic force which draws fluid into the distal end of vessels, balancing the hydrostatic force which causes fluid to flow out of the proximal end of the vessel.
In the brain, except under pathological conditions or in areas such as the hypothalamus or choroid plexus the blood brain barrier does not allow electrolytes to pass into interstitial fluid. As these are far more numerical than are proteins, these constitute the main osmotic force that determines the flow of fluid into or from the cerebral interstitial fluid space.
Pressures and glomerular function.
The force required to overcome resistance to flow of renal tubules is about 35 mmHg. Added to this is the osmotic force of plasma proteins, which is a further 35 mmHg. Thus the hydrostatic pressure in the glomerulus needs to exceed 70 mm Hg for filtration.