# Vapor of a volatile substance in equilibrium with a fluid

1. Jun 23, 2009

### MGren

Hey!

I'm in a research group in Gothenburg and we're planning a study with volatile anaesthetics. The problem is as follows:

In the clinical setting (operation room) this volatile anaesthetic is administred as a volume% of the inhaled gas. What we're going to do is take a part of this anaesthetic in it's liquid phase (a mass) and mix it with blood (volume).

So, what we need to do is to find a suitable way of calculating what blood concentration in mass/volume that an anaesthetic inhaled at X volume% causes.

I can tell you how we have reasoned:
Specific volume = (RT/PM) for an ideal gas, where R = Avogadro's constant, T = temperature, P = pressure och M = Molecular mass.

If I calculate it right, the unit is m^3/g

Density = 1/specific volume.

Densiteten is thus g/m^3 which is the same as a measure of the concentration of substance X in a solution containing only substance X.

If 2% of the inhaled volume of gas is composed of substance X, then the concentration of X X in that volume of gas would be 0,02 x the density of X.

The gas is the lungs (it is inhaled in the clinical setting) is at equilibrium with the gas in the blood (liquid) so that the partial pressure is the same in both.

The gases also have a property called distribution coefficient (D) which tells you the ratio (Concentration in blood) / Concentration in the gas.

So:

Volume% * Density of Substance X * Distribution coefficient, should equal a reasonable blood concentration in mass/volume.

What do you think?

The actual substances being used are: Sevoflurane and Isoflurane.

2. Jun 23, 2009

### chemisttree

If you are going to assume ideal gas behavior, then the volume% will also be equal to molar%, yes? Can you calculate molar fraction from that? For an ideal gas, V=nRT/P. For partial pressure, the partial pressure of the fluranes will be equivalent to the total pressure times their molar fraction, yes?

What are your units for the distribution coefficient?

3. Jun 23, 2009

### MGren

The distribution coefficient I think is just a ratio of the concentration in blood/concentration in gas, so it wouldn't have a unit.

There has been some study done on the relation to ideal gas behaviour for these drugs and I think it did vary a bit with temperature, but it was about right.

I guess the second thing I need some help in understanding more fully is the behaviour of a gas in relation to a liquid. It makes somewhat sense that the partial pressures should be the same when they have equilibrized with one another, but it makes less sense that the concentrations would be the same... but maybe that's where the blood/gas distribution coefficient comes into play.

4. Jun 23, 2009

### chemisttree

Sorry, I missed where you stated, "...distribution coefficient (D) which tells you the ratio (Concentration in blood) / Concentration in the gas."

Yes, definitely the coefficient handles all of that. Keep in mind that the results of your calculation will at best describe the upper limit of concentration for the two fluranes since such a simple model doesn't assume any elimination pathways.

Given that the distrubution coefficient is given, what value is knowing the partial pressures in the gas or the blood?

I would assume that the distribution coefficient could be used in the equality:

Molar fraction X in gas = distribution coefficient (concentration Xblood/concentration Xgas) * Molar fraction of X in blood

I would also assume the the molar mass of blood is roughly the same as 9% saline. That's just easier for me to visualize (rather than the specific volume, density terms).

Have you read the work of Lerou, J. G. C., et al in Anesthesiology, 75, 345-355 (1991), in Anesthesiology, 75, 230-237 (1991) and in Anesthesiology, 79, 932-942 (1993)?