i) chemical nature of the molecule

If a molecule is a lipid, it is necessarily lipid soluble and will readily pass through the lipid component of membranes.  That means that, if these substances get into the body, they are not restricted to any one location... they can diffuse to locations anywhere in the body.

Some examples of biological lipids include all of the steroid hormones and all of the lipid soluble vitamins.  Note that all of these molecules are built around a cholesterol "nucleus," so they are all structurally similar.

ii) atomic or molecular formula weight (directly proportional to size)

The smaller a molecule is, the more likely it is to fit through a space in the membrane.  Thus, the smaller the molecular weight of a substance, the more lipid soluble it is...  Neither of the following substances are lipids and neither will diffuse very quickly through a membrane... Nonetheless, molecule B is smaller and will diffuse through a membrane before molecule A will.

iii) valence or charge and sphere of hydration (polar versus nonpolar)

Any substance which is charged (eg. any ion) will attract water molecules.  Water molecules carry no charge but act as if they do.  The H+ containing end of H2O acts as if it is positively charged and the O2-containing end acts as if it is negatively charged.  Thus, the H+ bearing end of H2O is attracted to anions and the O2-bearing end is attracted to cations.  Molecules of H2O will literally form a "ball of water" or "sphere of hydration" that will diffuse along with the ion they surround.  This ball of water makes the ion physically bigger and, therefore, less lipid soluble.  Typically, the greater the valence, the greater the size of the sphere of hydration.

iv) charge density and sphere of hydration

Charge density is a difficult concept to grasp.  Let's suppose we have 2 ions with the same charge, for example, Li+ and K+.  Note that the atomic mass of Li+ (7) is much less than that of K+ (39).  That means that Li+ is smaller than K+.  Nonetheless, K+ and Li+ have the same charge.  Charges move.  As charges move around, sometimes they are close to the outside of the ion and sometimes they are closer to the center of the ion.  Whenever a charge is close to the outside of the atom, it will attract more H2O molecules into its sphere of hydration.  Note (below) tha Li+ is smaller than  K+.  Thus, on average, the charge on Li+ is almost always closer to the outside of the Li+ ion than is the charge on K+.  Because the charge on Li+ is closer to the outside of Li+ more of the time, Li+ ends up having a bigger sphere of hydration than K+.  That means that, even though K+ is bigger than Li+, Li+ is less lipid soluble than K+ because Li+ has a bigger sphere of hydration around itself.  Look back at the Table of the Elements.  Which ion would have a bigger sphere of hydration... Na+ or K+?  Which of these ions do we try to reduce in the diet of persons with high blood pressure (hypertension)?  Wouldn't the ion with the biggest sphere of hydration be the one that contributes the most to plasma volume and, therefore, increases blood pressure the most?

v) prevailing concentration gradient (slope or steepness of the gradient)

If it is possible for a substance to get across a membrane, the speed at which it diffuses through the membrane will be directly related to the concentration gradient.  Solutes diffuse from an area of high solute concentration to an area of low solute concentration.  If glucose was higher outside cells than inside cells, which direction would the glucose concentration gradient be driving the glucose?  That's right, into the cell.  Suppose we had a child with diabetes mellitus I and we wanted to reduce their plasma glucose level.  We ask them to exercise more frequently.  When they exercise, what happens to the glucose inside their cells.  That's right, they burn it!  If they burn glucose inside their cells, what are they doing to the glucose concentration gradient?  That's right, by reducing the amount of glucose inside their cells, they are making the glucose gradient steeper so that glucose will enter their cells more easily, in turn reducing their plasma glucose level.

vi) pKa of the diffusing substance and the pH of the environment

Let's look at aspirin.  Aspirin is a weak acid with a pka of 3.  Recall that pka refers to the pH at which a substance is 50% ionized and is also the pH at which a substance will act optimally as a buffer.  The chemical formula for aspirin is C9H8O4.  Thus, aspirin will ionize in the following manner in aqueous solution...

C9H8O4  <---->   H+ + C9H7O4-

Aspirin is a weak acid with a pka of 3.  Recall that the stomach is an acidic environment.  Gastric juices, for example, may have a pH of 1.0 and stomach contents (chyme) may have a pH of 2.0.  The presence of H+ in the stomach effectively adds H+ to the right side of the equation, above.  Addition of H+ to the right side of the equation will drive the equation to the left, holding most of the aspirin in the unionized form.   The unionized form (C9H8O4) is more lipid soluble than the ionized form (C9H7O4-) as the unionized form does not have a sphere of hydration.  Normally, this would mean that acidic substances are absorbed better in the acidic environment of the stomach than in the alkaline environment of the duodenum.   However, when the aspirin concentration in the stomach gets high enough, aspirin tends to precipitate out of solution and forms globs of aspirin (called pharmacobezoars) which are not well absorbed.  By the same token, if a person was suffering an acidosis, and took some aspirin, the acidosis would help hold the aspirin in the unionized form in the body.  The acidosis, then, would promote the distribution of aspirin throughout the body, as the aspirin would be held in the more lipid soluble unionized form because of the elevated H+ everywhere in the body.

vii) route of administration

The route of administration of a drug does not really affect the lipid solubility of a drug.  The route of administration does affect how long it will be until the drug appears in the bloodstream.  A drug or nutrient is not considered to have entered the body until it has been absorbed into the bloodstream.  If a drug is injected directly into the bloodstream, it has instantly entered the body.  If a drug is injected into a muscle, taken orally or applied topically to the skin, it may take longer to be absorbed into the bloodstream.