(8/18/10) - Diffusion and Osmosis

Fick's First Law
'''1. Write Fick’s first law. Explain what the symbols mean. Describe the purpose for which it is used.'''

J = -DA (dC/dx); where J is the net flow (mole/sec), D is the diffusion coefficient (different for each substance; cm2/sec), A is the area of the membrane (cm2), and (dC/dx) is the concentration gradient ((mol/cm3)/cm). This equation is used to determine how fast a substance diffuses across an area.

Stokes-Einstein Equation
2. Write the Stokes-Einstein Equation and explain the meaning of the symbols. Explain the purpose for which it is used.===

D = kT/6πrη; where D is the diffusion coefficent (cm2/sec), k is Bolzman's constant, T is the absolute temperature, r is the radius of the molecule, and η is the viscosity of the fluid. This equation is used to demonstrate that D is directly proportional to the cubed root of the radius or a spherical, so that a molecule that is 8 times the volume than another will diffuse only half as fast. We can also estimate the radius of a molecule if we know the diffusion coefficient.

Einstein Relation
3. Write the Einstein Relation and explain the meaning of the symbols. Explain the purpose for which it is used.

(Δx)2 = 2Dt; where Δx is the average distance of a molecule from the same starting point, D is the diffusion coefficient, and t is time (sec). This equation is used to determine the amount of time it would take a molecule to diffuse across a given distance. In general, molecules diffuse very rapidly over a small distance, but take much longer to diffuse over a larger distance.

Membrane Permeability and Substance Solubility
4. Explain why the membrane permeability of a substance is proportional to the solubility of the substance in non-polar solvents.

Since the interior of a membrane is hydrophobic, those molecules that diffuse more easily in non-polar solvents will diffuse across the membrane more quickly than those that do not easily dissolve in non-polar solvents. The concentration of hydrophobic molecules on the interior of the membrane is higher, so it is easier to diffuse.

High Permeability of Water
5. Explain what is responsible for the high permeability of biological membranes to H2O.

Water is a relatively small molecule, so it can diffuse more easily across a biological membrane than would otherwise be expected. There are also channels in most biological membranes called aquaporins which facilitate the diffusion of water (and other small, polar solutes, such as methanol) across the membrane.

Water Soluble substances with MW>200
6. Explain why membranes are essentially impermeable to water-soluble substances with MW > 200.

Due to the hydrophobic nature of the interior of plasma membranes, water-soluble substances cannot dissolve easily into the membrane. Furthermore, the larger the molecule, the slower its rate of diffusion. As such, very large water-soluble substances are essentially impermeable to the plasma membrane.

Osmosis, Osmotic Pressure, and Ideal Semipermeable Membranes
1. Define osmosis, osmotic pressure, and ideal semipermeable membrane.

Osmosis is the movement of water across a semi-permeable membrane from an area of high concentration to an area of low concentration. In other words, from a solution where the solute is in low concentration to a solution where the solute is in high concentration.

Osmotic Pressure is the pressure which must be applied to a solution to just prevent water from entering the solution across a semi-permeable membrane.

An ideal semi-permeable membrane is one which is permeable to water, but not to any solutes.

van't Hoff's Law
2. Write van’t Hoff’s Law and' the meaning of the symbols. Explain the purpose.'

π = iRTc, where π is the osmotic pressure, i is the # of molecules or ions into which a dissolved compound dissociates, R is the ideal gas constant, T is the temperature in K, and c is the concentration (mol/L). This equation determines the osmotic pressure of a solution, but is only strictly true for very dilute solutions.

Osmotic Coefficient
3. Describe the osmotic coefficient? Explain the reason why it is needed.

The osmotic coefficient is used in van't Hoff's Law when the solution is not very dilute.

Osmolar Solution
'''4. Define a 1 osmolar solution? Indicate its freezing point, and osmotic pressure at 0 'ｺ'C.'''

A 1 osmolar solution has one osmole of particles per liter of water in solution and is equal to Φic. It has a freezing point of -1.86 degrees Celcius. The osmotic pressure at 0 degrees Celcius would be 22.4 atm.

Isotonic Solutions
'''5. Define an isotonic solution of NaCl. '''

An isotonic solution of NaCl is one in which the molarity is equivalent to what is placed in the solution. For instance, a red cell has an molarity of 0.154 M, so an isotonic solution of NaCl would also be 0.154 M.

Hypertonic and Hypotonic Solutions
6. Describe what happens to the volume of a red blood cell when it is transferred from isotonic NaCl to a NaCl solution whose concentration is greater or less than isotonic.

In a hypertonic solution (that is, one in which the concentration is greater than isotonic), the cell would shrink due to water leaving the cell. In a hypotonic solution (that is, one in which the concentration is less than isotonic), the cell would lyse due to water entering the cell in amounts greater than what the cell could hold.

Reflection Coefficient
'''7. Define the reflection coefficient. Explain how it is used. Determine the reflection coefficient of an ideal semipermeable membrane to glycerol.'''

The reflection coefficient describes the rate of osmosis when solutes are more permeable to the membrane. When a solute is more permeable to a membrane, it does not cause as much osmotic flow. It is described as the ratio of observed osmotic flow to theoretical osmotic flow. σ = 1 – PS/PW, where PS is the permeability of the membrane to the solute, and PW is the permeability of the membrane to water. Since an ideal semipermeable membrane is completely permeable to water, and not at all permeable to any other solute, the reflection coefficient of glycerol would be 1.

Jv = σLPΔπ predicts the osmotic water flow, where Jv is the osmotic water flow, LP is the hydaulic conductivity, and pi is the osmotic pressure.