Diffusion of Solvent Through a Membrane
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Diffusion of solvent through a membrane
For this experiment you can design your own experiment where a membrane is separated between a solution and a pure solvent (Read the section on The Thermodynamics of Osmosis given in page 2). You can measure the permeability of the solvent through the membrane and/or other thermodynamics properties of the system.
The membrane supplied in the CME lab is dialysis membrane tubing which is a selectively permeable regenerated cellulose commonly used to demonstrate the fundamentals of osmosis and diffusion. Pores in the membrane permit the passage of water, most ions, and small molecules in solution. Particles of high molecular weight, such as polysaccharides, starch, and protein are restricted. When the membrane is utilized in laboratory dialysis or ultra filtration, normal molecular weight cut-off is reported to be about 13,000. However, molecular weight is not the only determining factor. Other factors affecting molecular transfer or membrane permeability include molecular size and shape, pH of the solution used, and variations in the porosity produced by tension on the membrane. Once thoroughly wetted, the membrane must not be allowed to dry. Wetted membrane may be stored in water containing 0.1% benzoic acid.
(Dialysis membrane tubing can be obtained from Amico Scientific Corp, 7231-A Garden Grove Blvd., Garden Grove CA 92941, (714) 894-6633)
Diffusion Through a Semi-permeable Membrane
1 Soak the needed length of dialysis tubing in de-ionized water for about 30 seconds. Open the tubing by rolling it between thumb and index finger; immediately proceed as follows.
To demonstrate the effect of water diffusion (osmotic) pressure, use about 20 cm (8 in.) of tubing. Knot one end tightly and fill to about 5 cm from the top with an 80% sugar solution. Insert the end of a graduated 1-ml pipet into the opening of the tube and secure tightly in place with a rubber band. Position the filled tube in a vessel of water and hold the pipet upright with a clamp on a support stand. Recond and plot the rise of solution in the pipe at 2 to 5-minute intervals. Rate of rise is proportional to the osmotic pressure generated by the solution in the dialysis tubing.
Report Format 1) Title Page (See page 9) + Table of Contents (10%) 2) Research and summarize in your report the permeability of solvent to various solutions. Summarize this research with proper referencing.(10%) 3) Permeability measurement: Research & summarize in your report methods for measuring the permeability of solvent. Use proper referencing.(15%) 4) Experimental Plan: Your report should include an appropriate drawing and description of the procedure that you used to determine the permeability of solvent in various solutions. Your experimental plan should include studying the following: different solutions and temperatures. What about the effect of temperature? What were the ambient pressure and the pressure at both sides of the membrane? Is it important to know these pressures & the temperature? Explain how you assured that temperature
2 was held constant or you accounted for the variation in temperature during an experiment in your data analysis. (15%) 5) Tabulate your experimental data (an appropriate measurement & temperature & ambient pressure vs time) in a spreadsheet & apply appropriate regression analysis. Based on this statistical analysis what is the +/-% uncertainty in your reported permeability of the solvent in various solutions. (35%) 6) Recommendation: Describe how you could improve your experimental procedure. (15%)
3 1. The Thermodynamics of Osmosis
We will consider the equilibrium state of liquid mixtures in two regions separated by a membrane that is permeable to some of the species present and impermeable to others. This situation is illustrated in Figure 1.-1 where a semi-permeable membrane separates regions A that contains a nondiffusing solute and region B that contains only water.
Figure 1.-1 Osmotic pressure = PA PB Agh
Water will diffuse from region B into region A until the chemical potential or fugacity of water on each side of the membrane is the same. This phenomenon is called osmosis and the pressure difference between regions A and B at equilibrium is the osmotic pressure of region A. The chemical potential of species i , i, is defined by the following relations
i = = = =
In these expressions, the subscript j denotes the moles of every species except i is a constant. The definition can be obtained from the following diagram
4 We now want an expression that gives us the solution osmotic pressure as a function of the solute concentration. At equilibrium
A B (T, P , xs) = (T, P ) (1.-1)
B A where (T, P ) is the fugacity of water as a pure component and (T, P , xs) is the fugacity of water as it exists in solution with solute at mole fraction xs. A similar equation is not written for the solute since it cannot diffuse through the membrane. Equation (1.-1) can be expressed in terms of the pure water fugacity using the activity coefficient
(T, PA) = (T, PB) (1.-2)
The fugacity is a thermodynamic function defined by
f(T, P) = Pexp = Pexp where G(T, P) is the molar Gibbs free energy and GIG(T, P) is the molar Gibbs free energy as the fluid approached ideal gas state. The water fugacities at states (T, PA) and (T, PB) are then
ln =
ln =
Since PA > PB
ln = +
ln = ln +
V is the molar volume of water, an incompressible liquid
ln = ln + ln
ln = ln+
= exp
From the equality of fugacity, equation (1.-2) (T, PA) = (T, PB), we have
(T, PB) exp = (T, PB)
Since (T, PB) = (T, PB) = pure water fugacity
= exp
The osmotic pressure is then
5 = PA PB = ln (1.-3)
o For an ideal aqueous solution at 298 K with xW = 0.98, W = 1, the osmotic pressure is
A B = P P = ln(xW)
= ln(0.98) = 27.8 bar
For ideal solution and small solute concentration, 1, and ln() (1 )
Hence = ln() (1 ) = (1.-4)
=
= = = CS
The ideal dilute solution osmotic pressure, described by equation (1.-4), is known as van’t Hoff’s law. This equation can also be written in terms of the mass concentration S
= = RT CS = RT (1.-5)
where S = and MwS = molecular weight of solute. Equation (1.-5) can be used to determine solvent activity coefficient in a solvent-solute system provided a semi-permeable membrane can be found.
= PA PB = ln
Osmotic pressure measurements are more commonly used to determine the molecular weights of proteins and other macromolecules using an osmometer shown in Figure 1.-2. At equilibrium the osmotic pressure is equal to gh, where is the solution density and h is the difference in liquid heights. Equation (1.-5) is then solved for the molecular weight of the solute.
MwS = RT
Figure 1.-2 A graphical depiction of a simple osmometer.
Example 1.-1. ------(Sandler, Chemical and Engineering Thermodynamics, Wiley, 1999, p.605) The polymer polyvinyl chloride (PVC) is soluble in solvent cyclohexanone. At 25oC it is found that if a 2 g of a specific batch of PVC per liter of solvent is placed in an osmometer, the height h to which the pure cyclohexanone rises is 0.85 cm. Use this information to estimate the molecular weight of the PVC polymer. Density of cyclohexanone is 0.98 g/cm3.
Solution ------
6 = gh = 9809.818.510-3 m = 81.72 Pa MwS = RT
MwS = 8.314298.15 K2,000 /81.72 Pa = 60,670 g/mol ------
If the dilute solution contains N ideal solutes then
= RT
The term osmole is defined as one mole of a nondiffusing and nondissociating substance. One mole of a dissociating substance such as NaCl is equivalent to two osmoles. The number of osmoles per liter of solution is called osmolarity. For physiological solutions, it is convenient to work in terms of milliosmoles (mOsm) or milliosmolar (mOsM). The number of particles formed by a given solute determines osmotic pressure. Each nondiffusing particle in the solution contributes the same amount to the osmotic pressure regardless of the size of the particle.
The osmotic pressure difference between the interstitial and plasma fluids is due to the plasma proteins since the proteins do not readily pass through the capillary wall. The osmotic pressure created by the proteins is given the special name of colloid osmotic pressure or oncotic pressure. For human plasma, the colloid osmotic pressure is about 28 mmHg; 19 mmHg caused by the plasma proteins and 9 mmHg caused by the cations within the plasma that are retained through electrostatic interaction with the negative surface charges of the proteins.
Figure 1.-3 Osmosis of water through red blood cell5.
If a cell such as red blood cell is placed in a hypotonic solution that has a lower concentration of solutes or osmolarity, then the establishment of osmotic equilibrium requires the osmosis of water into the cell resulting in swelling of the cell. If the cell is placed in a hypertonic solution with a higher concentration of solutes or osmolarity, then osmotic equilibrium requires osmosis of water out of the cell resulting in shrinkage of the cell. An isotonic solution has the same osmolarity of the cell and will not cause any osmosis of water as shown in Figure 1.-3. A 0.9 weight percent solution of sodium chloride or a 5 weight percent solution of glucose is just about isotonic with respect to a cell.
55 Seeley R.R, Stephens T.D., Tate P., Anatomy & Physiology, McGraw Hill, 2003
7 Example 1.-26. ------Experiments show that at 0oC a 0.2 molarity sucrose solution has an osmotic pressure (relative to pure water) of 4.76 atm whereas a 0.2 molarity NaCl solution has an osmotic pressure of 8.75 atm. Estimate the fraction of the NaCl molecules that are dissociated at this temperature and concentration. Solution ------
Assume that all the sucrose dissolves and let be the dissociated fraction of NaCl. When a salt dissociates each ion contributes to the osmotic pressure
NaCl Na+ + Cl
If is the fraction of NaCl that is dissociated then 1 is the fraction that is not dissociated. Since each dissociated NaCl molecule contributes 2 ions and each undissociated molecules contributes 1 molecules, the osmolarity of the NaCl solution is
= [2 + (1 )]CNaCl
The osmolarity of the sucrose solution is
= CSucrose
Therefore,
= = + 1 = = 1.838
Hence = 0.838
Table 1.-1 lists the osmotic pressure of aqueous sucrose solution at 30oC calculated using equation (1.-3) for non-ideal solution and equation (1.-4) for ideal solution. The values for non- ideal model agree well with the experimental data.
= ln (1.-3)
= = RT CS (1.-4)
Table 1.-1 Osmotic pressure (atm) of aqueous sucrose solution at 30oC
CS (mol/liter) Eq. (1.-4) Eq. (1.-3) Exp. Data 0.991 20.3 26.8 27.2 1.646 30.3 47.3 47.5
66 Weiss T.F., Cellular Biophysics Transport, MIT Press, 1996, p. 258
8 2.366 39.0 72.6 72.5 3.263 47.8 107.6 105.9 4.108 54.2 143.3 144.0 5.332 61.5 199.0 204.3
At a physiological temperature of 37oC, Equation (1.-4) may be written as follows to give the osmotic pressure in mmHg when the solute concentration of each non-diffusing species is expressed in mOsM:
= 19.33 CS (1.-5)
9 Title Page California State Polytechnic University, Pomona Chemical and Materials Engineering
CHE 313- MASS TRANSPORT SPRING QUARTER, 2012
EXPERIMENT #3
Measurement of Permeability through balloon wall
INSTRUCTOR: T. K. Nguyen
SECTION 01
GROUP #1 MEMBERS: Lau, Lee McCaffrey, Charles
DUE DATE: May 10 2013
Title Page (10) ______
Research binary gaseous diffusivity (10) ______
Diffusivity measurement (15) ______
Experimental Plan (15) ______
Tabulated Data & Analysis (35) ______
Recommendation (15) ______
TOTAL (100) ______
10