Five Misconceptions Osmosis

7/28/2019 Five Misconceptions Osmosis

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Five popular misconceptions about osmosisEric M. Kramerand David R. MyersCitation:Am. J. Phys. 80, 694 (2012); doi: 10.1119/1.4722325View online: http://dx.doi.org/10.1119/1.4722325View Table of Contents: http://ajp.aapt.org/resource/1/AJPIAS/v80/i8Published by theAmerican Association of Physics TeachersRelated ArticlesUniversity student and K-12 teacher reasoning about the basic tenets of kinetic-molecular theory, Part I: Volumeof an ideal gas

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Five popular misconceptions about osmosis

Eric M. Kramera)

Physics Department, Bard College at Simons Rock, Great Barrington, Massachusetts 01230

David R. MyersChemistry Department, Bard College at Simons Rock, Great Barrington, Massachusetts 01230

(Received 21 December 2011; accepted 11 May 2012)

Osmosis is the flow of solvent across a semipermeable membrane from a region of lower to higher

solute concentration. It is of central importance in plant and animal physiology and finds manyuses in industry. A survey of published papers, web resources, and current textbooks reveals that

numerous misconceptions about osmosis continue to be cited and taught. To clarify these issues,

we re-derive the thermodynamics of osmosis using the canonical formalism of statistical

mechanics and go on to discuss the main points that continue to lead to misunderstandings. VC 2012American Association of Physics Teachers.

[http://dx.doi.org/10.1119/1.4722325]

I. INTRODUCTION

Osmosis is the flow of solvent across a semipermeablemembrane from a region of lower to higher solute concentra-

tion. It is of central importance for growth and transport inplants, renal, and cardiovascular physiology in animals, anda range of industrial processes including recent attempts atcommercial power generation.1 Despite its importance, arange of surprising misconceptions about osmosis continueto appear in papers, web sites, and textbooks. Erroneousideas about osmosis are especially common in educationalmaterials aimed at students of chemistry and biology. Oncelearned, these errors influence the thinking of professionalsthroughout their careers. Popular misconceptions about os-mosis center around the five questions listed below. In thispaper, we present the correct answers to these questions anddiscuss the surprising persistence of the incorrect answers.

Five questions about osmosis. (Answers are summarized

in Sec. V).(1) Is osmosis limited to mixtures in the liquid state?(2) Does osmosis require an attractive interaction between

solute and solvent?(3) Can osmosis drive solvent from a compartment of lower

to higher solvent concentration?(4) Can the osmotic pressure be interpreted as the partial

pressure of the solute?(5) What exerts the force that drives solvent across the semi-

permeable membrane, overcoming both viscous resist-ance and an opposing hydrostatic pressure gradient?

The canonical osmosis experiment is shown in Fig. 1.Two compartments are separated by a membrane that can

pass molecular species A (the solvent) but not species B (thesolute). Membrane semi-permeability is due to the presenceof small pores, whose size and chemical affinity admit sol-vent but not solute molecules. One compartment (#1) con-tains a mixture of A and B, while the other compartment(#2) contains only A. The pressure in each compartment iscontrolled by a piston as shown. Mechanical equilibriumrequires that the solution be maintained at a higher pressurethan the pure solvent. The equilibrium pressure differenceis called the osmotic pressure G of the solution. If

P1 < P2 P, then additional solvent will continue to flowacross the membrane into the solution. IfP1 > P2 P, thensolvent will flow out of the solution and into the pure

solvent. This process is thermodynamically reversiblebecause an infinitesimal increase in P1 from just below tojust above P2 P will reverse the direction of solvent flow.There are two noteworthy features of osmosis. First, solvent

will flow from a region of lower to a region of higher hydro-static pressure as long as P1 < P2 P. Second, in the limitof a dilute solute, the osmotic pressure is equal to the pres-sure of an ideal gas with the same concentration as the sol-ute, P kBTcB, where kB is Boltzmanns constant, T is theabsolute temperature, and cB is the concentration of B. Theequivalence between osmotic pressure and the ideal gas lawwas first published by vant Hoff in 1887 (Ref. 2) and isknown as vant Hoffs law.

The correct thermodynamic theory of osmosis was firstpublished by Gibbs in 1897 (Ref. 3) and can be found inmany thermodynamics textbooks.4 The mixture has a higherentropy per particle than the pure solvent due to the entropyof mixing, so entropy increase favors the flow of additional

solvent into solution. Flow ceases when the hydrostatic pres-sure in the mixture exceeds that in the pure solvent byenough to make the solvent chemical potential in the twocompartments equal.

Many of the current misconceptions about osmosis springfrom the fact that Gibbs theory provides little insight intothe molecular kinetics of osmosis. That is, it offers no expla-nation for the flow in terms of interactions between solutemolecules, solvent molecules, and the semipermeable mem-brane. An additional challenge is that the Gibbs free energyhas the pressure, rather than the volume, as a natural coordi-nate, so the relationship between osmosis and solvent con-centration is not readily apparent. The solvent concentrationis central to discussions of the relationship (or lack thereof)

between osmosis and diffusion, as discussed further in thefollowing sections.

This paper is organized as follows. In Sec. II, we derivethe thermodynamics of binary mixtures using canonical sta-tistical mechanics. In Sec. III, we derive vant Hoffs lawand find a new expression for the solvent concentration dif-ference across the membrane. In Sec. IV, we discuss the con-ditions under which the solvent is more concentrated in thesolution compartment. In Sec. V, we answer the five ques-tions posed above and discuss the misconception surround-ing each of them. Readers wishing to avoid the moretechnical aspects of this paper may proceed directly toSec. V. The paper is concluded in Sec. VI.

694 Am. J. Phys. 80 (8), August 2012 http://aapt.org/ajp VC 2012 American Association of Physics Teachers 694

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II. THERMODYNAMICS OF A BINARY MIXTURE

Consider a binary mixture of molecular species with nonontrivial internal degrees of freedom (i.e., we neglect the

energy of molecular vibrational and rotational modes). Thereare NA molecules of species A and NB molecules of speciesB. The particles interact via a pairwise potential Uijri; rjthat depends on the positions of the particles as well as theirspecies. The total energy E of the mixture is then

Er1rN;p1pN XNi1

p2

2mi

1

2

XNi1

XNj1

i6j

Uijri;rj; (1)

where N NA NB; ri, and pi are the position and momen-tum of particle i, and particles of type A are indexed beforetype B, so that the molecular mass mi is mA for i 1NAand mB fori NA 1N.

The semi-classical partition function for the mixture attemperature Tin a volume Vis5

ZT;V;NA;NB 1

NA!NB!

V

k3A

!NAV

k3B

!NBQ; (2)

where ki h2p=mikBT1=2

is the thermal wavelength ofparticle i (h being Plancks constant divided by 2p), and

QT;V;NA;NB 1

VN

V

dr1drN

exp 1

2kBT

XNi1

XNj1

i6j

Uijri;rj

0

BB@

1

CCA(3)

is the contribution to the partition function due to the poten-tial energy. Using the Stirling approximation, the Helmholtzfree energy is then

FT;V;NA;NB kBTlnZ

NAkBTlncAk

3A

e

NBkBTlncBk

3B

e

VfT;cA;cB;

(4)

where e is the base of natural logarithms, ci Ni=V is theconcentration of species i, and f kBTlnQ=V is the con-tribution to the Helmholtz free energy per unit volume dueto potential energy terms. The rightmost term is sometimescalled the excess free energy because f 0 corresponds tothe case of an ideal gas mixture. In general, the integral rep-resented in Eq. (3) cannot be solved, so the excess freeenergy cannot be expressed in closed form. For simple fluids,there are a range of empirical approximations available

depending on the numerical accuracy desired in the equationof state. The simplest such approximation reproduces thevan der Waals equation of state. The form of f is left arbi-trary in the calculations that follow, and we require only thatthe mixture remains in a single, homogeneous phase.

Some insight into the thermodynamics of osmosis can begained by considering the entropy S and the internal energyUof the mixture, given by

ST;V;NA;NB @F

@T

NAkBlncAk3

A NBkBlncBk3

B

5

2

kBNA NB V@f

@T

; (5)

and

UT;V;NA;NB F TS

3

2kBTNA NB V f T

@f

@T

:

(6)

As expected, the logarithmic terms in the free energy arestrictly entropic in origin. We will see in Sec. III that the sol-ute entropic term lncB is the formal source of the osmoticpressure. The reader should not think of this as the solute

entropy, however, because entropy is only defined for themixture considered as a whole.

III. OSMOSIS

In this section, we consider an osmotic system. Becausevant Hoffs law arises in the case of a dilute solute(cB ( cA), it is helpful to Taylor expand the excess freeenergy to first order in cB as

fT; cA; cB gT; cA cBhT; cA Oc2

B; (7)

where g is the excess free energy of the pure solvent and h @f=@cBcB 0 is a measure of how the excess free energy

changes under an exchange of A for B (and not to be con-fused with Plancks constant). The pressure P and the chemi-cal potentials li are then

P @F

@V kBTcA cB g cAg

0 cAcBh0 Oc2B;

(8)

lA @F

@NA kBTlncAk

3A g

0 cBh0 Oc2B; (9)

lB @F

@NB kBTlncBk

3B h OcB; (10)

Fig. 1. The osmotic system: two compartments at temperature T are sepa-

rated by a semipermeable membrane (dashed) that can pass solvent mole-

cules of species A (gray) but not solute molecules of species B (black). Each

compartment is maintained at constant pressure Pi by a piston. Symbols cidenote concentrations.

695 Am. J. Phys., Vol. 80, No. 8, August 2012 E. M. Kramer and D. R. Myers 695



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where primes denote derivatives with respect to cA. Note thatthe chemical potential of the solvent lA, which controls theflux of solvent, includes the solute explicitly via a term thatderives from the energy of interaction between A and B,h

0 @2f=@cA@cBcB0. A sufficiently strong attraction

between A and B will give h0 < 0. We will see below thatthis condition is sufficient for the solvent concentration inthe mixture to exceed that in the pure solvent. Note also thatthe solute entropic term lncB contributes to the pressure as

kBTcB. This term will become the osmotic pressure.Now consider the osmotic system shown in Fig. 1. Twocompartments are separated by a membrane permeable tosolvent A but not to solute B. The solution compartment (#1)contains species A and B at concentrations cA1 and cB1,respectively. The pure solvent compartment (#2) containsonly A at concentration cA2. The compartments are main-tained in equilibrium by pistons exerting pressures P1 and

P2, respectively. At equilibrium, the solvent chemical poten-tials are equal across the membrane, lA1 lA2. SubstitutingEq. (9) for the chemical potential, this becomes

kBTlncA1k3

A g0T; cA1 cB1h

0T; cA1

kBTlncA2k3

A

g0T; cA2: (11)

In the dilute-B limit, the solvent concentrations in compart-ments 1 and 2 are approximately equal. Defining the solventconcentration difference DcA cA1 cA2, we substitutecA2 c1A DcA into the right hand side of Eq. (11) andexpand around c1A. Keeping terms to first order in c1B andDcA, Eq. (11) simplifies to

DcA

cA1 jTh

0cA1cB1; (12)

where jT cA1kBT cA1g001 is the isothermal compres-

sibility. The solvent concentration difference is proportionalto the solute concentration, but the sign may be positive ornegative depending on particle interactions. If h0 < 0, thenDcA > 0 and the concentration of solvent is higher in themixture than in the pure solvent.

Now we can confirm that this approach gives the correctexpression for the osmotic pressure. Substituting Eq. (8) intoP P1 P2 and expanding cA2 around cA1 as above gives

P kBTcB1 DcA DcAcA1g00 cA1cB1h

0: (13)

On substituting Eq. (12) for the concentration difference, thisreduces to vant Hoffs law P kBTcB1, as expected. Wesee that terms depending on the interaction between particlesall cancel to leading order, and the osmotic pressure origi-nates with the solute entropic term lncB. Thus, vant Hoffslaw is independent of the state of the mixture and applies toliquids, gases, and supercritical fluids.

In Sec. IV, we examine further the conditions under whichDcA > 0.

IV. THE CONCENTRATION DIFFERENCE

A. Gases

Although one does not usually think of gaseous mixtureswhen considering osmosis, we have already seen that vantHoffs law is independent of the phase of the mixture. In thissection, we consider both ideal and real gases.

There are no interactions between particles in an ideal gasmixture, so h 0 and Eq. (12) becomes cA1 cA2. At equi-librium, the solvent concentrations in the two compartmentsare exactly equal.

For a mixture of dilute real gases, the excess free energymay be described using a virial expansion in powers of theconcentration (see, for example, Ref. 5, Sec. 704) giving

fT; cA; cB kBTBAAc2

A 2BABcAcB BBBc2

B

Oc3; (14)

so gT; cA kBTBAAc2

A and hT; cA 2kBTBABcA. Equa-tion (12) then becomes

DcA 2BABcA1cB1 Oc3; (15)

so the sign of the solvent concentration difference is deter-mined by the mixed second virial coefficient BAB (positivewhen BAB < 0). The mixed second virial coefficient can inturn be related to the pairwise interaction potential betweensolute and solvent UAB, using the cluster expansion

5

BAB

1

2

dr1 eUABr=kB T

: (16)

A negative potential will tend to make the virial coefficientnegative and a positive potential will tend to make the virialcoefficient positive. In real gases at room temperature, thedominant contribution to the integral is the weakly attractivevan der Waals force between molecules, so BAB is typicallynegative (e.g., BN2O2 11:9 cm

3/mole at T 298K[Ref. 6)]. Thus, an osmotic system with gaseous species willusually have DcA > 0.

B. Liquids

To understand the solvent concentration difference in aliquid osmotic system, we begin by asking what transforma-tions are necessary to convert an isolated system of pure sol-vent at T, P2, and cA2 into an isolated dilute binary mixtureat T, P1, cA1, and cB1. One can accomplish this by a sequenceof two quasi-static, isothermal steps. First, increase the pres-sure on the pure solvent from P2 to P1. Second, exchangesome of the solvent molecules for an equal amount of solutewhile maintaining the pressure constant at P1. The first pro-cess will compress the solvent and increase its concentration,although the effect is typically small for a system far from itsliquid-vapor critical point. The reader might guess that thesecond process, in replacing solvent by solute, will alwaysyield a decrease in the solvent concentration. Surprisingly,

this is not the case. If there is a sufficiently large attractionbetween solvent and solute, the isobaric exchange is accom-panied by a decrease in the system volume and a correspond-ing increase in the concentration of the remaining solvent.The commonly tabulated quantity that describes isobaricvolume change under solute-solvent exchange is called the

partial molar volume of the solute.7 If the partial molar vol-ume of a solute is negative, then solvent concentrationincreases under the exchange. This indeed occurs for manyaqueous ionic solutions because cations organize adjacentwater molecules into a hydration layer that is denser than therelatively open hydrogen bond network that connects watermolecules.8,9




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As an example, consider sodium fluoride (NaF), a salt thatdissociates to Na+ and F. The partial molar volume of thecompound is the sum of the two ionic partial molar volumes,which in this case is 3.3 cm3/mol.8 We thus see that thereare both liquid and gaseous mixtures for which osmosis candrive solvent from a region of lower to higher solventconcentration.

V. ANSWERS TO THE QUESTIONS

Here, we provide the correct answer to each of the ques-tions posed in Sec. I, as well as the popular misconceptionthat contradicts each answer. We then discuss each answer indetail, paying particular attention to the likely reasons thatthe wrong answer remains popular.

Answers to questions presented in Sec. I.

(1) The phenomenology of osmosis is the same for gases,liquids, and supercritical fluids. The misconception isthat osmosis is limited to liquids.

(2) Osmosis does not depend on an attractive force betweensolute and solvent. The misconception is that osmosisrequires an attractive force.

(3) Osmosis can drive solvent from a lower to a higher sol-

vent concentration compartment. The misconception isthat osmosis always happens down a concentrationgradient.

(4) The osmotic pressure cannot be interpreted as the partialpressure of the solute. The misconception is that it can.

(5) The semipermeable membrane exerts the force thatdrives solvent flow. The misconception is that no force isrequired to explain the flow.

A. The state of the mixture

In Sec. III, we showed that vant Hoffs law, and the phe-nomenology of osmosis more generally, is the same whetherthe mixture is a liquid, gas, or supercritical fluid.

The misconception. Numerous chemistry educationalwebsites, and many chemistry textbooks, imply or stateexplicitly that osmosis is limited to liquids. There are tworeasons for this. First, common experimental demonstrationsof osmosis use a liquid solvent, typically water. Second,when vant Hoffs law is taught to students, it is invariablygrouped together with a collection of other laws collectivelycalled the colligative properties of dilute solutions (histori-cally, the word colligative was chosen to describe thoseproperties that are bound together by a shared, linear de-pendence on solute concentration). There are good reasonsto group the colligative properties together, namely, they allderive from the same solute contribution to the free energy. 4

However, two of the colligative properties are explicitly ap-

plicable only to liquids: the elevation of the boiling point byadded solute, and Raoults law for the vapor pressure abovea solution. Thus, students and professionals often infer thatvant Hoffs law is similarly applicable only to liquidmixtures.

B. The interaction between solute and solvent

In Sec. III, we showed that osmosis is independent of theinteractions between solute and solvent. There is no restric-tion on the shape of the interaction potentials other than thegeneral requirement that the pure solvent and the mixtureeach exist as a single, homogeneous phase.

The misconception. The central question of osmosis iswhy additional solvent will flow into the solution compart-ment despite the fact that it is held at a higher hydrostaticpressure. Below, we will see that there is a force that drivessolvent into the solution, but the explanation is subtle andnot generally known outside the field of physics. Instead,some authors favor the incorrect view that the solute mustexert an attractive force on the solvent to somehow pull itacross the membrane (e.g., Refs. 10 and 11). This idea has

the advantage of simplicity and is readily tied to the idea thatthe solute be miscible in the solvent.

C. Solvent flow and solvent concentration

In Sec. IV, we showed that osmosis can drive solvent fluxfrom a region of lower to higher solvent concentration. Thisobservation was published at least as early as 1969,12 yet itcontinues to surprise many professionals.

The misconception. Students in biology and chemistry aretypically taught that osmosis is a special case of simple dif-fusion. The idea is that solute molecules displace the solventand thereby decrease the solvent concentration. Then, it isargued that osmotic flow is simply the diffusion of solvent

through the pores of the membrane. Many textbooks offer anequivalent kinetic argument stating that solvent moleculesarrive at a membrane pore with greater frequency from thepure solvent side (e.g., Refs. 13 and 14). The confusion ofosmosis with simple diffusion dates to the turn of the 20thcentury. For example, in his 1904 textbook TheoreticalChemistry,15 Walter Nernst wrote (p. 157), the diffusion ofcane sugar in waterobviously involves the same expansiveforce which we have learned to call the osmotic pressure.

This analogy between osmosis and simple diffusion is notvalid. In addition to our comments about solvent concentra-tion we can offer a second objection. Unlike osmosis, diffu-sion is not a thermodynamically reversible process. There isno small change in the external conditions of a diffusing sys-

tem that will reverse the flux of solute and solvent. Osmosisand simple diffusion are distinct phenomena. Not surpris-ingly, the analogy also fails to make quantitatively correctpredictions. Experiments have repeatedly shown that thewater flux during osmosis is too large to be accounted for byFicks law for diffusion.1619

As for why the analogy between osmosis and diffusionhas persisted up to the present, the reasons seem to be sim-plicity and pedagogic utility. The osmosis-diffusion analogytreats both the membrane and the solute as passive compo-nents whose only role is steric. Then, by making the analogywith diffusion, no additional concepts are required. The anal-ogy is pedagogically useful in that it reinforces the idea thatosmotic water transport, like diffusion, is a passive process;

a cell does not need to metabolize ATP to drive the flux.

D. Osmotic pressure and partial pressure

The pressure of an ideal gas mixture may be formally writ-ten as the sum of the ideal gas pressures of each species sepa-rately, in which case the terms in the sum are called thepartial pressures.4,5 For an osmotic system of ideal gases,the pressure in the mixture compartment is P1 kBTcA1 kBTcB1 and one can say the first term on the right is the par-tial pressure of the solvent and the second term is the partialpressure of the solute. Comparing this to vant Hoffs law,P kBTcB1, we see that the osmotic pressure is equal to the




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partial pressure of the solute. However, this only applies to amixture of ideal gases, where the particles do not interact.

For a mixture of interacting particles, the concept of par-tial pressure ceases to be valid. For example, the virialexpansion for the pressure of a binary mixture, to secondorder in the concentrations, is5

P kBTcA cB BAAc2

A 2BABcAcB BBBc2

B

Oc3; (17)

where the Bij are the second virial coefficients at temperatureT. The nonzero cross-term means that the pressure is no lon-ger expressible as a sum, P 6 PAcA PBcB. Therefore,the concept of partial pressure is only well-defined for anideal gas mixture and not for interacting systems. In general,one cannot describe the osmotic pressure as the partial pres-sure of the solute.

From the perspective of molecular kinetics, the idea ofpartial pressure is appealing because it lets one understandthe pressure in a compartment as being due to the bombard-ment of each molecular species independently against thewalls. However, in the case of interacting systems, soluteand solvent particles are continuously exchanging momen-tum through their mutual forces of interaction. The pressureof the system cannot be divided among the species in anymeaningful way. To our knowledge, this point was firstmade in the context of osmosis in Ref. 20.

The misconception. The idea that osmotic pressure is thepartial pressure of the solute has a long and controversial his-tory. Superfically, it seems to offer a simple explanation forthe symbolic equivalence between vant Hoffs law and theideal gas law. However, when carried to its logical conclu-sion, it leads to a bizarre and unsupportable view of osmosiscalled the solvent tension theory.2124 The solvent tensiontheory assumes that the hydrostatic pressure in a fluid can betreated as the sum of a piece strictly due to the solute and apiece strictly due to the solvent, P P

Ac

A P

Bc

B. Then

the osmotic pressure is assigned ad hoc to the solute,PB kBTcB. This division is supposed to explain osmoticflow as follows. Consider a beaker of water, open to the airat room temperature and 1.0 atm of pressure. Next, dissolveenough sugar in the water to create an osmotic pressure of2.0 atm. Equating the osmotic pressure of the solution to thepartial pressure of the sugar, mechanical equilibrium at theair-water interface would require the water to be at a partialpressure of 1.0 atm (i.e., in tension). The solvent tensionmodel goes on to suggest that this tensile water, broughtinto contact with a supply of pure water across a semiperme-able membrane, will exert a tensile force that draws addi-tional solvent into the solution. The solvent tension theory

reached its greatest influence in the 1970s, including severalpublications in high-profile journals24 before beingdiscredited.20

E. The force driving osmotic flow

Unlike the preceding four misconceptions, the question ofthe force driving osmotic flow is not made clear by the usualthermodynamic treatments. In Sec. III, we discussed the factthat vant Hoffs law derives from a term in the entropy thatcan be assigned to the solute, but it is not immediately appa-rent how this entropic force acts on the solvent. To makeprogress, we turn to the molecular kinetic theory of osmosis.

This theory was developed gradually in the first half of the20th century with contributions from many authors2530 andwas first published in modern form in the 1950s.3134

Osmotic flow is properly described as a bulk or hydrody-namic flow through the pores of the membrane. However,because viscous drag would rapidly bring any spontaneousflow to a stop, one must seek a force that continuously drivessolvent through the pores into the solution. The force isexerted on the solvent by the semi-permeable membrane. A

simple thought-experiment illustrates how this happens.Consider an idealized semipermeable membrane as a forcefield that repels solute but has no effect on the solvent.25,27,31

The Brownian motion of the solute molecules bring theminto occasional contact with this field, at which time theyreceive some momentum directed away from the membrane.Viscous interactions between solute and solvent then rapidlydistribute this momentum to the solvent molecules in theneighborhood of the membrane. In this way, the membraneexerts a repulsive force on the solution as a whole. Sinceadditional pure solvent can freely cross our idealized mem-brane, it flows into the solution compartment, graduallyincreasing the hydrostatic pressure in the solution. Thus, apressure gradient builds up across the thickness of the mem-

brane. This pressure gradient exerts a second force on the so-lution, capable of counteracting the membrane force.Quantitative treatments31,32 show that the pressure differencerequired to stop solvent flow into a dilute solution is exactlyP kBTcB. Nelson has aptly called the mechanism by whichthe membrane drives fluid flow the rectification of Brownianmotion.34

The same force-balance argument can be applied to thecase of a membrane with pores. In one popular approxima-tion, semi-permeability is established by steric effects: sol-vent molecules are small enough to pass through the poreswhile solute molecules are too large.32 A more realisticexample is the movement of water molecules single-filethrough the hydrophilic channel of an Aquaporin (AQP) or

other integral membrane protein.19,35

In either case the poreor channel aperture defines a region that repels solute but notsolvent, approximating the idealized case described in theprevious paragraph. The basic features of the kinetic modelare unchanged.

The misconception. The reader may notice that in the pre-vious subsection we stated that the osmotic pressure couldnot be interpreted as the partial pressure of the solute, whilehere we are claiming that the force driving flow derives fromthe random thermal motions of the solute. The fact that bothstatements are true is at the heart of the difficulty some peo-ple have with osmosis. The rectified Brownian motion modelrequires two momentum transfers: first from membrane tosolute, and then from solute to solvent. Those people desir-

ing a simpler explanation will be inclined to make incorrectinferences. Notably, the failure of the concept of partial pres-sure in the mixture has been taken by some researchers tomean that the kinetics of the solute are entirely irrelevant forosmosis. They are then inclined to accept the incorrect ideathat the role of the solute is simply to dilute the solvent, andproceed from there to an analogy between osmosis anddiffusion.

VI. CONCLUSION

In this paper, we re-derive the thermodynamics of an os-motic system and discuss five misconceptions about osmosis




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that continue to appear in textbooks, websites, and occa-sional published papers. These misconceptions are surpris-ingly robust. Nearly all have been discussed by other authorsduring the long history of osmotic research, and yet theycontinue to find adherents in each generation of professio-nals. The main reasons for the continued popularity of vari-ous misconceptions are their simplicity, their pedagogicutility, and the appeal of an analogy with more easilyexplained phenomena (in particular, solvation and simple

diffusion). Part of the challenge facing those of us interestedin improving the situation lies with disciplinary insularity.While authors in physics and biophysics have generally set-tled on the correct understanding of osmosis, these ideashave not penetrated into the fields of chemistry and biology.We suggest that improved communication between the disci-plines on this topic would be beneficial.

ACKNOWLEDGMENTS

The authors are grateful to Tobias Baskin, Mike Bergman,and Larry Winship for helpful discussions. This work wassupported in part by a grant from the National Science Foun-dation (Grant No. IOS 0815453).

a)Electronic mail: [email protected]

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Five Misconceptions Osmosis

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