Vapor press Depression Boiling point Elevation and also Freezing suggest Depression
Colligative nature Calculations Osmotic Pressure

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Vapor PressureDepression

Physical properties deserve to be separated into two categories. Extensiveproperties (such as mass and also volume) depend on the size ofthe sample. Intensive properties (such as thickness andconcentration) are characteristic nature of the substance;they do not count on the size of the sample gift studied. Thissection introduces a third category the is a subset that theintensive nature of a system. This 3rd category, recognized as colligativeproperties, deserve to only be applied to solutions. Bydefinition, one of the nature of a solution is a colligativeproperty if it depends only on the ratio of the number ofparticles the solute and solvent in the solution, not the identityof the solute.

Very couple of of the physics properties the a solution arecolligative properties. As an instance of this restricted set ofphysical properties, let"s think about what wake up to the vaporpressure of the solvent once we add a solute to form a solution.We"ll specify Po as the vaporpressure of the pure liquid the solvent and P as the vaporpressure the the solvent after a solute has been added.

Po = vaporpressure the the pure liquid, or solvent

P = vapor press of the solvent in asolution

When the temperature that a liquid is below its boiling point,we can assume the the only molecules that deserve to escape from theliquid to kind a gas room those that lie near the surface ar of theliquid.

When a solute is included to the solvent, few of the solutemolecules accounting the space near the surface ar of the liquid, asshown in the number below. As soon as a solute is liquified in asolvent, the variety of solvent molecules near the surfacedecreases, and the vapor press of the solvent decreases.


This has no result on the rate at i m sorry solvent molecules inthe gas phase condense to kind a liquid. But it decreases therate in ~ which the solvent molecules in the liquid have the right to escape intothe gas phase. Together a result, the vapor pressure of the solventescaping indigenous a solution must be smaller than the vaporpressure that the pure solvent.

P o
vapor pressure of the solvent above a solution vapor push of the pure solvent

Between 1887 and 1888, Francois-Marie Raoult verified that thevapor push of a systems is equal to the mole fraction of thesolvent times the vapor pressure of the pure liquid.

P = Csolvent Po
vapor press of the solvent above a solution vapor press of the pure solvent

This equation, which is known as Raoult"s law,is straightforward to understand. Once the solvent is pure, and the molefraction the the solvent is same to 1, P is equal to Po.As the mole fraction of the solvent becomes smaller, the vaporpressure that the solvent escaping from the solution additionally becomessmaller.

Let"s assume, because that the moment, the the solvent is the onlycomponent that the equipment that is volatile enough to have actually ameasurable vapor pressure. If this is true, the vapor push ofthe systems will be equal to the vapor push of the solventescaping native the solution. Raoult"s law suggests that thedifference in between the vapor pressure of the pure solvent and also thesolution rises as the mole portion of the solvent decreases.

The change in the vapor pressure the occurs when asolute is added to a solvent is therefore a colligative property.If it counts on the mole portion of the solute, then it mustdepend on the proportion of the number of particles of solute tosolvent in the solution but not the identification of the solute.

Boiling PointElevation and also Freezing point Depression

The figure below shows the after-effects of the fact thatsolutes reduced the vapor pressure of a solvent. The solid lineconnecting clues B and also C in this step diagramcontains the combine of temperature and also pressure in ~ whichthe pure solvent and also its vapor are in equilibrium. Each suggest onthis line as such describes the vapor press of the puresolvent at that temperature. The dotted line in this figuredescribes the properties of a solution obtained by dissolving asolute in the solvent. At any given temperature, the vaporpressure that the solvent escaping native the solution is smallerthan the vapor pressure of the pure solvent. The dotted linetherefore lies listed below the solid line.

The to decrease in the vapor press of the solvent the occurs as soon as a solute is included to the solvent causes an increase in the boiling allude and decrease in the melting suggest of the solution.

According come this figure, the systems can"t cook at the sametemperature as the pure solvent. If the vapor press of thesolvent escaping from the systems is smaller than the vaporpressure the the pure solvent at any given temperature, thesolution should be heated come a greater temperature before it boils.The lowering the the vapor press of the solvent that occurswhen it is supplied to kind a solution thus increases theboiling allude of the liquid.

When step diagrams were introduced, the triple suggest wasdefined together the only combination of temperature and pressure atwhich the gas, liquid, and also solid deserve to exist in ~ the very same time. Thefigure above shows that the triple suggest of the systems occursat a lower temperature 보다 the triple point of the pure solvent.By itself, the adjust in the triple allude is not important. Butit outcomes in a adjust in the temperature in ~ which the solutionfreezes or melts. To recognize why, we have to look very closely atthe line the separates the solid and liquid regions in the phasediagram. This heat is practically vertical due to the fact that the melting pointof a problem is not very sensitive to pressure.

Adding a solute come a solvent doesn"t readjust the method themelting suggest depends on pressure. The line that separates thesolid and also liquid regions of the equipment is therefore parallel tothe line the serves the same duty for the pure solvent. Thisline need to pass v the triple suggest for the solution,however. The to decrease in the triple suggest that occurs as soon as asolute is liquified in a solvent as such decreases the meltingpoint of the solution.

The figure over shows just how the readjust in vapor press thatoccurs once a solute disappear in a solvent leader to alters inthe melting allude and the boiling allude of the solvent as well.Because the adjust in vapor pressure is a colligative property,which depends only on the relative number of solute and solventparticles, the alters in the boiling allude and the melt pointof the solvent are additionally colligative properties.

ColligativeProperties Calculations

The best way to demonstrate the importance of colligativeproperties is to research the aftermath of Raoult"s law. Raoultfound the the vapor push of the solvent escaping indigenous asolution is proportional to the mole fraction of the solvent.

P = CsolventPo

But the vapor push of a solvent is not a colligativeproperty. Only the change in the vapor pressure thatoccurs once a solute is included to the solvent have the right to be includedamong the colligative properties of a solution.

Because push is a state function, the change in the vaporpressure the the solvent that occurs when a solute is added to thesolvent deserve to be identified as the difference between the vaporpressure that the pure solvent and also the vapor push of thesolvent escaping native the solution.

P = Po - P

Substituting Raoult"s law into this equation gives thefollowing result.

P = Po - Csolvent Po= (1 - Csolvent)Po

This equation deserve to be streamlined by psychic therelationship in between the mole fraction of the solute and also the molefraction the the solvent.

Csolute+ Csolvent= 1

Substituting this relationship right into the equation that defines Pgives another form of Raoult"s law.

P = CsolutePo

This equation reminds united state that the adjust in the vapor pressureof the solvent that occurs as soon as a solute is included to the solventis proportional to the mole portion of the solute. As moresolute is dissolved in the solvent, the vapor pressure of thesolvent decreases, and the change in the vapor press of thesolvent increases.

Because changes in the boiling allude of the solvent (TBP)that occur when a solute is included to a solvent an outcome fromchanges in the vapor push of the solvent, the magnitude ofthe readjust in the boiling suggest is additionally proportional to the molefraction of the solute.

TBP = kbsolute

In dilute solutions, the mole fraction of the solute isproportional to the molality that the solution, as displayed in thefigure below.


The equation that describes the size of the boil pointelevation that occurs as soon as a solute is included to a solvent istherefore frequently written together follows.

TBP = kbm

Here, TBPis the boiling suggest elevation -- the readjust inthe boiling suggest that occurs when a solute disappear in thesolvent and also kb is a proportionality constantknown together the molal boiling suggest elevation constant forthe solvent.

A similar equation can be composed to describe what wake up tothe freezing point (or melt point) the a solvent once a soluteis included to the solvent.

TFP = -kfm

In this equation, TFP is the freezingpoint depression the change in the freezing suggest thatoccurs when the solute disappear in the solvent -- and also kfis the molal freezing suggest depression constant because that thesolvent. A negative sign is provided in this equation to indicatethat the freezing point of the solvent decreases as soon as a solute isadded.

Values of kf and also kbas well together the freezing points and boiling points because that a number ofpure solvents are offered in the tables below.

Freezing suggest Depression Constants

Compound Freezing point (oC) kf (oC/m)
water 0 1.853
acetic acid 16.66 3.90
benzene 5.53 5.12
p-xylene 13.26 4.3
naphthalene 80.29 6.94
cyclohexane 6.54 20.0
carbon tetrachloride -22.95 29.8
camphor 178.75 37.7

Compound Boiling allude (oC) kb (oC/m)
water 100 0.515
ethyl ether 34.55 1.824
carbon disulfide 46.23 2.35
benzene 80.10 2.53
carbon tetrachloride 76.75 4.48
camphor 207.42 5.611

Practice trouble 6:

Calculate the molecular weight of sulfur if 35.5 grams of sulfur dissolve in 100.0 grams the CS2 to create a solution that has a boiling point of 49.48oC.

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Practice difficulty 7:

Determine the molecular weight of acetic mountain if a systems that contains 30.0 grams that acetic mountain per kilogram the water freezes in ~ -0.93oC. Carry out these outcomes agree through the assumption that acetic acid has actually the formula CH3CO2H?

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What would occur in the calculate inPractice difficulty 7 were repeated with a more powerful acid, such ashydrochloric acid?

Practice problem 8:

Explain why one 0.100 m solution of HCl dissolved in benzene has actually a freezing suggest depression that 0.512oC, when an 0.100 m systems of HCl in water has actually a freezing allude depression of 0.352oC.

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In 1884 Jacobus Henricus van"t Hoff introduced an additional terminto the freezing suggest depression and boiling allude elevationexpressions to describe the colligative properties of options ofcompounds the dissociate when they dissolve in water.

TFP = -kf(i) m

Substituting the speculative value because that the freezing pointdepression of one 0.100 m HCl solution into this equationgives a worth for the i ax of 1.89. If HCl did notdissociate in water, i would certainly be 1. If it dissociatescompletely, i would certainly be 2. The experimental value the 1.89suggests at the very least 95% the the HCl molecules dissociate in thissolution.

Practice problem 9:

Explain why 0.60 grams of acetic acid dissolve in 200 grams that benzene to form a systems that lowers the freezing point of benzene to 5.40oC.

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Osmotic press

In 1784, the French physicist and also clergyman Jean AntoineNollet discovered that a pig"s bladder filled v a concentratedsolution the alcohol in water broadened when it to be immersed inwater. The bladder acted as a semipermeable membrane,which allowed water molecules to enter the solution, but keptalcohol molecules from relocating in the various other direction. Activity ofone ingredient of a equipment through a membrane to dilute thesolution is dubbed osmosis, and the pressurethis produce is dubbed the osmotic press ().

Osmotic pressure can be demonstrated through the device shownin the number below. A semipermeable membrane is tied throughout theopen finish of a thistle tube. The tube is then partially filledwith a equipment of sugar or alcohol in water and immersed in abeaker that water. Water will flow into the tube till the pressureon the column of water due to the pressure of gravity balances theosmotic press driving water through the membrane.

Water flows with the semipermeable membrane to dilute the alcohol systems until the force of gravity pulling under on the shaft of this systems balances the osmotic press pushing the water through the membrane.

The exact same year that Raoult found the connection betweenthe vapor push of a solution and the vapor push of a puresolvent, Jacobus Henricus van"t Hoff found that the osmoticpressure that a dilute systems ()obeyed an equation analogous come the ideal gas equation.

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= nRT

This equation says that osmotic press is anotherexample that a colligative property, because this push dependson the proportion of the variety of solute corpuscle to the volume ofthe equipment n/V no the identity of the soluteparticles. It likewise reminds united state of the size of osmoticpressure. According to this equation, a 1.00 M solutionhas an osmotic pressure of 22.4 atm at 0oC.


This way that a 1.00 M solution must be may be tosupport a shaft of water 670 inches, or nearly 56 feet, tall!

Biologists and also biorebab.netists regularly take advantage of osmoticpressure as soon as they isolate the components of a cell. As soon as a cellis added to an aqueous equipment that has a lot higherconcentration the ions 보다 the fluid within the cell, waterleaves the cabinet by flowing v the cell membrane until thecell shrinks so lot that the membrane breaks. Alternatively,when a cabinet is inserted in a solution that has actually a much smaller ionicstrength, water pours right into the cell, and the cell expands untilthe cell membrane bursts.