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This figure shows three scenarios relating to red blood cell membranes. In a, H subscript 2 O has two arrows drawn from it pointing into a red disk. Beneath it in a circle are eleven similar disks with a bulging appearance, one of which appears to have burst with blue liquid erupting from it. In b, the image is similar except that rather than having two arrows pointing into the red disk, one points in and a second points out toward the H subscript 2 O. In the circle beneath, twelve of the red disks are present. In c, both arrows are drawn from a red shriveled disk toward the H subscript 2 O. In the circle below, twelve shriveled disks are shown.
Red blood cell membranes are water permeable and will (a) swell and possibly rupture in a hypotonic solution; (b) maintain normal volume and shape in an isotonic solution; and (c) shrivel and possibly die in a hypertonic solution. (credit a/b/c: modifications of work by “LadyofHats”/Wikimedia commons)

Determination of molar masses

Osmotic pressure and changes in freezing point, boiling point, and vapor pressure are directly proportional to the concentration of solute present. Consequently, we can use a measurement of one of these properties to determine the molar mass of the solute from the measurements.

Determination of a molar mass from a freezing point depression

A solution of 4.00 g of a nonelectrolyte dissolved in 55.0 g of benzene is found to freeze at 2.32 °C. What is the molar mass of this compound?


We can solve this problem using the following steps.

This is diagram with five boxes oriented horizontally and linked together with arrows numbered 1 to 4 pointing from each box in succession to the next one to the right. The first box is labeled, “Freezing point of solution.” Arrow 1 points from this box to a second box labeled, “delta T subscript f.” Arrow 2 points from this box to to a third box labeled “Molal concentration of compound.” Arrow labeled 3 points from this box to a fourth box labeled, “Moles of compound in sample.” Arrow 4 points to a fifth box labeled, “Molar mass of compound.”
  1. Determine the change in freezing point from the observed freezing point and the freezing point of pure benzene ( [link] ).
    Δ T f = 5.5 ° C 2.32 ° C = 3.2 ° C
  2. Determine the molal concentration from K f , the freezing point depression constant for benzene ( [link] ), and Δ T f .
    Δ T f = K f m m = Δ T f K f = 3.2 ° C 5.12 ° C m −1 = 0.63 m
  3. Determine the number of moles of compound in the solution from the molal concentration and the mass of solvent used to make the solution.
    Moles of solute = 0.62 mol solute 1.00 kg solvent × 0.0550 kg solvent = 0.035 mol
  4. Determine the molar mass from the mass of the solute and the number of moles in that mass.
    Molar mass = 4.00 g 0.034 mol = 1.2 × 10 2 g/mol

Check your learning

A solution of 35.7 g of a nonelectrolyte in 220.0 g of chloroform has a boiling point of 64.5 °C. What is the molar mass of this compound?


1.8 × 10 2 g/mol

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Determination of a molar mass from osmotic pressure

A 0.500 L sample of an aqueous solution containing 10.0 g of hemoglobin has an osmotic pressure of 5.9 torr at 22 °C. What is the molar mass of hemoglobin?


Here is one set of steps that can be used to solve the problem:

This is a diagram with four boxes oriented horizontally and linked together with arrows numbered 1 to 3 pointing from each box in succession to the next one to the right. The first box is labeled, “Osmotic pressure.” Arrow 1 points from this box to a second box labeled, “Molar concentration.” Arrow 2 points from this box to to a third box labeled, “Moles of hemoglobin in sample.” Arrow labeled 3 points from this box to a fourth box labeled, “Molar mass of hemoglobin.”
  1. Convert the osmotic pressure to atmospheres, then determine the molar concentration from the osmotic pressure.
    Π = 5.9 torr × 1 atm 760 torr = 7.8 × 10 −3 atm Π = MRT M = Π R T = 7.8 × 10 −3 atm ( 0.08206 L atm/mol K ) ( 295 K ) = 3.2 × 10 −4 M
  2. Determine the number of moles of hemoglobin in the solution from the concentration and the volume of the solution.
    moles of hemoglobin = 3.2 × 10 −4 mol 1 L solution × 0.500 L solution = 1.6 × 10 −4 mol
  3. Determine the molar mass from the mass of hemoglobin and the number of moles in that mass.
    molar mass = 10.0 g 1.6 × 10 −4 mol = 6.2 × 10 4 g/mol

Check your learning

What is the molar mass of a protein if a solution of 0.02 g of the protein in 25.0 mL of solution has an osmotic pressure of 0.56 torr at 25 °C?


2.7 × 10 4 g/mol

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Colligative properties of electrolytes

As noted previously in this module, the colligative properties of a solution depend only on the number, not on the kind, of solute species dissolved. For example, 1 mole of any nonelectrolyte dissolved in 1 kilogram of solvent produces the same lowering of the freezing point as does 1 mole of any other nonelectrolyte. However, 1 mole of sodium chloride (an electrolyte) forms 2 moles of ions when dissolved in solution. Each individual ion produces the same effect on the freezing point as a single molecule does.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
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what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Damian Reply
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how do you find theWhat are the wavelengths and energies per photon of two lines
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The eyes of some reptiles are sensitive to 850 nm light. If the minimum energy to trigger the receptor at this wavelength is 3.15 x 10-14 J, what is the minimum number of 850 nm photons that must hit the receptor in order for it to be triggered?
razzyd Reply
A teaspoon of the carbohydrate sucrose contains 16 calories, what is the mass of one teaspoo of sucrose if the average number of calories for carbohydrate is 4.1 calories/g?
ifunanya Reply
4. On the basis of dipole moments and/or hydrogen bonding, explain in a qualitative way the differences in the boiling points of acetone (56.2 °C) and 1-propanol (97.4 °C), which have similar molar masses
Kyndall Reply
Calculate the bond order for an ion with this configuration: (?2s)2(??2s)2(?2px)2(?2py,?2pz)4(??2py,??2pz)3
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Which of the following will increase the percent of HF that is converted to the fluoride ion in water? (a) addition of NaOH (b) addition of HCl (c) addition of NaF
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