# 6.4 Colligative properties  (Page 2/30)

 Page 2 / 30

## Converting mole fraction and molal concentrations

Calculate the mole fraction of solute and solvent in a 3.0 m solution of sodium chloride.

## Solution

Converting from one concentration unit to another is accomplished by first comparing the two unit definitions. In this case, both units have the same numerator (moles of solute) but different denominators. The provided molal concentration may be written as:

$\phantom{\rule{0.2em}{0ex}}\frac{3.0\phantom{\rule{0.2em}{0ex}}\text{mol NaCl}}{1.0\phantom{\rule{0.2em}{0ex}}\text{kg}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}$

The numerator for this solution’s mole fraction is, therefore, 3.0 mol NaCl. The denominator may be computed by deriving the molar amount of water corresponding to 1.0 kg

$1.0\phantom{\rule{0.2em}{0ex}}\text{kg}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}\left(\phantom{\rule{0.2em}{0ex}}\frac{1000\phantom{\rule{0.2em}{0ex}}\text{g}}{1\phantom{\rule{0.2em}{0ex}}\text{kg}}\right)\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}{18.02\phantom{\rule{0.2em}{0ex}}\text{g}}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}55\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}$

and then substituting these molar amounts into the definition for mole fraction.

$\begin{array}{ccc}\hfill {X}_{{\text{H}}_{2}\text{O}}& =& \phantom{\rule{0.2em}{0ex}}\frac{\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}{\text{mol NaCl}+\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}\hfill \\ \hfill {X}_{{\text{H}}_{2}\text{O}}& =& \phantom{\rule{0.2em}{0ex}}\frac{55\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}{3.0\phantom{\rule{0.2em}{0ex}}\text{mol NaCl}+55\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}\hfill \\ \hfill {X}_{{\text{H}}_{2}\text{O}}& =& 0.95\hfill \\ \hfill {X}_{\text{NaCl}}& =& \phantom{\rule{0.2em}{0ex}}\frac{\text{mol NaCl}}{\text{mol NaCl}+\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}\hfill \\ \hfill {X}_{\text{NaCl}}& =& \phantom{\rule{0.2em}{0ex}}\frac{3.0\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}\text{NaCl}}{3.0\phantom{\rule{0.2em}{0ex}}\text{mol NaCl}+55\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}}\hfill \\ \hfill {X}_{\text{NaCl}}& =& 0.052\hfill \end{array}$

## Check your learning

The mole fraction of iodine, I 2 , dissolved in dichloromethane, CH 2 Cl 2 , is 0.115. What is the molal concentration, m , of iodine in this solution?

1.50 m

## Vapor pressure lowering

As described in the chapter on liquids and solids, the equilibrium vapor pressure of a liquid is the pressure exerted by its gaseous phase when vaporization and condensation are occurring at equal rates:

$\text{liquid}\phantom{\rule{0.2em}{0ex}}⇌\phantom{\rule{0.2em}{0ex}}\text{gas}$

Dissolving a nonvolatile substance in a volatile liquid results in a lowering of the liquid’s vapor pressure. This phenomenon can be rationalized by considering the effect of added solute molecules on the liquid's vaporization and condensation processes. To vaporize, solvent molecules must be present at the surface of the solution. The presence of solute decreases the surface area available to solvent molecules and thereby reduces the rate of solvent vaporization. Since the rate of condensation is unaffected by the presence of solute, the net result is that the vaporization-condensation equilibrium is achieved with fewer solvent molecules in the vapor phase (i.e., at a lower vapor pressure) ( [link] ). While this kinetic interpretation is useful, it does not account for several important aspects of the colligative nature of vapor pressure lowering. A more rigorous explanation involves the property of entropy , a topic of discussion in a later text chapter on thermodynamics. For purposes of understanding the lowering of a liquid's vapor pressure, it is adequate to note that the greater entropy of a solution in comparison to its separate solvent and solute serves to effectively stabilize the solvent molecules and hinder their vaporization. A lower vapor pressure results, and a correspondingly higher boiling point as described in the next section of this module.

The relationship between the vapor pressures of solution components and the concentrations of those components is described by Raoult’s law    : The partial pressure exerted by any component of an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.

#### Questions & Answers

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
how do you find theWhat are the wavelengths and energies per photon of two lines
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?
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?
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
Calculate the bond order for an ion with this configuration: (?2s)2(??2s)2(?2px)2(?2py,?2pz)4(??2py,??2pz)3
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

#### Get Jobilize Job Search Mobile App in your pocket Now!

Would you like to follow the 'Ut austin - principles of chemistry' conversation and receive update notifications?

 By Robert Murphy By OpenStax By Brooke Delaney By Janet Forrester By OpenStax By Jonathan Long By Rhodes By P. Wynn Norman By OpenStax By Stephen Voron