# 11.4 Colligative properties  (Page 3/30)

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${P}_{\text{A}}={X}_{\text{A}}{P}_{\text{A}}^{°}$

where P A is the partial pressure exerted by component A in the solution, ${P}_{\text{A}}^{°}$ is the vapor pressure of pure A, and X A is the mole fraction of A in the solution. (Mole fraction is a concentration unit introduced in the chapter on gases.)

Recalling that the total pressure of a gaseous mixture is equal to the sum of partial pressures for all its components (Dalton’s law of partial pressures), the total vapor pressure exerted by a solution containing i components is

${P}_{\text{solution}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\sum _{i}{P}_{i}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\sum _{i}{X}_{i}{P}_{i}^{°}$

A nonvolatile substance is one whose vapor pressure is negligible ( P ° ≈ 0), and so the vapor pressure above a solution containing only nonvolatile solutes is due only to the solvent:

${P}_{\text{solution}}={X}_{\text{solvent}}{P}_{\text{solvent}}^{°}$

## Calculation of a vapor pressure

Compute the vapor pressure of an ideal solution containing 92.1 g of glycerin, C 3 H 5 (OH) 3 , and 184.4 g of ethanol, C 2 H 5 OH, at 40 °C. The vapor pressure of pure ethanol is 0.178 atm at 40 °C. Glycerin is essentially nonvolatile at this temperature.

## Solution

Since the solvent is the only volatile component of this solution, its vapor pressure may be computed per Raoult’s law as:

${P}_{\text{solution}}={X}_{\text{solvent}}{P}_{\text{solvent}}^{°}$

First, calculate the molar amounts of each solution component using the provided mass data.

$\begin{array}{}\\ \\ 92.1\phantom{\rule{0.2em}{0ex}}\overline{)\text{g}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{3}{\text{H}}_{5}\left(\text{OH}{\right)}_{3}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{1\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{3}{\text{H}}_{5}\left(\text{OH}{\right)}_{3}}{92.094\phantom{\rule{0.2em}{0ex}}\overline{)\text{g}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{3}{\text{H}}_{5}\left(\text{OH}{\right)}_{3}}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}1.00\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{3}{\text{H}}_{5}\left(\text{OH}{\right)}_{3}\\ 184.4\phantom{\rule{0.2em}{0ex}}\overline{)\text{g}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{2}{\text{H}}_{5}\text{OH}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{1\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{2}{\text{H}}_{5}\text{OH}}{46.069\phantom{\rule{0.2em}{0ex}}\overline{)\text{g}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{2}{\text{H}}_{5}\text{OH}}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}4.000\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{C}}_{2}{\text{H}}_{5}\text{OH}\end{array}$

Next, calculate the mole fraction of the solvent (ethanol) and use Raoult’s law to compute the solution’s vapor pressure.

$\begin{array}{}\\ {X}_{{\text{C}}_{2}{\text{H}}_{5}\text{OH}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{4.000\phantom{\rule{0.2em}{0ex}}\text{mol}}{\left(1.00\phantom{\rule{0.2em}{0ex}}\text{mol}+4.000\phantom{\rule{0.2em}{0ex}}\text{mol}\right)}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}0.800\\ {P}_{\text{solv}}={X}_{\text{solv}}{P}_{\text{solv}}^{°}=0.800\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}0.178\phantom{\rule{0.2em}{0ex}}\text{atm}=0.142\phantom{\rule{0.2em}{0ex}}\text{atm}\end{array}$

A solution contains 5.00 g of urea, CO(NH 2 ) 2 (a nonvolatile solute) and 0.100 kg of water. If the vapor pressure of pure water at 25 °C is 23.7 torr, what is the vapor pressure of the solution?

23.4 torr

## Elevation of the boiling point of a solvent

As described in the chapter on liquids and solids, the boiling point of a liquid is the temperature at which its vapor pressure is equal to ambient atmospheric pressure. Since the vapor pressure of a solution is lowered due to the presence of nonvolatile solutes, it stands to reason that the solution’s boiling point will subsequently be increased. Compared to pure solvent, a solution, therefore, will require a higher temperature to achieve any given vapor pressure, including one equivalent to that of the surrounding atmosphere. The increase in boiling point observed when nonvolatile solute is dissolved in a solvent, Δ T b , is called boiling point elevation    and is directly proportional to the molal concentration of solute species:

$\text{Δ}{T}_{\text{b}}={K}_{\text{b}}m$

where K b is the boiling point elevation constant    , or the ebullioscopic constant and m is the molal concentration (molality) of all solute species.

Boiling point elevation constants are characteristic properties that depend on the identity of the solvent. Values of K b for several solvents are listed in [link] .

Boiling Point Elevation and Freezing Point Depression Constants for Several Solvents
Solvent Boiling Point (°C at 1 atm) K b (C m −1 ) Freezing Point (°C at 1 atm) K f (C m −1 )
water 100.0 0.512 0.0 1.86
hydrogen acetate 118.1 3.07 16.6 3.9
benzene 80.1 2.53 5.5 5.12
chloroform 61.26 3.63 −63.5 4.68
nitrobenzene 210.9 5.24 5.67 8.1

who are the alchemist?
alchemy science of transmutation. typically it is aim at tranforming lead to or other base metals to gold and the creation of the philosophers stone which in reality isn't a stone it's something priceless something we all need for coming times. don't be fooled
Kendrick
read Corinthians 5 verses 50 to the end of the chapter then read revelations chapter 2 verse 17
Kendrick
The word "Alchemy" comes from the forgotten name for Ancient Egypt, Khemmet. Khem was the name for the Egyptian Empire, but the actual land of Egypt was called Khemmet because the "T" on the end of a word denoted a physical location on Earth and not just an idea.
Michael
Wow!
mendie
What's the mass number of carbon
Akinbola
mass number of carbon is 12.
Nnenna
wat d atomic number of oxygen
safiya
atomic number of oxygen is 8
Nnenna
which quantum number divides shell into orbitals?
azimuthal
Emmanuel
hi
Charlie
azimuthal
reinhard
azimuthal
Charlie
what is atom
an atom is a smallest indivisible part of an element
Henry
an atom is the smallest part of an element that takes part in a chemical reaction
Nana
wat is neutralization
when any acid reacts with base to decrease it's acidity or vice-versa to form salt and solvent.. which is called neutralization
Santosh
explain buffer
Organic
buffer is a solution which resists changes in pH when acid or alkali added to it..
Santosh
hello, who is online
UTHMAN
buffer is the solution which resist the change in pH by addition of small amount of acid or alkali to it
KAUSIK
neutralisation is the process of mixing of a acid and a base to form water and corresponding salt
KAUSIK
how to solve equation on this
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Princewill
what is gases
Its one of the fundamental sate of matter alone side with liquid, solid and plasma
John
What is chemical bonding
John
To my own definitions. It's a unit of measurement to express the amount of a chemical substance.
What is mole
It's the unit of measurements used to express the amount of chemical substance.
Ozoaniehe
What is pressure
force over area
Jake
force applied per unit area
john
force applied per unit area
Prajapati
Why does carbonic acid don't react with metals
Why does carbonic acid don't react with metal
Some metals will react depending on their Standard Electrode Potential. Carbonic acid is a very weak acid (i.e. a low hydrogen ion concentration) so the rate of reaction is very low.
Paul
sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
a sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
an object of weight 10N immersed in a liquid displaces a quantity of d liquid.if d liquid displaced weights 6N.determine d up thrust of the object
how human discover earth is not flat
We don't fall off. If set off in any direction in a straight line and keep going. You'll end up back where you started.
earth is spherical
Unique
Also, every other planet is spherical as that is the most energy efficient shape. gravity pulls equally on all areas. Sphere.