# 11.4 Colligative properties  (Page 8/30)

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## 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?

## Solution

We can solve this problem using the following steps.

1. Determine the change in freezing point from the observed freezing point and the freezing point of pure benzene ( [link] ).
$\text{Δ}{T}_{\text{f}}=5.5\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}-2.32\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}=3.2\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$
2. Determine the molal concentration from K f , the freezing point depression constant for benzene ( [link] ), and Δ T f .
$\begin{array}{l}\hfill \text{Δ}{T}_{\text{f}}={K}_{\text{f}}m\hfill \\ \\ m\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\text{Δ}{T}_{\text{f}}}{{K}_{\text{f}}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{3.2\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}}{5.12\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\phantom{\rule{0.2em}{0ex}}{m}^{-1}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}0.63\phantom{\rule{0.2em}{0ex}}m\end{array}$
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.
$\text{Moles of solute}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{0.62\phantom{\rule{0.2em}{0ex}}\text{mol solute}}{1.00\phantom{\rule{0.2em}{0ex}}\overline{)\text{kg solvent}}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}0.0550\phantom{\rule{0.2em}{0ex}}\overline{)\text{kg solvent}}=0.035\phantom{\rule{0.2em}{0ex}}\text{mol}$
4. Determine the molar mass from the mass of the solute and the number of moles in that mass.
$\text{Molar mass}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{4.00\phantom{\rule{0.2em}{0ex}}\text{g}}{0.034\phantom{\rule{0.2em}{0ex}}\text{mol}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}1.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}\text{g/mol}$

## 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

## 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?

## Solution

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

1. Convert the osmotic pressure to atmospheres, then determine the molar concentration from the osmotic pressure.
$\begin{array}{}\\ \Pi \phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{5.9\phantom{\rule{0.2em}{0ex}}\text{torr}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}1\phantom{\rule{0.2em}{0ex}}\text{atm}}{760\phantom{\rule{0.2em}{0ex}}\text{torr}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}7.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\text{atm}\\ \Pi =\mathit{\text{MRT}}\\ \\ M\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\Pi }{RT}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{7.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\phantom{\rule{0.2em}{0ex}}\text{atm}}{\left(0.08206\phantom{\rule{0.2em}{0ex}}\text{L atm/mol K}\right)\left(295\phantom{\rule{0.2em}{0ex}}\text{K}\right)}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}3.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\text{M}\end{array}$
2. Determine the number of moles of hemoglobin in the solution from the concentration and the volume of the solution.
$\text{moles of hemoglobin}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{3.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\text{mol}}{1\phantom{\rule{0.2em}{0ex}}\overline{)\text{L solution}}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}0.500\phantom{\rule{0.2em}{0ex}}\overline{)\text{L solution}}=1.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\text{mol}$
3. Determine the molar mass from the mass of hemoglobin and the number of moles in that mass.
$\text{molar mass}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{10.0\phantom{\rule{0.2em}{0ex}}\text{g}}{1.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\text{mol}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}6.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\text{g/mol}$

## 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

## 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

Why does carbonic acid don't react with metals
Why does carbonic acid don't react with metal
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.
what is an ion
an atom that loses or gains an electron. Atoms normally have the same number of protons and electrons, therefore there is no charge as each + cancels out each -. When an atom loses an electron, it has more protons that electrons. Therefore the ion is called positive.
When an atom gains electrons it has more of them than protons. Therefore the ion is negative. You cannot change the number of protons as this results in a different element.
Gaining or losing electrons is based around the octet rule. 8 electrons in the outer shell is the most stable electron configuration (for the first three rows in the periodic table. After that it gets confusing so don't worry) So all atoms want to achieve this configuration.
Wat is chemical bonding
how to determine the number of atoms and the mass of zirconium, silicon, and oxygen found in 0.3384 mol of zircon4
what is a catalyst
A substance that speeds up the rate of a given reaction but does not react with any reactants
Brandon
something that speeds up a chemical reaction without being used up itself. It lowers the activation energy
something that speed up a chemical reaction without its self been used
Zainab
Faraday's first law of electrolysis state that...
the mass of a substance librated during electrolysis is directly proportional to the quantity of electricity passing through the electrolyte
Zainab
nice
Owolabi
greeaat
Abdul
another question
Owolabi
ys
Abdul
good
olanrewaju
gud one pls write it mathematically
Lekan
How can ionic bonds dissociate in aqueous solution
Because of the polarity of both ionic compounds and water the ionic compound will dissolve as "like dissolves like", and the molecule forms bonds with the water.
Claud
are all aqueous solutions water contained?
blossom
No, but a lot are.
Claud
it dissociate when d metal is combined wit oxygen
Lekan
I wanna understand more about isomers
Isomers are essentially the same molecules of one particular substance, except with different bonding points along the molecule. if you want a better example, look up xylene, p-xylene, and m-xylene. isomers are more for organic chemistry
Aaron
what is catenation
The property of carbon to form long chain with other atom!
Lareb
hydrocarbons can be classified as..1.Aliphatic compounds 2.cyclic compounds.under aliphatic compounds there are two types saturated hydrocarbons(alkanes) and unsaturated hydrocarbons(alkenes and alkynes).
thanks but i have also heard of aromatic hydrocarbons
emmanuel
so am kinda confused
emmanuel
how
Emmanuel
hydrocarbons are classified into 2 namely: aliphatic compound and aromatic compound
Mgbachi
aliphatic compound and aromatic compound
Mgbachi
hello i have big problems in understanding organic chemistry
what are the main types of hydrocarbon
emmanuel
I'm not exactly sure what you mean by 'main types' but I think you should be talking about aliphatic and cyclic hydrocarbons
blossom
What's the difference?
Claud
what is the difference between atomic theory and modern atomic theory
Yakubu
Or are you referring to the types being alkane, alkene and alkyne? alkane - hydrocarbon molecule with only single bonds alkene - hydrocarbon molecule with at least 1 double bond alkyne - hydrocarbon with at least 1 triple bond. alkane least reactive, alkene in the middle alkynes most reactive
I think that is what he is talking about
IBRAHIM
jamiu I'm here so whatsup
promise