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Class 12

Chemistry

Unit : Solutions

Solutions
• Solutions are homogeneous mixtures of two or more than two
components.
• The component that is present in the large quantity is known as
Solvent.
• one or more components present in the solution other than the
solvent are called solutes.

Types of state solvent Common

solutions examples
Gaseous Gas Gas Mixture of oxygen
solutions and nitrogen
gases.
Chloroform mixed
Liquid Gas with nitrogen gas.
Camphor in
Solid Gas nitrogen gas.

Liquid solutions Gas Liquid Oxygen

dissolved in
water.
Ethanol
Liquid Liquid dissolved in

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water.
Glucose
Solid Liquid dissolved in
water.

Solid solutions Gas Solid Solution of

hydrogen in
palladium.
Amalgam of
Liquid Solid mercury with
sodium.
Copper
Solid solid dissolved in
gold.

Terms used to define the concentration

1. Mass%(w/w)
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
Mass % of a component= 𝑚𝑚𝑚𝑚𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑜𝑜𝑙𝑙𝑢𝑢𝑡𝑡𝑠𝑠𝑠𝑠𝑜𝑜𝑛𝑛 ×

2. volume%(v/v)
𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑜𝑜𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
volume % of a component= 𝑡𝑡𝑜𝑜𝑡𝑡𝑎𝑎𝑙𝑙 𝑣𝑣𝑜𝑜𝑙𝑙𝑙𝑙𝑚𝑚𝑒𝑒 𝑜𝑜𝑜𝑜𝑜𝑜 𝑠𝑠𝑜𝑜𝑙𝑙𝑢𝑢𝑡𝑡𝑠𝑠𝑠𝑠𝑜𝑜𝑛𝑛

mass by volume%(w/v)is the mass of solute which is

dissolved in 100ml of solution.

3. Parts per million(ppm)

𝑛𝑛𝑢𝑢𝑚𝑚𝑏𝑏𝑒𝑒𝑟𝑟 𝑜𝑜𝑜𝑜 𝑜𝑜 𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑠𝑠 𝑜𝑜𝑜𝑜 𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑐𝑐𝑜𝑜𝑚𝑚𝑝𝑝𝑜𝑜𝑛𝑛𝑒𝑒𝑛𝑛𝑡𝑡 6
Parts per million= 𝑡𝑡𝑜𝑜𝑡𝑡𝑎𝑎𝑙𝑙 𝑛𝑛𝑜𝑜 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑠𝑠 𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎𝑙𝑙𝑙𝑙 𝑐𝑐𝑜𝑜𝑚𝑚𝑝𝑝𝑜𝑜𝑛𝑛𝑒𝑒𝑛𝑛𝑡𝑡 𝑜𝑜𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑜𝑜𝑙𝑙𝑢𝑢𝑡𝑡𝑠𝑠𝑠𝑠𝑜𝑜𝑛𝑛 ×𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

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It is the ratio of number of moles of one component to the

total number of components present in the solution .

4. Mole fraction(x)
𝑛𝑛(𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)
Mole fraction of the solute(xsolute) 𝑛𝑛(𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)+𝑛𝑛(𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)

5. Molarity(M)
It is defined as the number of moles of solute dissolved in
one litre (or one cubic decimeter) of solution.
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
Molarity(M) 𝑣𝑣𝑜𝑜𝑙𝑙𝑙𝑙𝑚𝑚𝑒𝑒 𝑜𝑜𝑜𝑜𝑜𝑜 𝑠𝑠𝑜𝑜𝑙𝑙𝑢𝑢𝑡𝑡𝑠𝑠𝑠𝑠𝑜𝑜𝑛𝑛 𝑠𝑠𝑠𝑠𝑛𝑛 𝑙𝑙𝑠𝑠𝑠𝑠𝑡𝑡𝑟𝑟𝑒𝑒

6. Molality(m)
It is defined as the number of moles of the solute per kg of
the solvent.
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
Molality 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠 𝑘𝑘𝑘𝑘

Solubility

Solubility is defined as the maximum amount of substance

that can be dissolved in a specific amount of solvent at the
particular temperature. It depends upon the nature of the
solute and solvent at specified temperature and pressure.

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Solubility of a solid in a liquid

Every solid does not dissolve in a given liquid.

Polar solute dissolve in polar solvent and non polar solute
dissolve in non polar solvent, if the intermolecular
interactions are same or we can say that like dissolves like.
Saturated solutions are those solutions in no more solute
can be added dissolve at the same temperature and
pressure for unsaturated solutions it is vice-versa.
• There are two factors which affect the solubility of a solid in a
liquid.
1. Temperature
If dissolution of solid is endothermic ie,(∆𝐻𝐻 = −𝑣𝑣𝑣𝑣 ).
Then solubility decreases with increase in temperature.
If it is exothermic ie, (∆𝐻𝐻 = +𝑣𝑣𝑣𝑣).
Then solubility increases with decreases in temperature.
2. Pressure
It does not have any effect on solubility because solid and
liquids are highly incompressible.

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Solubility of a gas in a liquid

Many gases dissolve in a liquid.

• Factors affecting the solubility of a gas in a liquid

1. Temperature
Temperature increases the intermolecular attraction
between the molecules becomes decreases hence
solubility of gas in liquid decreases.
2. Pressure
The solubility of gases increase with increase of pressure.
Henry he was the first who gives the relationship
between pressure and solubility of a gas in a solvent which
is known as Henry’s Law.

Henry’s law states that at the constant temperature

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“the partial pressure of the gas in a vapour phase(p) is

proportional to the mole fraction of the gas(x) in the
solution”
P=kHX
KH is the henry’s constant.
different gases has different value of kH
Higher the value of kH at a given pressure, lower the solubility of
gas in a liquid.

• Applications of henry’s law

1. Soda cans or cold drink bottles are sealed at high pressure for
increasing the solubility of co2 gas in the solvent.
2. Scuba divers air tanks are diluted by addition of He to prevent
formation of bends(11.7%He,56.2%N2 and 32.1%o2).

Aquatic animals are more comfortable in cold water rather then

warm water because dissolving power of oxygen in water
decreases with rising temperature and increases with lowering
the temperature.

• Limitations of henry’s law

1. For non ideal solutions this law is not applicable.

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2. This law is only applicable for those gases which do not

react with solvent.

Vapour pressure

Pressure exerted by vapour at the surface of the liquid at

equllibrium.

Factors on which vapour pressure is depend.

1. Temperature
Vapour pressure is directly proportional to the
temperature.
temp𝗍𝗍𝗍𝗍 v.p 𝗍𝗍𝗍𝗍
2. Intermolecular force of attraction
𝟏𝟏 𝟏𝟏 𝟏𝟏 𝟏𝟏
Vapour pressure𝖺𝖺 𝐼𝐼𝑛𝑛𝑡𝑡𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑙𝑙𝑒𝑒𝑒𝑒𝑢𝑢𝑙𝑙𝑎𝑎𝑟𝑟 𝑜𝑜𝑜𝑜𝑜𝑜𝑟𝑟𝑐𝑐𝑒𝑒 𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎𝑡𝑡𝑡𝑡𝑟𝑟𝑎𝑎𝑐𝑐𝑡𝑡𝑠𝑠𝑠𝑠𝑜𝑜𝑛𝑛

Roult’s law

It states that for solution of volatile liquids, the partial vapour pressure
of each component in the solution is directly proportional to its mole
fraction.

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P1 𝖺𝖺 X1 P1= partial pressure of 1

P1 =P°1X1 P°1= vapour pressure of pure 1
P2 𝖺𝖺 X2 P2= partial pressure of 2
P2 =P°2X2 P°2= vapour pressure of pure 2

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According to Dalton’s law of partial pressure. The total pressure of the

solution phase in the container will be the sum of partial pressure of
the the component of the solutions.

Ptotal = p1 + p2 (1)
Putting the value of p1 & p2 in (1)
Ptotal = x1 P°1 + x2 P°2
= (1-x2) P°1+ x2 P°2 (2)
= P°1 + (P°2 - P°1)x2 (3)

If y1 & y2 are the mole fraction of component 1 & 2 in vapour phase

then using Dalton’s law of partial pressure.

P1 = y1ptotal
P2 = y2ptotal
P1 = y1ptotal

So mole fraction of component in vapour phase

𝑝𝑝𝟏𝟏 𝟏𝟏 𝟏𝟏𝟏𝟏
Y1 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

Ideal solution
The solutions which obeys the Roult’s law over the entire range of
concentration.
In ideal solution

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• The enthalpy of mixing of pure component to form the solution is

zero and the volume of mixing is also zero.( means no heat is
absorbed or evolved when two components are mixed and
volume of solution would be equal to the sum of the volume of
the components.)

Non ideal solution

The solution which do not obey the Roult’s law over the entire range of
concentration.
In non ideal solution
• The vapour pressure of such a solution is either higher or lower
than that predicted by the Roult’s law. If it is higher then the
solution exhibits positive deviation if it is lower then the
solutionexhibits negative deviation.

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Azeotropes

These are the mixture

There are two types of azeotropes

Minimum boiling azeotropes Maximum boiling azeotropes

They are made from those liquid They are made from those liquid
pairs which show positive pairs which show negative
deviation from ideal behavior. deviation from ideal behavior.
e.g., ethanol-water mixture. e.g., nitric acid-water mixture.

Colligative properties

These are the property which depends only on the numbers of solute
particles dissolve in a definite amount of the solvent not on the nature
of the solute particles.

They are of four types

1. Relative lowering of vapour pressure

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When a non volatile solute is dissolved in a solvent, vapour pressure of

the solution is lower than that of the pure solvent which is known as
lowering of vapour pressure.

Relative lowering of vapour pressure is equal to the mole fraction of the

solute in the solution.

P1 = x1p°1

The reduction in the vapour pressure pf solvent(∆p1)is given as

∆p1 = p°1 - p1

= p°1 - x1p°1

= p°1(1-x1)

∆p1 = x2 p°1

In a solution containing several non-volatile solutes, the lowering of the

vapour pressure depends on the sum of the mole fraction of different
solutes.
∆𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏 𝟏𝟏 𝟏𝟏 𝟏𝟏 −
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩= = x2
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏 𝟏𝟏 𝟏𝟏 𝟏𝟏 − 𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 𝐧𝐧 𝐧𝐧 𝐧𝐧
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩 = 𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 + 𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏 𝟏𝟏 𝟏𝟏 𝟏𝟏 −
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩°𝟏𝟏 𝟏𝟏 𝟏𝟏 𝟏𝟏 −
𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩
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𝑛𝑛𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧
𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 =
𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 ×𝑀𝑀𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏
=
𝑀𝑀𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 ×𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

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2. Elevation in boiling point

The boiling point of a solution containing a non volatile solute is always
higher than the boiling point of the pure solvent. This increase in boiling
point is termed as elevation in boiling point.

∆Tb = Tb - T°b

∆Tb 𝖺𝖺 m or ∆Tb = Kbm

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𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧×𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏
= Kb( )
𝑀𝑀𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧×𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏(𝑠𝑠𝑠𝑠𝑛𝑛 𝑔𝑔)

𝐾𝐾𝑏𝑏 ×𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧×𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝑂𝑂𝑂𝑂𝑂𝑂
Or M2 =
∆T𝐛𝐛𝐛𝐛𝐛𝐛𝐛𝐛 ×W𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

Kb is called the boiling point elevation constant or molal elevation or

(ebullioscopic constant) constant, having unit K kg mol-1

3. Depression in freezing point

The freezing point of a solution containing a non volatile solute is
always less than the freezing point is termed ass as depression in
freezing point.

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∆Tf = T°f - Tf

∆Tf 𝖺𝖺 m or ∆Tf = kfm

𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧×𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏
= K f( )
𝑀𝑀𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧×𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏(𝑠𝑠𝑠𝑠𝑛𝑛 𝑔𝑔)
𝐾𝐾𝑜𝑜𝑜𝑜 ×𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧×𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝑂𝑂𝑂𝑂𝑂𝑂
Or M2 = ∆T𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟 ×W𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

Kf is known as the freezing point depression constant or molal

depression constant, having unit K kgmol-1

The values of Kf & Kb which depends upon the nature of the solvent, can
be ascertained from the following relations.
𝑅𝑅 ×𝑀𝑀𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 ×𝑇𝑇𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 𝑜𝑜𝑜𝑜 𝑅𝑅 ×𝑀𝑀𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 ×𝑇𝑇𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 𝑏𝑏
Kf = Kb =
𝟏𝟏000 × ∆𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝟏𝟏000 × ∆𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣

Osmosis
When solvent molecules flows from lower concentration to higher
concentration through semi permeable membrane.

Endoosmosis
When water enter in a cell through semi permeable membrane is called
endoosmosis.

Exoosmosis

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When water comes out from a cell through semi permeable membrane
is called exoosmosis.

Osmotic pressure(𝜋𝜋)
It is the pressure which stops the flow of solvent

𝜋𝜋 𝖺𝖺 C (C=molarity)

𝜋𝜋 = CRT
𝑛𝑛𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧
𝜋𝜋 = ( )RT
𝑣𝑣
𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝑅𝑅𝑇𝑇
𝜋𝜋 =
𝑉𝑉𝑀𝑀𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧

Isotonic solution
Solution having same osmotic pressure at a given temperature is known
as isotonic solution.

Solution with higher osmotic pressure is called Hypertonic solution.

Solution with lower osmotic pressure is called Hpotonic solution.

Reverse osmosis
When solvent moves from solution of higher concentration to solution
of lower concentration through semi permeable membrane. this
phenomenon is known ass reverse osmosis.

Abnormal molecular mass

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When the molecular mass of the substance which is determined by any

of the colligative properties comes out to be different from the
expected value, then the substance is used to show abnormal
molecular mass. This difference is shown when the solution is non ideal
or the solute is undergoes association or dissociation.

Van’t Hoff Factor

It is the ratio of the experimental value of the colligative property to
the calculated value of the colligative property.
𝑁𝑁𝑜𝑜𝑎𝑎𝑟𝑟𝑙𝑙
𝑚𝑚 𝑚𝑚𝑜𝑜𝑙𝑙𝑎𝑎𝑟𝑟 𝑚𝑚𝑎𝑎𝑠𝑠𝑠𝑠
i=
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
i=
𝑐𝑐𝑎𝑎𝑙𝑙𝑐𝑐𝑢𝑢𝑙𝑙𝑎𝑎𝑡𝑡𝑒𝑒𝑑𝑑 𝑐𝑐𝑜𝑜𝑙𝑙𝑙𝑙𝑠𝑠𝑠𝑠𝑔𝑔𝑎𝑎𝑡𝑡𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣 𝑝𝑝𝑟𝑟𝑜𝑜𝑝𝑝𝑒𝑒𝑟𝑟𝑡𝑡𝑦𝑦
𝑚𝑚𝑡𝑡
𝑙𝑙𝑜𝑜 𝑛𝑛
𝑏𝑏𝑒𝑒𝑟𝑟 𝑜𝑜𝑜𝑜𝑜𝑜 𝑚𝑚𝑜𝑜𝑙𝑙𝑒𝑒𝑠𝑠 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑒𝑒𝑟𝑟𝑡𝑡𝑠𝑠𝑠𝑠𝑐𝑐𝑙𝑙𝑒𝑒𝑠𝑠 𝑎𝑎𝑜𝑜𝑜𝑜𝑡𝑡𝑒𝑒𝑟𝑟 𝑎𝑎𝑠𝑠𝑠𝑠𝑜𝑜𝑐𝑐𝑠𝑠𝑠𝑠𝑎𝑎𝑡𝑡𝑠𝑠𝑠𝑠𝑜𝑜𝑛𝑛/𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑜𝑜𝑐𝑐𝑠𝑠𝑠𝑠𝑎𝑎𝑡𝑡𝑠𝑠𝑠𝑠𝑜𝑜𝑛𝑛
i=
𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎/𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

van’t hoff modifies the equation for the colligative properties

• Relative lowering pressure p°1 − p1

p = i. 𝑛𝑛1
𝑛𝑛2

• Elevation of boiling point ∆Tb = i.Kbm

• Depression of freezing point ∆Tf = i. Kfm
• Osmotic pressure of solution 𝜋𝜋 = i.n2RT/V

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