Ideal solution

An ideal solution is a solution where the intermolecular interactions between solute-solute (A-A) and
solvent-solvent (B-B) are similar to the interaction between solute-solvent (A-B). An ideal solution fulfils
the following criteria: It obeys Raoult’s law for all the concentration and temperature ranges, which states
that the partial vapour pressure of each component is proportional to the mole fraction of the
component in a solution at a given temperature. .The enthalpy of mixing is zero, i.e. ΔHmix = 0. It means that
no heat is absorbed or released..The volume of mixing is zero, ΔVmix = 0. It means that the volume of the
solution is equal to the sum of the volume of components.
The ideal solution is possible with components of the same size and polarity. There is no association,
dissociation or reaction taking place between components. A perfect ideal solution is rare, but some
solutions are near to the ideal solution. Examples are Benzene and toluene, hexane and heptane,
bromoethane and chloroethane, chlorobnzene and bromobenzene, etc.

Non-Ideal Solutions

Characteristics of Non-ideal Solutions

A colligative property is a property of a solution that is dependent on the ratio between the total
number of solute particles (in the solution) to the total number of solvent particles. Colligative
properties are not dependent on the chemical nature of the solution’s components. Thus,
colligative properties can be linked to several quantities that express the concentration of a
solution, such as molarity, normality, and molality. The four colligative properties that can be
exhibited by a solution are given below:1.Boiling point elevation.2Freezing point
depression.3Relative lowering of vapour pressure.4Osmotic pressure
What Are Colligative Properties?
A dilute solution containing non-volatile solute exhibits some properties which depend only on
the number of solute particles present and not on the type of solute present. These properties
are called colligative properties, and they are mostly seen in dilute solutions.
We can further consider colligative properties as those properties that are obtained by the
dissolution of a non-volatile solute in a volatile solvent. Generally, the solvent properties are
changed by the solute, where its particles remove some of the solvent molecules in the liquid
phase. This also results in the reduction of the concentration of the solvent.
Besides, when we talk about the given solute-solvent mass ratio, colligative properties are said
to be inversely proportional to the solute molar mass.
Different Types of Colligative Properties of Solution
There are different types of colligative properties of a solution, which include vapour pressure
lowering, boiling point elevation, freezing point depression and osmotic pressure.
1. Lowering of Vapour Pressure
In a pure solvent, the entire surface is occupied by the molecules of the solvent. If a non-volatile
solute is added to the solvent, the surface now has both solute and solvent molecules; thereby
fraction of the surface covered by solvent molecules gets reduced. Since the vapour pressure of
the solution is solely due to the solvent alone, at the same temperature, the vapour pressure of
the solution is found to be lower than that of the pure solvent.
If P0 is the vapour pressure of pure solvent and Ps is the vapour pressure of the solution, the
difference Po – Ps is termed as the lowering in vapour pressure. The ratio, Po – Ps / Po, is known
as the relative lowering of vapour pressure.
Raoult, in 1886, established a relation between relative lowering in vapour pressure and mole
fraction. The relationship is known as Raoult’s law. It states that the relative lowering in vapour
pressure of a dilute solution is equal to the mole fraction of the solute present in the solution.
If n moles of solute is dissolved in N moles of the solvent, then, according to Raoult’s law,
Po – Ps / Po = n / n + N
2. Elevation in Boiling Point
The boiling point of a liquid is the temperature at which the vapour pressure is equal to
atmospheric pressure. We know that with the addition of a non-volatile liquid to a pure solvent,
the vapour pressure of a solution decrease. Therefore, to make vapour pressure equal to
atmospheric pressure, we have to increase the temperature of the solution. The difference in the
boiling point of the solution and the boiling point of the pure solvent is termed elevation in boiling
point.
If T0b is the boiling point of the pure solvent and Tb is the boiling point of the solution, then
elevation in boiling point is given as
∆Tb =T0b-Tb
Experimental results show that there is a relation between elevation in boiling point and molality
‘m’ of the solute present in the solution.
∆Tb ∝ m
∆Tb = kb m
Where,

kb = molal elevation constant

Substituting the value of ‘m’ in the above relation, we get

∆Tb = 1000 x kb x m2 / M2 x m1

Where,

m2 = mass of solvent in g

M1 = mass of solvent in kg

M2 = molar mass of solute

3. Depression in Freezing Point

The freezing point of a substance may be defined as the temperature at which the vapour
pressure of the substance in its liquid phase is equal to its vapour pressure in the solid phase.
According to Raoult’s law, when a non-volatile solid is added to the solvent, its vapour pressure
decreases, and now it would become equal to that of a solid solvent at a lower temperature. The
difference between the freezing point of the pure solvent and its solution is called depression in
freezing point.

If T0f is the freezing point of the pure solvent and Tf is the freezing point when a non-volatile solute
is dissolved in it, then depression in the freezing point is given as

∆Tf =T0f -Tf

Just like elevation in boiling point, depression in freezing point is also directly related to molality
‘m’.

∆Tf = 1000 x kf x m2 / M2 x m1

Where,

k f = molal depression constant

m2 = mass of solvent in g

M1 = mass of solvent in kg

M2 = molar mass of solute

4. Osmotic Pressure

When a semipermeable membrane is placed between a solution and solvent, it is observed that
solvent molecules enter the solution through the semipermeable membrane, and the volume of
the solution increases. The semi-permeable membrane allows only solvent molecules to pass
through it, but prevents the passage of bigger molecules like solute. This phenomenon of the
spontaneous flow of solvent molecules through a semipermeable membrane from a pure
solvent to a solution or from a dilute to a concentrated solution is called osmosis.

The flow of solvent molecules through the semipermeable membrane can be stopped if some
extra pressure is applied from the solution side. This pressure that prevents the flow of solvent is
called the osmotic pressure of the solution.

Osmotic pressure is a colligative property as it depends on the number of solutes present and
not on the nature of the solute. Experimentally, it was proved that osmotic pressure (⫪) is directly
proportional to molarity (C) and temperature (T).
Mathematically, ℼ = CRT, where R is the gas constant.
⇒ ℼ = (n2/V) RT
Here, V is the volume of solution in litres, and n2 is moles of solute
If m2 is the weight of solute and M2 molar mass of solute, then n2= m2/M2
ℼ = W2 RT / M2V
Thus, by knowing the values of ℼ,w2, T and V, we can calculate the molar mass of the solute.

Raoult’s Law in chemistry relates partial pressures of volatile liquid components to their mole
fractions in a liquid solution. It states that the partial pressure of each component in the
solution is directly proportional to its mole fraction. Thus, it helps us to calculate the total
vapour pressure of the solution. Based on Raoult’s law, liquid solutions are classified as Ideal
Solutions and Non-Ideal Solutions.
In this article, we will discuss the definition of Raoult’s law, ideal and non-ideal solutions,
Raoult’s law for non-volatile solutes and some solved numerical problems based on Raoult’s
law.
Raoult’s Law Definition
Raoult’s law states that,
For a liquid solution having volatile components, the partial vapour pressure of a component is
directly propotional to its mole fraction in the solution.
p1 = p10x1 and p2 = p20x2where,
• p1 is Partial Pressure of Component 1
• p2 is Partial Pressure of Component 2
• p10 is Vapour Pressure of Component 1 in Pure Form
• p20 is Vapour Pressure of Component 2 in pure form
• x1 is Mole Fraction of Component 1 in Solution
• x2 is Mole Fraction of Component 2 in Solution
Now, according to Dalton’s law of partial pressures which states the total vapour pressure of
a solution is the sum of partial pressures of its constituents. Thus,
pTotal = p10x1 + p20x2where,
• pTotal is Total Vapour Pressure of Solution
Thus, we can determine the total vapour pressure of a liquid solution using Raoult’s law and
Dalton’s law of partial pressures.
Raoult’s Law Formula
Raoult’s law equation mathematically is written as:
Psolution = ΧsolventP0solvent
where,
• Psolution is Vapour pressure of Solution
• Χsolvent is Mole Fraction of Solvent
• P0solvent is Vapour Pressure of Pure Solvent
Osmotic press
• The minimum pressure required to prevent the inward flow of a solution’s pure solvent
through a semipermeable membrane is known as the osmotic pressure. It’s also known as
the osmosis index, which measures a solution’s inclination for absorbing a pure solvent.
The highest osmotic pressure that a solution could create if separated from its pure
solvent by a semipermeable membrane is known as potential osmotic pressure.

• When a selectively permeable membrane separates two solutions with varying solute
concentrations, osmosis occurs. From a low-concentration solution to a solution with a
higher solute concentration, solvent molecules move selectively through the membrane.
Solvent molecules will continue to be transferred until equilibrium is reached.

What is Osmotic Pressure?

Osmotic pressure can be defined as the minimum pressure that must be applied to a solution to
halt the flow of solvent molecules through a semipermeable membrane (osmosis). It is
a colligative property and is dependent on the concentration of solute particles in the solution.
Osmotic pressure can be calculated with the help of the following formula:

π = iCRT

Where,

• π is the osmotic pressure

• i is the van’t Hoff factor
• C is the molar concentration of the solute in the solution
• R is the universal gas constant
• T is the temperature

This relationship between the osmotic pressure of a solution and the molar concentration of its
solute was put forward by the Dutch chemist Jacobus van’t Hoff. It is important to note that this
equation only holds true for solutions that behave like ideal solutions.

Boiling Point

The boiling point goes up when a substance is dissolved in a liquid. This is an example of a
colligative property, which is a property that depends on the number of solute molecules and
the number of solvent molecules but not on the type of solute.

What is the Elevation of Boiling Point?

When a solute is added to a solvent, the solvent's boiling point goes up. This is called "boiling
point elevation." When a non-volatile solute is added to a solvent, the boiling point of the
resulting solution is higher than that of the solvent by itself. For instance, a solution of sodium
chloride (salt) and water has a higher boiling point than pure water.
The height of the boiling point is a colligative property of matter, which means that it depends
on the ratio of solute to solvent but not on what the solute is. This means that the amount of
solute added to a solution changes how high its boiling point goes. The boiling point rises the
higher the concentration of solute in the solution.
Uses of Boiling Point Elevation
As we know that it doesn't have many applications of elevation in boiling point, but it does have
a few uses in everyday life that you may have seen. Let's discuss the uses of boiling point
elevation:
• Antifreeze - Ethylene Glycol or Antifreeze helps prevent radiator water from freezing. You
may not have noticed it also raises the fluid's boiling point. Raising the boiling point
prevents boil-overs. Many antifreeze manufacturers list boil-over and freeze-up
prevention.

• Cooking - Adding salt to water increases its boiling point, making it hotter when it boils.
Adding a few grams of salt to 10 cups of water raises the boiling point by 0.015 degrees
Celsius, which won't affect your cooking. Cooking uses boiling point elevation. Contrary to
 misconception, salting water won't help it boil quicker. Since its boiling point has risen, it
will take longer to boil.

• Molar Mass - Boiling point relies on the solvent and solute concentration, not the solute.
Like freezing point depression, boiling point elevation may determine a solute's molar
mass. The number of solute particles must also be considered if the solution contains an
electrolyte, like sodium chloride, which splits when dissolved. Chemists employ mass
spectrometry to estimate the molar mass of substances; however, boiling point elevation
and freezing point depression are still options.

• Refinery - Once sugarcane is harvested and the juice removed, it must be processed to
make crystalline sugar. The temperature at which cane juice or syrup boils depends on its
sugar content. The boiling point elevation helps monitor solution saturation, which is
critical for crystallization.

Boiling Point Elevation Examples in Real Life

• Pressure Cookers

• Cooking with Salt

• Sugar Refining

• Antifreeze

• Boiling Milk

• Storage of Chemicals

• Poor Cup of Tea at Mountains

• High Altitude Cooking

Equivalent conductance
The conductivity of a volume of solution containing one equivalent of an electrolyte is measured in equivalent
conductivity units. Consider the volume of a V cm3 solution containing one electrolyte equivalent, which is
represented by the symbol It has the same conductance as a conductance that is comparable. The
conductance exhibited by a 1 cm3 solution containing this electrolyte is referred to as its specific conductance
(between two electrodes with a cross-sectional area of 1 cm2 separated by a distance of 1 cm).
In mathematical terms, the following is the definition and formula for equivalent conductance:
the conductance of V cm3 ————- Λ
the conductance of 1 cm3 ————- κ
Therefore:
Λ = κ.V ————— equation (3)
We already know that the normalcy (N) of a solution can be calculated using the equation below.
N = n/V 1000
The equivalent conductance formula is as follows:
V = 1000/n .
For the electrolytic solution described above, the number of equivalents is n = 1.V = K x 1000/n
In this case, the relationship between V and NEquivalent conductance can be expressed as kx V.
Units of Λ: units of equal conductance (also known as conductance units).
The equiv-1 value is equal to cm2. mho. The equiv-1 value is also known as m2 Siemens.
Variation of Equivalent conductivity with dilution In general for strong and weak electrolytes, conductance as well as
equivalent conductance and molar conductance increases with dilution. This is due to the reason that as dilution
increases more ions are produced so the conductance increase since conductivity is due to ions. The specific
conductivity of an electrolyte falls with dilution because the number of current carrying particles i,e., ions present per
centimetre cube of the solution become less and less on dilution. However, the increase of equivalent and molar
conductivity on dilution is due to the fact these are the product of specific conductivity and the volume of the solution ,V
containing one gram equivalent of the electrolyte. As the decreasing value of specific conductivity is more than
compensated by the increasing value of V, so that the values of ꓥ increase with dilution. Conductance behaviour of
Strong electrolytes and weak electrolytes For strong electrolytes, ꓥm increases slowly with dilution and can be
represented by the equation, ꓥm =ꓥ0 m ‒ A√c The above equation is called Debye Huckel-Onsager equation and is
found to hold good at low concentration. If a graph is plotted between ꓥm and √c , a straight line is obtained for low
concentration, but it is not linear for higher concentration.
Migration of ions under influence of electric field: Cu  On passing electric current through electrolyte solution, ions
migrate and discharged oppositely charged electrodes. The migration of ions can be demonstrated by simple experiment.
 The lower portion of U-tube is filled with 5% agar-agar solution in water with small quantity of CuCr2O7.  It is
allowed to set by cooling as dark green jelly. Some charcoal powder is sprinkled in both limbs.  Then solution of
KNO3 and agar-agar is placed in each limb and allowed to set as jelly.  Finally solution of KNO3 in water is filled in
each limb and platinum electrodes are placed as shown in figure.  When electric current is passed, Cu2+ ions migrate
towards cathode (-ve electrode). Due to this blue colour appears in cathode side and yellow colour in anode side by
Cr2O7 2- ions. From the movement of these colour bands, speed of ions can be compared.

What is Kohlrausch’s Law?

The Kohlrausch Law, named after the German chemist Friedrich Kohlrausch, is a principle that helps us
understand how the conductivity of an electrolyte solution depends on the concentration of ions within it. In
other words, it describes the relationship between the conductivity of a solution and the concentration of its ions.

Definition:
Kohlrausch's law states that the limiting molar conductivity of an electrolyte can be represented as the sum of the
individual contributions of the anions and cations of the electrolyte.

Formula for Kohlrausch's law

The mathematical formula for Kohlrausch's law is as follows:

Λ∞ = Λ∞+ + Λ∞−

where:

Λ∞ = Equivalent conductivity of the electrolyte at infinite dilution

Λ∞+ = Equivalent conductivity of the cation at infinite dilution

Λ∞− = Equivalent conductivity of the anion at infinite dilution

Applications
Kohlrausch's law has a number of important applications in chemistry, including:

• Determining degree of dissociation: The degree of dissociation of an electrolyte is the fraction of the
electrolyte molecules that have dissociated into ions. Kohlrausch's law can be used to determine the
degree of dissociation of an electrolyte by measuring its equivalent conductivity at different
concentrations.
 • Calculating limiting molar conductivity: The limiting molar conductivity of an electrolyte is the
equivalent conductivity of that electrolyte at infinite dilution. It can be computed by adding the limiting
molar conductivities of the individual ions in the electrolyte.
• Determining solubility of sparingly soluble salts: Kohlrausch's law can be used to determine the
solubility of sparingly soluble salts by measuring the equivalent conductivity of the salt solution.
• Determining dissociation constant for weak electrolytes: Kohlrausch's law can be used to determine
the dissociation constant for a weak electrolyte by measuring the molar conductivity or specific
conductivity of the electrolyte at different concentrations.

Arrhenius theory of electrolyte dissociation and its limitations:  Arrhenius put forward the theory of electrolyte
dissociation in…. It is based on the following postulates:  When dissolved in water, neutral electrolyte molecules split
into charged particles. The positively charged particles are called cations and the negatively charged particles are called
anions. The process of formation of ions from the neutral molecules is called ionization. AB A + B + - (Old view) A + B
- A + + B - (Modern view)  The ions in solution constantly reunite to form neutral molecules and thus there is a state of
equilibrium between ions and the dissociated molecules. AB A + B + - k = [A + ][B - ] [AB] where k is called the
dissociation constant Applying the law of mass action;  Charged ions are free to move through the solution to the
oppositely charged electrodes. The movement of these ions constitutes electric current through the solution of
electrolyte. This explains the conductivity of electrolytes and the process of electrolysis.  Electrical conductivity of an
electrolyte solution depends on the number of ions present in solution. i. e. the degree of dissociation determines
whether the electrolyte is strong or weak.  Degree of dissociation (α) is the fraction of the total number of molecules
which undergo dissociation.  Degree of dissociation (α) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑐𝑢𝑙𝑒𝑠 𝑑𝑖𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑖𝑛𝑡𝑜 𝑖𝑜𝑛𝑠 𝑇𝑜𝑡𝑎𝑙
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠  Limitations of Arrhenius theory: 1. Strong electrolytes conduct electricity in fused state also.
It is in contradiction with Arrhenius theory, according to which the presence of solvent is essential for ionization. 2. This
theory fails to explain the factors affecting the mobility of ions. 3. The Ostwald dilution law which is completely based
on the Arrhenius theory is applicable only for weak electrolytes and fails in case of strong electrolytes.

Ostwald's dilution law is a relationship between the degree of dissociation (α) and the dilution of a weak
electrolyte. It is named after the German chemist Friedrich Wilhelm Ostwald who first proposed it. The law is
applicable only to weak electrolytes which partially dissociate into ions in a solution.
The law is mathematically expressed as:
𝐾𝑎=𝛼2⋅𝐶1−𝛼
Where:
• 𝐾𝑎 is the dissociation constant of the weak electrolyte.
• 𝛼 is the degree of dissociation, which is the fraction of the total number of molecules that have dissociated.
• 𝐶 is the molar concentration of the electrolyte.
According to Ostwald's dilution law, the degree of dissociation of a weak electrolyte is increased on dilution. As
the concentration of the electrolyte solution decreases, the degree of dissociation increases.