# Solutions

Solutions are homogeneous mixtures of two or more than two components. Homogeneous mixture have its composition and properties uniform throughout the mixture.

Solvent

• In a solution, the component which is present in largest quantity is known as solvent and it determines the physical state of a solution.

Solute

• Another component of solution which is present in smaller quantity is known as solute.

## Solid Solutions

• Substitutional Solid Solution e.g. Brass (Components have almost similar size).
• Interstitial Solid Solution e.g. Steel (Smaller component occupies the interstitial voids).

## Expressing Concentration Of Solutions Of Solids In Liquids

 Type of Solution Solute Solvent Common Examples Gaseous Solutions Gas Liquid Solid Gas Gas Gas Mixture of oxygen and nitrogen gases Chloroform mixed with nitrogen gas Camphor in nitrogen gas Liquid Solutions Gas Liquid Solid Liquid Liquid Liquid Oxygen dissolved in water Ethanol dissolved in water Glucose dissolved in water Solid Solutions Gas Liquid Solid Solid Solid Solid Solution of hydrogen in palladium Amalgam of mercury with sodium Copper dissolved in gold
• Mass percentage (w/w):
Mass % of a component =(Mass of the component in the solution/Total mass of the solution)× 100
• Volume percentage (V/V):
Volume % of a component =(Volume of the component in the solution/Total volume of the solution)× 100
• Parts per million (ppm): It is used to express the concentration when a solute is present in trace quantities.
Parts per million =(Number of parts of the component in the solution/Total number of parts of all components of the solution)× -106
• Mole fraction (X):
Mole fraction of a component =(Number of moles of the component/Total number of moles of all the components)It has no unit
• Molarity (M):
Molarity =(Moles of solute/Volume of solution in litre)Unit is mol/L or mol L-1. Molarity is temperature dependent.
• Molality (m):
Molality (m) =(Moles of solute/Mass of solvent in kg)Unit is mol/kg or mol kg-1. It does not change with temperatures as it is mass to mass ratio. Thus, it is
temperature independent.

## Solubility Of A Gas In A Liquid

Henry’s Law

The law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of liquid or solution.
If we use the mole fraction of a gas in the solution as a measure of its solubility, then it can be said that the mole fraction of gas in the solution is proportional to the partial pressure of the gas over the solution.
The most commonly used form of Henery’s law states that “the partial pressure of the gas in vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution” and expressed as :

p = KHx Slope of the line = KH Where p is partial pressure of gas
• KH is the Henry’s law constant and function of the nature of the gas.
• X is mole fraction of the gas in solution.
• Higher the value of KH at a given pressure, the lower is the solubility of the gas in the liquid.
• KH values increase with increase of temperature indicating that the solubility of gases decrease with decrease of temperature.
• It is due to this reason that aquatic species are more comfortable in cold water rather than in warm water.

Limitations of Henr y’s Law

• This law is only applicable when the molecules of the system are in a state of equilibrium.
• This law does not hold true when gases are placed under extremely high pressure.
• This law is not applicable when the gas particles and the solution participate in chemical reactions with each other.

Vapour Pressure

It is defined as the pressure exerted (in a system featuring thermodynamics equilibrium) by a vapour with its condensed phases (solid or liquid) in a closed system at a given temperature.
• Vapour pressure of liquid depends upon the nature of liquid and temperature.

## Raoult’s Law

For the solution containing non-volatile solute, the vapour pressure of the solution is directly proportional to the mole fraction of solvent at particular temperature.

PA ∝ X

PA = P0

A . XA

For the solution consisting of two misciblle and volatile liquids, the partial
vapour pressure of each component is directly proportional to its own mole
fraction in the solution at particular temperature.

PA = P0 A . XA PB = P0 B  .X And total vapour pressure is equal to sum of partial pressure, Ptotal = PA + PB

## Types Of Solutions

Ideal Solution

The solution which obeys Raoult’s law under all conditions of temperature and concentration and during the preparation of which there is no change in enthalpy and volume on mixing the component.

Conditions :

PA = P0 A . XA

PB = P0 B . XB

ΔHmix(enthalpy of mixing) = 0 (it means that no heat is absorbed or released) ΔVmix (Volume of mixing) = 0 (it means that the volume of the solution is equal to the sum of the volume of components). This is only possible if A-B interaction is same as A-A and B-B interaction nearly. E.g. Benzene and Toluene, Chlorobenzene and Bromobenzene Very dilute solution exhibit ideal behavior to greater extent.

Non-Ideal Solution

When a solution does not obey Raoult’s law for all concentration and temperature ranges. May show positive or negative deviation from Raoult’s law.

(a) PA ≠ P0
A . XA (b) PB ≠ P0
B . XB (c) ΔHmix ≠ 0 (d) ΔVmix ≠ 0

For non-ideal solution the A-B interaction is different from A-A and B-B interactions

(i) For solution showing positive deviation

PA > PA 0 . XA , PB > PB 0 . XB
ΔHmix = Positive, ΔVmix = Positive (A-B interaction is weaker than A-A and B-B) E.g. alcohol and water, aectone and benzene.

(ii) For the solution showing negative deviation

PA > PA 0 . XA , PB > PB 0 . XB
ΔHmix = Positive, ΔVmix = Positive (A-B interaction is weaker than A-A and B-B) E.g. alcohol and water, aectone and benzene.

## Azeotropes

The mixture of liquids at particular composition which constant boiling point and behaves like a pure liquid and cannot be separated by simple distillation. Azeotropes are of two types :
• Minimum boiling Azeotrope (mixture which shows positive deviations) example: alcohol and water.
• Maximum boiling Azeotrope (which shows negative deviations) example: acetone and chloroform.

## Colligative Properties

The properties of solution which depends upon the number of solute particles (molecules or ions), but not upon their chemical nature are called Colligative Properties. There are four colligative properties. They are :

• Relative lowering of vapour pressure : According to Raoult’s Law, the relative lowering of vapour pressure is equal to the mole fraction of the solute in the solution and is given by :

(P 0 -p)/p 0 = Xsolute

(Xsolute=(n/n+N)

Where, P° = Vapour pressure of pure solvent
P = Vapour pressure of solution
and Xsolute = Mole fraction of solute in solution

• Depression of freezing point : M =1000Kf .  ω/ΔTf W

Where, Kf = cryoscopic constant (or molal depression constant), ω = weight of solute, W = weight of solvent (where M = molecular weight of solute) f = (ΔTf = Tf° - Tf ) depression in freezing point.

Elevation in boiling point : ΔTb =(1000 x Kb x w)/M x W

(Where ΔTb = Tb - Tb°) (elevation of boiling point) Where, Kb = Esbullio copic constant (or model elevation constant), M = molecular mass of solute, W = weight
of solvent,  ω = weight of solute

• Osmotic Pressure : π = CRT

where, c =(weight in gms/litre)/Molecular weight

π = osmotic pressure, C = molarity of solution, T = temperature of the solution on kelvin scale, R = gas constant.
Osmotic pressure is also defined as the hydrostatic pressure built up on the solution which just stops the osmosis.

## Abnormal Molecular Mass

In solution when the substance undergoes dissociation or association, there is discrepancy between observed colligative property and calculated colligative property and the molecular weights are lower and higher respectively than expected. These are known as abnormal molecular masses-e.g., Al2Cl6, P4O6, As4O6.

## Van’t H Off Factor

To account for abnormal cases, Van’t Hoff introdced a factor (i) known as the Van’t Hoff factor.

i =Observed Colligative Property/Calculated (normal) Colligative Property

Van’t Hoff Factors (i) =(1-α+(α/n))/1 (where -n = Number of molecules or ions in solution

Relation between degree of dissociation, and vant Hoff factors (i).

Van’t Hoff Factors (i) =(1-α+(αn))/1 (where n = Number of molecules or ions in solution)

• For association, i < 1.
• For dissociation, i > 1
• For no association and no dissociation, i = 1