Solutions are the homogeneous mixture of two or more than two components. In solution, a solute is a substance dissolved in another substance, known as the solvent which is present in larger quantity.
Terms Used in Solutions:
The following terms are used in solutions
Binary solutions are the solutions which contain 2 components. Example: salt solution.
Aqueous solution: When a solute is dissolved in water, it is known as an aqueous solution. E.g.: ethanol in water.
Non-aqueous solution: When a solute is dissolved in a solvent other than water, it is known as a non-aqueous solution. Example: iodine in alcohol (tincture of Iodine).
Neutral solution has equal concentration of H+ ions (hydrogen ions) and OH– ions (hydroxyl ions).
Acidic solution have more H+ ions (hydrogen ions) than that of OH– ions (hydroxyl ions) while a basic solution has more OH– ions (hydroxyl ions) than that of H+ ions (hydrogen ions).
Types of solutions:
- On the basis of state of solute and solvent, the solution may be of the following types
Expression of the concentration of solutions of solids in liquids:The concentration of a solution may be defined as the amount of solute present in the quantity of the solution. There are several ways by which we can describe the concentration of the solution.Molarity:It is defined as the number of moles of solute dissolved in one litre or one cubic decimeter of the solution.Molarity, M = No. of moles of solute x 1000 / Volume of solution (mL)(Moles of solute= W2/M2, where W2= mass of solute (g) and M2= molar mass of solute)Molality:
It is defined as the no. of moles of solute per kilogram of the solvent.
Molality, m= No. of moles of solute x 1000 / Mass of solvent (g)
It is the number of gram equivalent of the solute dissolved in one litre of the solution.
Normality, N= No. of gram equivalent of solute x 1000 / Volume of solution (mL)
( Where, gram equivalents of solute= W2/Equivalent weight)
Relation between Molarity and Molality:
Molality, m = M x 1000/ (1000 x d) – (M-M2)
where M is the molarity and M2 is the molar mass of component 2 (generally solute) and d is the density of solution in g cm-3. For dilution, M1V1 = M2V2, similarly N1V1= N2V2 (for all cases like acids-bases, dilution, etc.)
It is the number of one component to the total number of moles of all the components present in the solution. Mole fraction for a binary solution, if solvent = 1 and solute= 2.
Mole fraction of solute X2 = n2/n1 + n2
Similarly, mole fraction of solvent X1 = n1/n1 + n2
X1 + X2 = 1
Note: Molarity and mole fraction do not change with the change in temperature.
Parts Per Million:
When a solute is present in trace quantities, the concentration is expressed in parts per million.
Parts per million = Number of parts of the component x 106/Total number of parts of all the components of the solution
The mass percentage of a component in a given solution is the mass of the component per 100 gram of the solution.
Mass per cent = Mass of solute x 100/Mass of solution
The volume percentage is the volume of the component per 100 parts by volume of the solution.
Volume per cent = Volume of the component x 100/Total volume of the solution
Mass by volume percentage:
Mass by volume percentage is the mass of the solute dissolved in 100 ml of the solution.
The solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent it depends on the nature of solvent, nature of solute, temperature and pressure.
Solubility of a solid in a liquid:
Every solid does not dissolve in a given liquid polar solutes dissolved in polar solvents and non-polar solutes in nonpolar solvents. In general, a solute dissolved in a solvent if the intermolecular interactions are similar in the two or it can be said that like dissolves like.
Terms to know for solubility of solid in a liquid:
The term that will help in understanding the solubility of solid in a liquid is given below.
Crystallization: Some solute particles in solution collide with solid solute particles and get precipitate out this process is known as crystallization.
Dissolution: On dissolving the solid solute in a solvent, its concentration increases, this is dissolution.
Dynamic equilibrium is the condition is equal to the solute particles separating out i.e. dissolution and crystallization occur at the same rate.
Factors affecting solubility of a solid in a liquid:
The following factors affect the solubility of a solid in a liquid.
Effect of temperature:
If in a newly saturated solution, the dissolution process is endothermic (Δsol H>0), the solubility should increase with the rise in temperature and if it is exothermic (Δsol H<0), that solubility should decrease.
Effect of pressure:
Pressure does not have any significant effect on the solubility of solid in a liquid. It is so because solid and liquid are highly incompressible and practically remain unaffected by changes in pressure.
Solubility of a gas in a liquid:
The solubility of different gases in the same solvent varies, e.g., gases like hydrogen, oxygen, nitrogen and helium, etc., dissolves in water to a small extent whereas the gases like NH3, HCl, SO2, etc., are highly soluble in water. The solubility of gases in a liquid is greatly affected by pressure and temperature.
It states that at a constant temperature the solubility of a gas in a liquid is directly proportional to the pressure of the gas.
The partial pressure of the gas in the vapour phase (p) is proportional to the mole fraction (x) of the gas in the solution.
p α x or p= KH.x
(where KH is Henry’s law constant or Henry’s constant)
Note: Higher the value of KH at a given pressure, the lower is the solubility of the gas in the liquid.
Application of Henry’s law:
Ø To increase the solubility of carbon dioxide in soft drinks and soda water, the bottle is sealed under high pressures.
Ø To avoid bends and the toxic effects of high concentration of Nitrogen in the blood, the tanks used by scuba divers are filled with air diluted with helium.
The pressure exerted by the vapours above the liquid surface in equilibrium with the liquid at a given temperature is called vapour pressure.
The solution containing two components
- Liquid in liquid
- Solid in liquid
Vapour pressure of liquid-liquid solution:
In a binary solution of two volatile liquids in a closed vessel, components evaporated and finally, a state of equilibrium is reached between the vapour and liquid phase. The total vapour pressure, in this case, is equal to the sum of the partial pressure of each of the two components (according to Dalton’s law of partial pressures).
Raoult’s law for volatile solute:
This law states that for a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction.
For component 1,
p1 α x1 or p1= p1o x1
Similarly, for component 2,
p2 α x2 or p2= p2o x2
ptotal = p1 + p2 = p1o x1 + p2o x2
If y1 and y2 are the mole fraction of the components 1 and 2 respectively in the vapour phase, then p1= ptotal y1. Similarly, p2= ptotal y2.
Raoult’s Law as a special case of Henry’s law:
According to Raoult’s law, the vapour pressure of a volatile component in a given solution is given by
pi= pio xi
Then according to Henry’s law, p= KH.x, i.e., the partial pressure of the volatile component (gas) is directly proportional to the mole fraction of that component (gas) in the solution. Therefore, Raoult’s law and Henry’s law become identical except that their proportionality constants (KH– Henry’s constant and pio for Raoult’s law) are different. Therefore, Raoult’s law becomes a special case of Henry’s law in which KH becomes equal to pio.
Ideal solution obeys Raoult’s law over the entire range of concentration For these solutions, Δmix H=0 and Δmix V=0. In an ideal solution, A-B interaction is nearly equal to A-A or B-B interactions. The solution of n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene, etc. are nearly ideal in behaviour.
Non-ideal solutions do not obey Raoult’s law over the entire range of concentration. Example: n-hexane and n-heptane.
Positive and negative deviation:
In case of positive deviation from Raoult’s law (example: mixture of ethanol and acetone), A-B interaction are weaker than those of A-A or B-B interactions, while in case of negative deviation from Raoult’s law (example mixture of phenol and aniline), A-B interactions are stronger than those of A-A or B-B interactions.
For positive deviation, Δmix H= +ve Δmix V= +ve
For negative deviation, Δmix H= -ve Δmix V= -ve
The solutions showing positive deviation and negative deviation from the Raoult’s law are shown in the figure below.
The binary mixture (liquid mixtures) composition having the same composition in liquid and vapour phase, boil at constant temperature are called azeotropic mixture or azeotropes. In such cases, it is not possible to separate the components by fractional distillation. There are two types of azeotropes:
Maximum boiling azeotropes: The solutions which show large negative deviation from Raoult’s law, form maximum boiling azeotropes. Example: ethanol-water mixture.
Minimum boiling azeotropes: The solutions which show large positive deviation from Raoult’s law, form minimum boiling azeotropes. Example: nitric acid-water mixture.
The properties of solution which depend only on the number of solute particles, not on the nature of the solute particles are known as colligative properties.
Colligative properties α number of particles in the solution α 1/molar mass of solute.
There are 4 important colligative properties
Ø Relative lowering of vapour pressure of solvent
Ø Depression of freezing point of the solvent
Ø Elevation of boiling point of a solvent
Ø Osmotic pressure of the solution
Relative lowering of vapour pressure:
The relative lowering of vapour pressure of an ideal solution containing the non-volatile solute is equal to the mole fraction of the solute at a given temperature. Hence, relative lowering of vapour pressure (Raoult’s law for non-volatile solute)
p1o–p1/p1o= x2 => p1o– p1/p1o = n2/n1+n2
(since x2= n2/n1+n2)
p1o– p1/p1o = n2/n1 (For dilute solutions n2<< n1)
p1o– p1/p1o = W2 x M1/W1 x M2
Elevation in boiling point:
The boiling point of a liquid is the temperature at which its vapour pressure becomes equal to the atmospheric pressure.
Elevation of boiling point ΔTb α m or ΔTb= Kb m
where Kb= boiling point elevation constant or molal elevation constant or ebullioscopic constant
Depression in freezing point:
When a non-volatile solute is added to a solvent, the freezing point of the solution is always lower than that of pure solvent as the vapour pressure of the solvent decreases in the presence of a non-volatile solute. This difference in freezing point is known as depression of freezing point.
Depression of freezing point ΔTf α m or ΔTf= Kf m
where Kf=freezing point depression constant or molal depression constant or cryoscopic constant
Osmosis and osmotic pressure:
The process of flow of solvent molecules from lower concentration solution to solution of higher concentration is known as osmosis and Osmotic pressure of the solution is the pressure which just prevents the flow of solvent molecules
π= CRT or π=n2 RT/V ,where C= n2/V
Types of solutions on the basis of osmotic pressure:
There are following types of solution on the basis of osmotic pressure
Isotonic solution: Two solutions having same osmotic pressure at a given temperature are called isotonic solutions.
Hypotonic and hypertonic solution: A solution having lower osmotic pressure than the other is called hypotonic, while the one with higher osmotic pressure is called hypertonic.
Note: People taking salty food and water retention in tissue cells and intercellular spaces due to osmosis. The resulting puffiness is called edema.
If the pressure larger than the osmotic pressure is applied to the solution side, then the pure solvent flows out of the solution through the semipermeable membrane this phenomenon is called reverse osmosis this method is used in desalination to get salt free water from seawater.
Abnormal molecular mass:
For the substances undergoing association, dissociation in the solution, molecular mass determined from the colligative property is different from the expected value. this is known as abnormal molecular mass.
Van’t Hoff factor:
It is the ratio of the experimental value of the colligative property to the calculated value of the colligative property it is used to find out the extent of dissociation of association.
Van’t Hoff factor, i
= normal molar mass / abnormal molar mass
= Total number of moles of particles after association dissociation/number of moles of articles before association /dissociation
= Observed colligative property / calculated colligative property
If i> 1 solute undergoes dissociation, and if i<1, solute undergoes dissociation.
When there is dissociation of solute into ions such as KCl, the experimentally determined molar mass is always lower than the true value. While for an association of solute such as acetic acid, the experimentally determined molar mass is always greater than the true value.
Inclusion of van’t Hoff factor modify the equation for colligative properties as follows
Relative lowering of vapour pressure of solvent= i p1o– p1/p1o = n2/n1
Elevation of boiling point= ΔTb= i Kbm
Depression of freezing point= ΔTb= i Kbm
Osmotic pressure of solution= π= i n2 RT/V