Class 12 Chemistry Book Chapter Solutions (chapter 2) Notes based on CBSE book.
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Solutions (chapter 2)
Brass (mixture of copper and zinc)
German silver (mixture of copper, zinc and nickel)
Bronze (mixture of copper and tin)
1 part per million (ppm) of fluoride ions in water prevents tooth decay, while 1.5 ppm causes the tooth to become mottled and high concentrations of fluoride ions can be poisonous.
Sodium fluoride is used in rat poison.
Intravenous injections are always dissolved in water containing salts at particular ionic concentrations that match with blood plasma concentrations.
Types of Solutions
Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture.
Solvent-The component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists.
Solutes- One or more components present in the solution other than solvent are called solutes.
We shall consider only binary solutions (consisting of two components).
| Type of solution | Solute | Solvent | Example | |
|---|---|---|---|---|
| Gaseous Solutions | Gas | Gas | Mixture of oxygen and nitrogen gases | |
| Liquid | Gas | Chloroform mixed with nitrogen gas | ||
| Solid | Gas | Camphor in nitrogen gas | ||
| Liquid Solutions | Gas | Liquid | Oxygen dissolved in water | |
| Liquid | Liquid | Ethanol dissolved in water | ||
| Solid | Liquid | Glucose dissolved in water | ||
| Solid Solutions | Gas | Solid | Solution of hydrogen in palladium | |
| Solid | Amalgam of mercury with sodium | ||
| Solid | Solid | Copper dissolved in gold |
Expressing Concentration of Solutions
Composition of a solution can be described by expressing its concentration. The latter can be expressed either qualitatively or quantitatively. For example, qualitatively we can say that the solution is dilute (i.e., relatively very small quantity of solute) or it is concentrated (i.e., relatively very large quantity of solute).
There are several ways by which we describe the concentration of the solution quantitatively.
Mass percentage (w/w): The mass percentage of a component of a solution is defined as:
Mass % of a component =
Mass of the component in the solutionTotal mass of the‘solution×100
A solution is described by 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution. Concentration described by mass percentage is commonly used in industrial chemical applications.
commercial bleaching solution contains 3.62 mass percentage of sodium hypochlorite in water.
Volume percentage (V/V): The volume percentage is defined as:
Volume percentage of a component=Volume of the componentTotal volume of solution×100
For example, 10% ethanol solution in water means that 10 mL of ethanol is dissolved in water such that the total volume of the solution is 100 mL. Solutions containing liquids are commonly expressed in this unit. For example, a 35% (v/v) solution of ethylene glycol, an antifreeze, is used in cars for cooling the engine. At this concentration the antifreeze lowers the freezing point of water to 255.4K (–17.6°C).
Mass by volume percentage (w/V): Another unit which is commonly used in medicine and pharmacy is mass by volume percentage. It is the mass of solute dissolved in 100 mL of the solution.
Parts per million: When a solute is present in trace quantities, it is convenient to express concentration in parts per million (ppm) and is defined as:
Parts per million=Number of parts of the componentTotal number of parts of all components of the solution×106
As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume and mass to volume. A liter of sea water (which weighs 1030 g) contains about 6 × 10–3 g of dissolved oxygen (O2 ). Such a small concentration is also expressed as 5.8 g per 106 g (5.8 ppm) of sea water. The concentration of pollutants in water or atmosphere is often expressed in terms of µg mL–1 or ppm.
Mole fraction: Commonly used symbol for mole fraction is x and subscript used on the right hand side of x denotes the component. It is defined as:
Mole fraction of a component =
Number of moles of the componentTotal number of moles of all the componentsA binary mixture, if the number of moles of A and B are n_A and n_B respectively, the mole fraction of A will be
xA=nAnA+nBFor a solution containing i number of components, we have:
xi=nin1+n2+...+ni=ni∑ni
It can be shown that in a given solution sum of all the mole fractions is unity, i.e.
x1 + x2 + .................. + xi = 1
Mole fraction unit is very useful in relating some physical properties of solutions, say vapour pressure with the concentration of the solution and quite useful in describing the calculations involving gas mixtures.
Molarity: Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimeter) of solution,
Molarity=moles of soluteVolume of solution in liter
0.25 molL–1 (or 0.25 M) solution of NaOH means that 0.25 mol of NaOH has been dissolved in one liter (or one cubic decimeter).
Molality: Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:
Molality(m)=Moles of soluteMass of solvent in kgFor example, 1.00 mol kg–1 (or 1.00 m) solution of KCl means that 1 mol (74.5 g) of KCl is dissolved in 1 kg of water. Each method of expressing concentration of the solutions has its own merits and demerits. Mass %, ppm, mole fraction and molality are independent of temperature, whereas molarity is a function of temperature. This is because volume depends on temperature and the mass does not.
Solubility
Solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent at a specified temperature. It depends upon the nature of solute and solvent as well as temperature and pressure.
Solubility of a Solid in a Liquid
sodium chloride and sugar dissolve readily in water, naphthalene and anthracene do not.
Naphthalene and anthracene dissolve readily in benzene but sodium chloride and sugar do not.
Polar solutes dissolve in polar solvents and non-polar solutes in non-polar solvents.
A solute dissolves in a solvent if the intermolecular interactions are similar in the two or we may say like dissolves like.
Dissolution - When a solid solute is added to the solvent, some solute dissolves and its concentration increases in solution. This process is known as dissolution.
Crystallisation - When Some solute particles in solution collide with the solid solute particles and get separated out of solution. This process is known as Crystallisation.
Equilibrium - A stage is reached when the two processes occur at the same rate. Under such conditions, number of solute particles going into solution will be equal to the solute particles separating out and a state of dynamic equilibrium is reached.
Solute + Solvent ⇋ Solution
The concentration of solute in solution will remain constant under the given conditions, i.e., temperature and pressure.
Saturated solution - A solution in which no more solute can be dissolved at the same temperature and pressure is called a saturated solution.
Unsaturated solution - An unsaturated solution is one in which more solute can be dissolved at the same temperature.
The solution which is in dynamic equilibrium with undissolved solute is the saturated solution and contains the maximum amount of solute dissolved in a given amount of solvent. Thus, the concentration of solute in such a solution is its solubility.
Solubility of one substance into another depends on the nature of the substances. In addition to these variables, two other parameters, i.e., temperature and pressure also control this phenomenon.
Effect of temperature
The solubility of a solid in a liquid is significantly affected by temperature changes. In a nearly saturated solution, the dissolution process is endothermic (∆sol H > 0), the solubility should increase with rise in temperature and if it is exothermic (∆sol H < 0) the solubility should decrease.
Effect of pressure
Pressure does not have any significant effect on solubility of solids in liquids. It is so because solids and liquids are highly incompressible and practically remain unaffected by changes in pressure.
Solubility of a Gas in a Liquid
Many gases dissolve in water.
Oxygen dissolves only to a small extent in water.
On the other hand, hydrogen chloride gas (HCl) is highly soluble in water.
Solubility of gases in liquids is greatly affected by pressure and temperature. The solubility of gases increase with increase of pressure.
When increase the pressure over the solution phase by compressing the gas to a smaller volume. This will increase the number of gaseous particles per unit volume over the solution and also the rate at which the gaseous particles are striking the surface of solution to enter it.
The solubility of the gas will increase until a new equilibrium is reached resulting in an increase in the pressure of a gas above the solution and thus its solubility increases.
Henry’s law
Henry was the first to give a quantitative relation between pressure and solubility of a gas in a solvent which is known as 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.
The solubility of a gas in a liquid solution is a function of partial pressure of the gas. 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 Henry’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
Henry’s law is expressed as:
p = Kн.x ...................(Here Kн is the Henry’s law constant)
Different gases have different Kн values at the same temperature. Kн is a function of the nature of the gas. Higher the value of Kн at a given pressure, the lower is the solubility of the gas in the liquid.
Kн values increase with increase of temperature indicating that the solubility of gases increases with decrease of temperature. Because aquatic species are more comfortable in cold waters rather than in warm waters.
Several applications of Henry’s law
• To increase the solubility of CO2 in soft drinks and soda water, the bottle is sealed under high pressure.
• Scuba divers must cope with high concentrations of dissolved gases while breathing air at high pressure underwater. Increased pressure increases the solubility of atmospheric gases in blood. When the divers come towards surface, the pressure gradually decreases. This releases the dissolved gases and leads to the formation of bubbles of nitrogen in the blood. This blocks capillaries and creates a medical condition known as bends, which are painful and dangerous to life. To avoid bends, as well as, the toxic effects of high concentrations of nitrogen in the blood, the tanks used by scuba divers are filled with air diluted with helium (11.7% helium, 56.2% nitrogen and 32.1% oxygen).
• At high altitudes the partial pressure of oxygen is less than that at the ground level. This leads to low concentrations of oxygen in the blood and tissues of people living at high altitudes or climbers. Low blood oxygen causes climbers to become weak and unable to think clearly, symptoms of a condition known as anoxia.
Effect of Temperature
Solubility of gases in liquids decreases with rise in temperature.
Dissolution process involves dynamic equilibrium and thus must follow Le Chatelier’s Principle.
Dissolution is an exothermic process, the solubility should decrease with increase of temperature.
Vapour Pressure of Liquid Solutions
Liquid solutions are formed when solvent is a liquid. The solute can be a gas, a liquid or a solid.
Generally, the liquid solvent is volatile. The solute may or may not be volatile.
Vapour Pressure of Liquid-Liquid Solutions
A binary solution of two volatile liquids and denote the two components as 1 and 2.
The total vapour pressure at this stage be Ptotaland P1 and P2 be the partial vapour pressures of the two components 1 and 2 respectively.
x1 and x1of the two components 1 and 2 respectively.
The French chemist, Francois Marte Raoult (1886) gave the quantitative relationship between them. The relationship is known as the Raoult’s law which states that for a solution of volatile liquids the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.
Thus, for component 1,
p1∝x1 and p1=p01x1
where p01 is the vapour pressure of pure component 1 at the same temperature.
Similarly, for component 2
p=p02x2
where p02 represents the vapour pressure of the pure component 2.
According to Dalton’s law of partial pressures, the total pressure ( Ptotal ) over the solution phase in the container will be the sum of the partial pressures of the components of the solution and is given as:
ptotal=p1+p2
Substituting the values of p1 and p2 ,
we get,
ptotal=x1p01+x2p02
=(1–x2)p01+x2p02
=p01+(p02–p01)x2
Following conclusions can be drawn from equation.
(i) Total vapour pressure over the solution can be related to the mole fraction of any one component.
(ii) Total vapour pressure over the solution varies linearly with the mole fraction of component 2.
(iii) Depending on the vapour pressures of the pure components 1 and 2, total vapour pressure over the solution decreases or increases with the increase of the mole fraction of component 1.
The composition of vapour phase in equilibrium with the solution is determined by the partial pressures of the components.
p1=y1ptotal
p2=y2ptotal
In general
pi=yiptotal
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=xip01 .
In the solution of a gas in a liquid, one of the components is so volatile that it exists as a gas and we have already seen that its solubility is given by Henry’s law which states that p = Kн x.
When we compare the equations for Raoult’s law and Henry’s law, it can be seen that the partial pressure of the volatile component or gas is directly proportional to its mole fraction in solution. Only the proportionality constant Kн differs from p01 .
Thus, Raoult’s law becomes a special case of Henry’s law in which Kн becomes equal to p01 .
Vapour Pressure of Solutions of Solids in Liquids
Sodium Chloride, Glucose, urea and cane sugar in water and iodine and sulphur dissolved in carbon disulphide. Vapour pressure of these solutions are quite different from those of pure solvents.
Vapour pressure - liquids at a given temperature vapourise and under equilibrium conditions the pressure exerted by the vapours of the liquid over the liquid phase is called vapour pressure.
In a pure liquid the entire surface is occupied by the molecules of the liquid. A non-volatile solute is added to a solvent to give a solution, the vapour pressure of the solution is solely from the solvent alone. Vapour pressure of the solution at a given temperature is found to be lower than the vapour pressure of the pure solvent at the same temperature.
In the solution, the surface has both solute and solvent molecules; thereby the fraction of the surface covered by the solvent molecules gets reduced. Consequently, the number of solvent molecules escaping from the surface is correspondingly reduced, thus, the vapour pressure is also reduced. The decrease in the vapour pressure of solvent depends on the quantity of non-volatile solute present in the solution, irrespective of its nature.
Raoult’s law in its general form can be stated as, for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.
When the solute is non-volatile, only the solvent molecules are present in vapour phase and contribute to vapour pressure.
p1 be the vapour pressure of the solvent,
x1 be its mole fraction,
pi 0 be its vapour pressure in the pure state.
Then according to Raoult’s law
and
p1=x1p01
The proportionality constant is equal to the vapour pressure of pure solvent, p01 .
Ideal and Non-ideal Solutions
Liquid-liquid solutions can be classified into ideal and non-ideal solutions on the basis of Raoult’s law.
Ideal Solutions
The solutions which obey Raoult’s law over the entire range of concentration are known as ideal solutions. The ideal solutions have two other important properties. The enthalpy of mixing of the pure components to form the solution is zero and the volume of mixing is also zero, i.e.,
∆mixH=0, ∆mixV=0
No heat is absorbed or evolved when the components are mixed. Also, the volume of solution would be equal to the sum of volumes of the two components. Solution of n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene, etc are examples of this type solution.
Non-ideal Solutions
When a solution does not obey Raoult’s law over the entire range of concentration, then it is called non-ideal solution. The vapour pressure of such a solution is either higher or lower than that predicted by Raoult’s law (equation p01+(p02–p01)x2). If it is higher, the solution exhibits positive deviation and if it is lower, it exhibits negative deviation from Raoult’s law.
In case of positive deviation from Raoult’s law, A-B interactions are weaker than those between A-A or B-B.
Mixtures of ethanol and acetone behave as positive deviation.
A solution formed by adding carbon disulphide to acetone, the dipolar interactions between solute-solvent molecules are weaker than the respective interactions among the solute-solute and solvent-solvent molecules. This solution also shows positive deviation.
In case of negative deviations from Raoult’s law, the intermolecular attractive forces between A-A and B-B are weaker than those between A-B and leads to decrease in vapour pressure resulting in negative deviations.
A mixture of phenol and aniline. In this case the intermolecular hydrogen bonding between phenolic proton and lone pair on nitrogen atom of aniline is stronger than the respective intermolecular hydrogen bonding between similar molecules.
A mixture of chloroform and acetone forms a solution with negative deviation from Raoult’s law. Because chloroform molecule is able to form hydrogen bond with acetone molecule
Azeotropes - On mixing, binary mixtures having the same composition in liquid and vapour phase and boil at a constant temperature. Azeotropes are not possible to separate the components by fractional distillation.
Two types of azeotropes called minimum boiling azeotrope and maximum boiling azeotrope.
Minimum boiling azeotrope - The solutions which show a large positive deviation from Raoult’s law form minimum boiling azeotrope at a specific composition. Ethanol-water mixture (obtained by fermentation of sugars) on fractional distillation gives a solution containing approximately 95% by volume of ethanol.
Maximum boiling azeotrope- The solutions that show large negative deviation from Raoult’s law form maximum boiling azeotrope at a specific composition. Nitric acid and water is an example of this class of azeotrope. This azeotrope has the approximate composition, 68% nitric acid and 32% water by mass, with a boiling point of 393.5 K.
Colligative Properties and Determination of Molar Mass
Relative lowering of vapour pressure of the solvent, Depression of freezing point of the solvent, Elevation of boiling point of the solvent and, Osmotic pressure of the solution. All these properties depend on the number of solute particles irrespective of their nature relative to the total number of particles present in the solution. Such properties are called colligative properties.
NOTE -(colligative: from Latin: co means together, ligare means to bind)
Relative Lowering of Vapour Pressure
Raoult established that the lowering of vapour pressure depends only on the concentration of the solute particles and it is independent of their identity.
A relation between vapour pressure of the solution, mole fraction and vapour pressure of the solvent, i.e.,
p1=x1p01
The reduction in the vapour pressure of solvent (∆p1 ) is given as:
∆p1=p01–p1=p01−p01x1
∆p1=x2p01 ...(1−x1=x2)
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. Equation can be written as-
∆p1p01=p01−p1p01=x2
The expression on the left hand side of the equation as mentioned earlier is called relative lowering of vapour pressure and is equal to the mole fraction of the solute. The above equation can be written as:
p01−p1p01=n2n1+n2(since x2=n2n1+n2)
Here n1 and n2 are the number of moles of solvent and solute respectively present in the solution. For dilute solutions n2< < n1, hence neglecting n2 in the denominator we have
p01−p1p01=n2n1
Or
p01−p1p01=w2×M1w1×M2
Here w1 and w2 are the masses and M1 and M2 are the molar masses of the solvent and solute respectively.
Elevation of Boiling Point
The vapour pressure of a liquid increases with increase of temperature. It boils at the temperature at which its vapour pressure is equal to the atmospheric pressure.
Water boils at 373.15 K (100° C) because at this temperature the vapour pressure of water is 1.013 bar (1 atmosphere).
Vapour pressure of the solvent decreases in the presence of non-volatile solute.
The vapour pressure of an aqueous solution of sucrose is less than 1.013 bar at 373.15 K. In order to make this solution boil, its vapour pressure must be increased to 1.013 bar by raising the temperature above the boiling temperature of the pure solvent (water).
The boiling of a solution is always higher than that of the boiling point of the pure solvent.
The elevation of boiling point also depends on the number of solute molecules rather than their nature.
Dilute solutions the elevation of boiling point (∆Tb ) is directly proportional to the molal concentration of the solute in a solution. Thus
∆Tb∝m or ∆Tb=Kbm
w2 gram of solute of molar mass M2 is dissolved in w1 gram of solvent, then molality, m of the solution is-
Here m is molality,
And Kb is called Boiling Point Elevation Constant or Molal Elevation Constant (Ebullioscopic Constant).
The unit of Kb is K kg mol-1.
m=w2/M2w1/1000=1000×w2M2×w1
T0f be the freezing point of pure solvent and T
f be its freezing point when non-volatile solute is dissolved in it. The decrease in freezing point.
∆Tf=Tf−T0f is known as depression in freezing point.
Tb=Kb×1000×w2M2×w1
M2=Kb×1000×w2Tb×w1
Depression of 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 solid solvent at lower temperature. Thus, the freezing point of the solvent decreases.
f be its freezing point when non-volatile solute is dissolved in it. The decrease in freezing point.
Depression of freezing point (∆Tf ) for dilute solution (ideal solution) is directly proportional to molality, m of the solution. Thus,
∆Tf∝m or ∆Tf=Kfm
The proportionality constant, Kf, which depends on the nature of the solvent is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant. The unit of Kf is K kg mol-1.
w2 gram of solute of molar mass M2 is present in w1 gram of solvent, produces the depression in freezing point ∆Tf of the solvent then molality of the solute is
m=w2/M2w1/1000=1000×w2M2×w1
Tf=Kf×1000×w2M2×w1
M2=Kf×1000×w2Tf×w1
The values of Kf and Kb , which depend upon the nature of the solvent,
Kb=R×M1×T2b1000×∆vapH
Kf=R×M1×T2f1000×∆fusH
Osmosis and Osmotic Pressure
Osmosis - Solvent molecules can pass through these semi-permeable membranes. This membrane is placed between the solvent and solution, the solvent molecules will flow through the membrane from pure solvent to the solution. This process of flow of the solvent is called osmosis.
Semipermeable membranes (SPM) - These membranes appear to be continuous sheets or films, yet they contain a network of submicroscopic holes or pores. Small solvent molecules, like water, can pass through these holes but the passage of bigger molecules like solute is hindered. Membranes having this kind of properties are known as semipermeable membranes (SPM).
Osmotic pressure - The flow will continue till the equilibrium is attained. The flow of the solvent from its side to solution side across a semipermeable membrane can be stopped if some extra pressure is applied on the solution. This pressure that just stops the flow of solvent is called osmotic pressure of the solution.
Solvent molecules always flow from lower concentration to higher concentration of solution. The osmotic pressure has been found to depend on the concentration of the solution.
osmotic pressure is proportional to the molarity, C of the solution at a given temperature T. Thus:
Î = C R T
Here Î is the osmotic pressure and R is the gas constant. Î = (n2 /V) R T
Here V is volume of a solution in litres containing n2 moles of solute. If w2 grams of solute, of molar mass, M2 is present in the solution, then n2 = w2 / M2 and we can write,
∏V=w2 R TM2 or M2=w2 R T∏V
Isotonic solutions -Two solutions having same osmotic pressure at a given temperature are called isotonic solutions.
Hypertonic - A solution containing more than 0.9% (mass/volume) sodium chloride, water will flow out of the cells and they would shrink. Such a solution is called hypertonic.
Hypotonic - A solution containing less than 0.9% (mass/volume) sodium chloride, water will flow into the cells if placed in this solution and they would swell. Such a solution is called hypotonic.
Phenomena of Osmosis -
A raw mango placed in concentrated salt solution loses water via osmosis and shrivel into pickle.
Wilted flowers revive when placed in fresh water.
A carrot that has become limp because of water loss into the atmosphere can be placed into the water making it firm once again.
Water will move into its cells through osmosis. When placed in water containing less than 0.9% (mass/ volume) salt, blood cells swell due to flow of water in them by osmosis.
People taking a lot of salt or salty food experience water retention in tissue cells and intercellular spaces because of osmosis. The resulting puffiness or swelling is called edema.
Water movement from soil into plant roots and subsequently into upper portion of the plant is partly due to osmosis.
The preservation of meat by salting and of fruits by adding sugar protects against bacterial action.
Through the process of osmosis, a bacterium on salted meat or candid fruit loses water, shrivels and dies.
Reverse Osmosis and Water Purification
Reverse osmosis - When the direction of osmosis be reversed and a pressure larger than the osmotic pressure is applied to the solution side. Then the pure solvent flows out of the solution through the semi permeable membrane. This phenomenon is called reverse osmosis.
Reverse osmosis is used in desalination of sea water.
These days many countries use desalination plants to meet their potable water requirements.
Abnormal Molar Masses
Abnormal molar mass - Such a molar mass that is either lower or higher than the expected or normal value is called as abnormal molar mass.
In 1880 van’t Hoff introduced a factor i, known as the van’t Hoff factor, to account for the extent of dissociation or association. This factor i is defined as:
i=Normal molar massAbnormal molar mass
i=Observed colligative propertyCalculated colligative property
i=Total number of moles of particles after association/dissociationNumber of moles of particles before association/dissociation
Colligative properties are obtained by assuming that the non-volatile solute is neither associated nor dissociated.
Inclusion of van’t Hoff factor modifies the equations for colligative properties as follows:
Relative lowering of vapour pressure of solvent,
p01−p1p01=i.n2n1
Elevation of Boiling point,
∆Tb=iKbm
Depression of Freezing point,
∆Tf=iKfm
Osmotic pressure of solution,
Î =in2RTV
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12TH CHEMESTRY