NOTES -THEORY OF DILUTE SOLUTIONS

THEORY OF DILUTE SOLUTION

Solution;Asolution is a homogeneous mixture of two or more chemically non-reacting substances whose composition can be varied with in certain limits.

In a solution partical size is less than 10^-9nm & different constituents of the mixture can not be seperated by any of the physical methods.

Every solution is made up of a solvent and one or more solutes. The component of the solution which is present in large quantity is called as solvent and the other component which is present in small quantity AND changes its state is called as solute.

TYPES OF SOLUTIONS;

S.NO.	TYPE OF SOLUTION	SOLUTE	SOLVENT	EXAMPLE
1.	Solid-solid	Solid	Solid	alloys
2.	Solid-liquid	Solid	liquid	Solutions of sugar,salts …..in water
3.	Solid-gas*	Solid	gas	Sublimed substances like iodin, camphor in air
4.	Liquid-Solid*	Liquid	Solid	Hydrated salts
5.	Liquid-Liquid	Liquid	Liquid	Alcohol in water
6.	Liquid-gas*	Liquid	gas	Water vapour in air
7.	gas-Solid	gas	Solid	H2/Pd
8.	gas-Liquid	gas	-Liquid	Aerated drinks
9.	Gas-gas	gas	gas	air

*- These systems are usually colloidal in nature. Our studies are restricted to solutions of non-volutile solutes in to liquid solvents& some of their important properties.

The factors which affects solubality of a solid in a liquid are 1.Nature of solute & solvent. 2.Temperature

COLLIGATIVE PROPERTIES;The properties of the solutions which depends upon the no. of solute particals& not on the nature of solute are called as colligative properties.Ex; 1)lowering of vapourpressure of the solvent.2)elevation in boiling point of the solvent. 3)depression in freezing point of the solvent. d)osmotic pressure of the solution.

1.VAPOUR PRESSURE OF SOLUTIONS .When a pure liquid is is taken in an evacuated vessel placed in a thermostat at a constant temp. & connected to a monometer , the amount of vapour collected above the liquid keeps on increasing & finally becomes constant.At this equilibrium state the rate of evoporation becoms equal to rate of condensation .This pressure exerted by the vapours is called as vapour pressure. Hence “ vapour pressure of a liquid is the pressure exerted by the vapours

in equilibrium with the liquid at a perticular temperature.” T The vapour pressure of a liquid depends on a) nature of the liquid b)temperature. Effect of adding a non- volatile solute on vapour pressure of a solvent;

When a non volatile solute is added to a solvent,the few liquid molecules at the surface is replaced by solute particals .Due to this no. of solvent molecules at the surface decreases. Due to this evoporation decreases as the rate evoporation depends on no. of solvent molecules at the surface.

Hence vapour pressure of the solution decreases.thus vapourpressure of a solution containing a non-volatile solute is always less than that of the pure solvent.this is called as

lowering of vapourpressure.If P₀ is the vapourpressure of the solvent& P is the vapourpressure of the solution then P₀>P.

( P_{0 –} P)IS CALLED AS Lowering of vapourpressure & ( P_{0 –} P)/ P₀ CALLED AS RELATIVE LOWERING OF VAPOURPRESSURE.

F.RAOULT, a french chemist related lowering of vapourpressure & conc. Of the solution . The Raoults law states that ‘the relative lowering of vapour pressure is equal to the ratio of the no. of moles of the solute to the total no. of moles of the solute and solvent in the solution.’ i.e. ( P_{0 –} P)/ P₀ =n₂/n₁+n₂ where n₁ & n₂ are the no. of moles of the solvent and the solute respectively.

n₂/n₁+n₂ =x₂ where x₂ is called as mole fraction of the solute. Hence the relative lowering of vapourpressure is equal to the molefraction of the solute.

Solutions can be classifide in to two types a)Ideal solution b)Non-ideal solution

IDEAL SOLUION; An Ideal solution is one which obeys Raoults law at all conc. &at all temperature.

Ex.; 1)n-hexane+n- heptane 2)benzene+toluene 3)bromo ethane+iodoethane 4)chloro benzene+bromo benzene

characteristics of an ideal solution; a)they obeys raoults law b)change in volume on mixing is zero c)change in enthalpy on mixing is zero

NON-IDEAL SOLUION;A Non- Ideal solution is one which does not obeys Raoults law .

characteristics of a non- ideal solution; a)they does not obeys raoults law b)change in volume on mixing is not equal to zero c)change in enthalpy on mixing is not equal to zero .

Non -ideal solutions deviates from idel behaviour. Based on the type of deaviation they are classifide in to two types

Non -ideal solutions with possitive deaviation; In this type of solutions , the observed vapourpressure of each component & the total vapourpressure are greater than predicted by Raoults law.

The cause of deaviation is due to inter molecular forces. Let us assume that the two components mixed are A&B . A +ve deaviation is shown when the inter molecular force between A-Bis weaker than A-A&B-B. There fore on mixing ,molecules of AorB will escape more easily than these were as pure components. As a result V.P. Increases. The solution showes +ve deaviation.

EX; 1)acetone+ethylalcohol b)water+ethylalcohol c)CCl₄+CHCl₃ d)acetone+ CS₂ e)acetone+benzene

Non -ideal solutions with negative deaviation;In this type of solutions , the observed vapourpressure of each component & the total vapourpressure are less than predicted by Raoults law.Let us assume that the two components mixed are x&y . A -ve deaviation is shown when the inter molecular force between x-yis stronger than X-X & Y-Y. There fore on mixing ,molecules of X or Y will not escape easily than these were as pure components. As a result V.P. decreases. The solution showes -ve deaviation.

EX;a)acetone + aniline b)HCl + water c)HNO₃ + water d)acetone + chloroform e)benzene + chloroform f)H₂SO₄+ water

MEASUREMENT OF RELATIVE LOWERING OF VAPOUR

PRESSURE BY OSTWALDS- WALKER DYNAMIC METHOD;

PRINCIPLE; In this method dry air is passed through solution , pure solvent& then through anhydrous CaCl₂ tube respectively. By knowing the loss in mass of solution , solvent& gain mass of anhydrous CaCl₂ tube , relative lowering of vapour pressure can be calculated

FIGURE;

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PROCEDURE;The apparatus consist of two sets of bulbs A&B. In set A bulbs ,solution is taken& in set B bulbs pure solvent is taken. Both these sets of bulbs are weighed & then placed in a thermostate to maintain constant temperature.these bulbs are connected as shown in fig. The last solvent bulb is connected to a eighed U- tube containing anhydrous CaCl_2. A guard tube containing soda lime is connected to the CaCl_2. Tube to prevent the entry of moisture from outside.

A slow current of dry air is passed through the bulbs containing solution . The air takes up vapour from the solution & gets saturatedup to pressure P which is vapourpressure of the solution at that temperature. this air is than passed through solvent bulbs.since the vapourpressure of the pure solvent P₀ is higher , more vapours are taken up by the air. The air gets saturated to the pressure P0 by absorbing extra vapour.the air coming out of solvent bulbs is then passed through U- tube containing anhydrous CaCl_2.anhydrous CaCl₂. Absorbs all moisture. solvent bulbs &anhydrous CaCl_2.tube is weighed again .the increase in mass of CaCl₂ tube is praportional to vapourpressure of pure solvent P₀.The decrease in mass of solvent bulbs is praportional to the difference in vapourpressure of solvent &the solution.

There fore the relative lowering of vapour pressure=loss in mass of solvent bulbs

gain in mass of CaCl₂

Determination of molecular mass;according to Raoults law,

( P_{0 –} P)/ P₀ =n₂/n₁+n₂ where n₁ & n₂ are the no. of moles of the solvent and the solute respectively.

Let W₂g be the amount of solute dissolved in W₁ g of solvent. Let M₂ & M₁ be the molecular mass of solute & solvent respectively.then n₂=W₂/M₂ &n₁= W₁/M₁

2. ELEVATION IN BOILING POINT;

BOILING POINT OF A LIQUID; Boiling point of a liquid is defined as the temperature at which the vapourpressure of the liquid becoms equal to atmospearic pressure.

Vapour pressure of a solution is always less than that of pure solvent.hence boiling point of a solution is higher than that of the solvent. Thus addition of asolute to a pure solvent increases its boiling point. The increase in the boiling point of a solvent on addition of a solute to it is called as the ELEVATION IN BOILING POINT .hence the ELEVATION IN BOILING POINT is directly praportional to the lowering of vapourpressure.

i.e.( T-T₀ )α ( P_{0 –} P) since P₀ is a constat , ∆ T α ( P_{0 –} P)/ P₀

according to Raoults law , ( P_{0 –} P)/ P₀ =W₂M₁/W₁M₂ i.e. ∆ T α W₂M₁/W₁M₂

∆ T = kW₂M₁/W₁M₂(multiply the numaretor &denominator by 1000) =1000 kW₂M₁/1000W₁M₂

for a given solvent , the molarmass M₁ is a constant.so k M₁/1000 is a constant and taken as K_b– molal elevation constant.∆ T=1000 K_bW₂/W₁M_{2 .} When W₂/M₂=1, AND W₁=1000,∆ T=K_b

i.e. The molal elevation constant K_b is the elevation of the boiling point , when one mole of solute is dissolved in 1000g Of the solvent.

3. DEPRESSION IN FREEZING POINT;

FREEZING POINT OF A LIQUID; freezing point of a liquid is defined as the temperature at which the vapourpressure of the liquid becoms equal to vapourpressure of solid.or that temperature at which solid & the liquid co exists.

Vapour pressure of a solution is always less than that of pure solvent. hence freezing point of a solution is lesser than that of the solvent.addition of a solute to a solvent decreases the freezing point of a solvent. The decrease in freezing point of a solvent caused by the addition of a nonvolatile solute to it is called as depression of freezing point.hence the depression in freezing point is directly praportional to the lowering of vapourpressure.

( T₀-T )α ( P_{0 –} P) since P₀ is a constat , ∆ T α ( P_{0 –} P)/ P₀ according to Raoults law ,( P_{0 –} P)/ P₀ =W₂M₁/W₁M₂ i.e. ∆ T α W₂M₁/W₁M₂

∆ T = kW₂M₁/W₁M₂ (multiply the numaretor &denominator by 1000)=1000 kW₂M₁/1000W₁M₂

for a given solvent , the molarmass M₁ is a constant.so k M₁/1000 is a constant and taken as K_f– molal depression constant.∆ T=1000 K_fW₂/W₁M_{2 .} When W₂/M₂=1, AND W₁=1000,∆ T=K_f

i.e. The molal depression constant K_f is the depression of the freezing point , when one mole of solute is dissolved in 1000g. Of the solvent.

4.OSMOSSIS & OSMOTIC PRESSURE;

SEMIPERMIABLE MEMBRANE; a membrane which allows the passage of only solvent molecules & not of solute particles. Ex; animal membrane, copper ferrocyanide , silicates of iron , cobalt, nickel etc.

OSMOSIS; ( IN GREEK OSMOS MEANS PUSH) When a semipermiable membrane is placed between a solution & a pure solvent , the solvent molecules flows from a region of pure solvent in to solution.in the same way when the two solutions of different conc. Are separated by a semipermiable membrane , the solvent molecules flows from a region oflower conc. To a region of higher conc. Spontaneously. ‘ this spontaneous flow of solvent molecules through a semipermiable membrane from a pure solvent to a solution is called as osmosis.’

osmotic pressure;

consider an apparatus consists of two chambers separated by means of a semipermiable membrane. One compartment is filled with solvent & the other one with solution prepared in the same solvent.the solution chamber is fitted with a movable piston.solvent chamber is fitted with a glass tube. Since there is a difference in vapour pressure of solvent & solution , movement of solvent molecules occurs in to solution .this movement of solvent molecules in to solution can be stopped by applying certain external pressure on solution. The external pressure applyid on solution is equal to the osmotic pressure.

‘osmotic pressure may be defined as the external pressure which should be applied to the solution in order to stop the flow of solvent in to the solution when the two are separated by a semipermiable membrane.’

according to VantHoffs equation ,πV=nRT i.e.πV= W₂ RT/M₂ i.e.M₂= W₂RT/ πV where M₂=molecular mass of the solute.W₂= mass of the solute , T=temp. V= volume of the solution, &π=osmotic pressure of the solution.

NOTE;1. THE SOLUTIONS WHICH ARE HAVING SAME OSMOTIC PRESSURE ARE CALLED AS ISOTONIC SOLUTIONS OR ISO-OSMOTIC SOLUTIONS.

1. THE SOLUTION WHICH IS HAVING HIGHER OSMOTIC PRESSURE WHEN COMPARED TO OTHER SOLUTION ARE CALLED AS HYPERTONIC SOLUTIONS.

2. THE SOLUTION WHICH IS HAVING LOWER OSMOTIC PRESSURE WHEN COMPARED TO OTHER SOLUTION ARE CALLED AS HYPOTONIC SOLUTIONS.

VantHoff’s-theory of dilute solution; VantHoff correllated the properties of gases & that of dilute solution.he found similarity between different priperties. Solute particals in dilute solution behaves as same as the gas molecules in in a gas. i.e. There is a close parallel between the pressure exerted by a gas & the osmotic pressure developed by a solution.concluded that osmotic pressure of dilute solutions varied with their conc. & temp. in the same way as the pressure of the gases. His final conclusions are

1. at a given temp. the osmotic pressure of a solution is directly praportional to conc.

2. For a given conc. , the osmotic pressure is praportional to its absolute temp.

3. equimolar solution at same temp. have same osmotic pressure.

Based on above observation VantHoffstated following laws.

1.VantHoff’s Boyles law; this law states that at constant temperature osmotic pressure of the solution is directly praportional to molar conc. Of the solution.

Π α c at constant temperature or π α n/v where n is the no. of moles&v is the volume i.e. π α 1/v or Πv=constant

2. VantHoff’s charles law; this law states that at , at constant volume the osmotic pressure of a solution is directly praportional to its absolute temp. Π α T OR Π /T=CONSTANT

1. VantHoff’s Avogadros law; this law states that at constant temperature the solutions having equal molar conc. Of different solute has same osmotic pressure.i.e. π α n

   ABNORMAL MOLECULAR MASS;Experimentaly observed molecular mass of a substance determined on the basis of a colligative property is found to be different from the normal value as expected from its chemical formula .

   Cause for abnormal molecular mass; 1.colligative property shows normal value for the molecular mass when the molecular state of the solute remains unchanged in the solution.

   2. the observed value of colligative property decreases when solute undergoes association in solution as molecular assosiation leads to decreases in no. of particles of solute in solution.eg. Assosiation of benzoic acid in benzeneto form dimer. Due to this observed molecular mass of the solute shows higher value.

   3. the observed value of colligative property increases when solute undergoes dissociation in solution as molecular dissosiation leads to increases in no. of particles of solute in solution.eg. Dissociation of NaCl, BaCl₂ to form ions. Due to this observed molecular mass of the solute shows lower value.