solutions

solution

a homogenous mixture of 2+ substances

characteristics of solutions

• single phase system

• doesnt allow a beam of light to scatter

• stable & cannot be separated through filtration

• density, BP, RI etc. are uniform throughout

• particle size of solute - 10^-7 - 10^-8

classification of solutions on the basis of solvent

• aqueous: solute is dissolved in water

• non-aqueous: solute is dissolved in something else

classification of solutions on the basis of solute

• concentrated: large amt. of solute

• diluted: small amt. of solute

classification of solutions on the basis of no. of components

• binary: 2 components

• tertiary: 3 components

mass/mass %

mass of component/ total mass x 100

vol/vol%

vol. of component/ total vol. x 100

mass/vol %

mass of component/ total vol. x 100

ppm

no. of parts of component/ total no. of parts x 10^6

mole fraction

no. of moles of component/ total no. of moles

molarity

no. of moles of solute/ vol. of sol (L)

(note: it varies with temperature)

molality

no. of moles of solute/ mass of solvent (kg)

(note: it is independent of temperature

solubility of solid in liquid

it is the maximum weight of solute that can be dissolved in 100g of solvent.

it depends on nature & temperature

concept of solubility of solid in liquid

• when solid is added in liquid, the solid keeps dissolving and the concentration increases (dissolution)

• but some of the particles already in the solution collide with the ones coming in and get separated out (crystallisation)

dynamic equilibrium: when the no. of particles going in is equal to the no. of particles separating out. at this point, the concentration of solution is max.

how nature of the solid & liquid affects the solubility

like dissolves like

• polar solids dissolve in polar liquids (ex: NaCl & H2O)

• non-polar solids dissolve in non-polar liquids (ex: some covalent compounds)

how temperature affects the solubility of solids in liquids

the affect of temperature follows the le-chatelier’s principle;

• \Delta solH = --ve

  • dissolution is exothermic

  • solubility decreases as temperature increases

• \Delta solH = +ve

  • dissolution is endothermic

  • solubility increases as temperature increases

affect of pressure on solubility of solids in liquids

no effect as solids and liquids are highly incompressible in nature

solubility of gas in liquid

it is the volume of gas that can be dissolved in 1cc of liquid

almost all gases are soluble in water, but at different extents

how nature of gas and liquid affects the solubility

gases which are easily liquified are more soluble in liquids

ex: NH3, HCl, SO2

how temperature affects solubility of gases in liquids

• solubility decreases with increase in temperature

  • this is because molecular motion increases, resulting in them escaping out of the solution

• also, dissolution of gas is exothermic

  • \Delta solH = —ve

  • increase in temperature → decrease in solubility

affect of pressure on solubility of gases in liquids

pressure increases → solubility increases

• when gas is put in liquid,

  • some are dissolved in the liquid

  • some are above the liquid in gaseous state

• if we increase the pressure by compressing the gas, more particles enter the liquid

• the solubility would then keep increasing until a new equilibrium is achieved

henry’s law

at constant temperature, the partial pressure of the gas in vapour phase is directly proportional to the mole fraction (solubility) of the gas in solution

p = KhX

p-X graph → straight line

key points on Kh

• it depends on the nature of gas

• it is different in different solvents

• Kh \alpha T

• Kh \alpha 1/ solubility

henry’s law in relation to deep sea diving

• scuba divers breathe high pressure air underwater. this high pressure increases the solubility of gases in blood

• when the diver comes back up, the pressure decreases and the dissolved gases are released, which may block the capillaries

• to prevent this, they wear tanks filled with air diluted with He

henry’s law in relation to high altitudes

• at high altitudes, the pressure of O2 is low

• hence, solubility in blood and tissues is also low, which may make us feel weak

limitations of henry’s law

• if the pressure is too high or temperature is too low, the law becomes too inaccurate

• the gas cant undergo any chemical change

• it cant undergo association or dissolution in the solution

vapor pressure

it is the pressure exerted by the vapors, when the system is in equilibrium

how a liquid achieves equilibrium

• at a certain temperature, when a liquid is in a closed vessel, some of the liquid gets converted into vapor to fill the empty space

• more the evaporation, more the molecules in the vapor

• these molecules move randomly, and some strike the water and get condensed

• when the rate of evaporation and condensation is equal, it is in equilibrium

how nature of liquid affects the v.p

weaker the intermolecular forces, greater the v.p

this is because more molecules can enter the vapor

how temperature affects the v.p of liquid

v.p increases with increase in temperature

this is because the kinetic energy increases

raoult’s law

at a given temperature, in a liquid-liquid solution, the partial v.p of each component is directly proportional to its mole fraction in the solution

p1 \alpha X1 → p1 = p1*X1

p2 \alpha X2 → p2 = p2*X2

Ptotal from raoult’s law

P = P1 + P2

= P1*X1 + P2*X2

but, X1 + X2 = 1

thus,

P = P1* + (P2* - P1*)X2

raoult’s law with respect to henry’s law

we know,

p = p*X for any volatile component

if a gas is volatile, then

p = KhX

hence,

p* = Kh

v.p of solids in liquids

• solids are non-volatile

• hence, the v.p only depends on the solvent, which would be less than that of pure solvent

  • this is because the surface is covered by both solute and solvent molecules, reducing the no. of evaporated solvent molecules

ideal solutions

• they are solutions which obey raoult’s law over the entire range of concentration

• enthalpy of mixing, \Delta mix H = 0

• volume of mixing, \Delta mix V = 0

  • this implies that no heat is evolved during mixing, and total volume remains same

explanation of ideal solutions

• consider solute A and solvent B

• in pure components, the intermolecular interactions will be A—A and B—B

• in solution, there will be A—A, B—B and A—B

an ideal solution is one where

A—A = B—B = A—B

non-ideal solutions

• they are solutions which do not obey raoult’s law over the entire range of concentration

• enthalpy of mixing, \Delta mix H =/ 0

• volume of mixing, \Delta mix V =/ 0

the v.p is either higher or lower as predicted by raoult’s law

• if higher → positive deviation

• if lower → negative deviation

explanation of positive deviation in non-ideal solutions

• in this case, A—A, B—B are stronger than A—B

  • this means the molecules find it easier to escape in solution form (A—B), increasing the v.p

• here,

  • Pa > Pa*Xa

  • Pb > Pb*Xb

• \Delta mixH > 0 (+ve)

• \Delta mixV > 0 (+ve)

• here, heat is absorbed

explanation of negative deviation in non-ideal solutions

• here, A—B is stronger than A—A and B—B

  • this results in molecules finding it harder to escape in solution form (A—B), decreasing the v.p

• here,

  • Pa < Pa*Xa

  • Pb < Pb*Xb

• \Delta mixH < 0 (-ve)

• \Delta mixV < 0 (-ve)

• here, heat is evolved

azeotropes

• they are liquid mixtures having same composition in both liquid and vapor phase

• they boil at constant temperature

• it is not possible to separate these via fractional distillation

minimum boiling azeotropes

• they are non-ideal solutions with large +ve deviation

• here, there is an intermediate composition where

  • v.p is highest

  • b.p is lowest

maximum boiling azeotropes

• non-ideal solutions with large -ve deviation

• here, there is an intermediate composition where

  • b.p is highest

  • v.p is lowest

colligative properties

they are properties of solutions which depend only on the number of solute particles, irrespective of their nature

there are 4 main properties

• relative lowering of vapor pressure

• elevation in boiling point

• depression in freezing point

• osmotic pressure of solution

relative lowering of vapor pressure

• we know, addition of non-volatile solute decreases the v.p

• let X1 be mole fraction of solvent, X2 be that of solute, p1* the v.p of pure solvent and p be v.p of solution

thus, from raoult’s law, p = p1 = p1*X1

reduction in v.p, \Delta p1 = p1* - p1 = p1*(1 -X1)

but, X1 = 1 - X2

hence,

\Delta p1 = p1*X2

expression of relative lowering of v.p in terms of molar mass

let W1, W2 be masses and M1, M2 be molar masses of solvent and solute respectively

we know,

X2 = n2/ (n1 + n2)

= W2/M2 // (W1/M1) + (W2/M2)

but, for dilute solutions, n2 ««« n1

hence,

X2 = W2/M2 // W1/M1

substitute this in the previous conclusion, and we get

M2 = W2M1/ [W1(\Delta p1/ p1*)]

elevation in boiling point

• the boiling point of a liquid is the temperature at which the vapor pressure and atmospheric pressure are equal

• when a non-volatile solute is added, the b.p becomes higher than that of pure solvent

• the difference in boiling point of solution Tb and pure solvent Tb* is called elevation in boiling point (\Delta Tb)

\Delta Tb = Tb - Tb*

boiling point elevation constant/ ebullioscopic constant

for dilute solutions, elevation in boiling point is directly proportional to the molal concentration of solute in the solution (molality)

\Delta Tb \alpha m

=> \Delta Tb = KbM

where Kb = boiling point elevation constant

expression of elevation in b.p in terms of molar maas

molality, m = n2 × 1000/ W1 (g)

but, n2 = W2/M2

thus,

m = W2 × 1000/ M2 x W1

but, \Delta Tb = Kbm

= Kb x W2 × 1000/ M2 x W1

thus,

M2 = Kb x W2 × 1000/ \Delta Tb x W1

depression in freezing point

• the freezing point is the temp. at which the solid and liquid phases have same v.p

• it decreases with the addition of non-volatile solute

  • this is because the v.p deceeases

• if Tf* is f.p temp of pure solvent and Tf is the f.p temp of solution then

\Delta Tf = Tf* - Tf

freezing point depression constant/ cryoscopic constant

the depression in freezing point is directly proportional to the molality of the solute in solution

\Delta Tf\alpha m

=> \Delta Tf = Kf x m

relationship of Kf and Kb with enthalpy change

• Kf = R x M1 x Tf²/ 1000 x \Delta fus H

• Kb = R x M1 x Tb² / 1000 x \Delta vap H

where R = gas constant, M1 = m.m of solvent

osmosis

• it is the phenomenon of the flow of solvent molecules through a semipermeable membrane from pure solvent to solution

• if the osmosis takes place between solutions of different concentrations, then the solvent molecules will move from low to high solute concentration until equilibrium is attained

examples of osmosis

• lot of salty food will lead to water retention in tissue cells and intercellular spaces because of osmosis

• water movement from soil to plant

• raw mango placed in concentrated salt solution will lose water via osmosis and shrivel into pickle

• salting meats and veggies preserves them as through osmosis, the bacteria would lose water and die

osmotic pressure (\pi)

• it is the excess pressure that must be applied to the solution side of membrane (as opposed to solvent), to prevent osmosis

• it is a colligative property

osmotic pressure is proportional to the molarity (C) of solution at temperature T

\pi \alpha C

\pi = CRT

in terms of molar mass,

M2 = W2RT/V$$\pi$

advantage of osmotic pressure to determine molar mass

• it is done in room temperature

• molarity is used instead of molality

• magnitude is large even for very dilute solutions

types of solutions based on osmotic pressure

• isotonic: two solutions having same osmotic pressure at a given temperature

  • no osmosis occurs as they have same molar concentration

  • eg: saline solution: 0.9% mass/vol NaCl solution which has same o.p as blood

• hypertonic: a solution having more osmotic pressure than the other

  • solvent would move into the solution

  • eg: a sol. of more than 0.9% mass/vol NaCl would make the blood cells shrink as the water would come out of it

• hypotonic: a solution having less osmotic pressure than the other

  • solvent would move out of the solution

  • eg: a sol. of less than 0.9% mass/vol NaCl would make the blood cells swell as water would enter it

reverse osmosis

• if a pressure larger than the osmotic pressure is applied to the solution side, it would start flowing towards the solvent instead of the other way around. this is called reverse osmosis

• it is used to desalinate sea water to get fresh water

abnormal. molar mass

• in association and dissociation of compounds, we cannot use the colligative properties to get correct value of molar mass; we may get something thats either lower or higher

• association: association leads to decrease in no. of particles in the solution, decreasing the value of colligative properties. hence, we get a higher value than the actual one

  • eg: ethanoic acid in benzene (predicted value = 120, actual value = 60)

• dissociation: dissociation leads to increase in no. of particles in the solution, increasing the value of colligative properties. hence, we get a lower value than the actual one

  • eg: KCl in water (predicted value = 37.25, actual value = 74.5)

van’t hoff factor (i)

it is the ratio of experimental value of colligative property to the calculated value of colligative property

i = calculated normal molar mass/ observed abnormal molar mass

= observed colligative property/ calculated colligative property

• hence, colligative property is inversely proportional to molar mass

• in association, i < 1

• in dissociation, i > 1

• if neither association nor dissociation takes place, i = 1

degree of dissociation and association

• degree of dissociation: fraction of total substance that undergoes dissociation

  • \alpha = i - 1/ n - 1

• degree of association: fraction of total substance that exists as associated molecules

  • \alpha = 1 - i/ 1 - 1/n

inference from different values of i

• i = 1 → solute behaves normally

• i = ½ → solute is dimer

• i = ¼ → solute is tetra-atomic (eg: P4)

• i = 1/8 → solute is octa-atomic (eg: S8)

forms of colligative properties with respect to i

• relative lowering of v.p: \Delta p = ip*X2

• elevation in boiling point: \Delta Tb = iKbm

• depression in freezing point: \Delta Tf = iKfm

• osmotic pressure: \pi = iCRT