Osmosis

PYQ-2023- Solutions and colligative properties-Q8

Osmosis is the phenomenon of spontaneous flow of the solvent molecules through a semipermeable membrane from pure solvent to solution or from a dilute solution to concentrated solution. It was first observed by Abbe Nollet.

Some natural semipermeable membranes are animal bladder, cell membrane etc. $\mathrm{CU}_2\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ is an artificial semipermeable membrane which does not work in non-aqueous solutions as it dissolves in them.

Osmosis may be

(i) Exosmosis:- It is outward flow of water or solvent from a cell through semipermeable membrane.

(ii) Endosmosis:- It is inward flow of water or solvent from a cell through a semipermeable membrane.

The hydrostatic pressure developed on the solution which just prevents the osmosis of pure solvent into the solution through a semipermeable membrane is called osmotic pressure.

(iii) Electrophoresis :- Movement of charged particles in aqueous solution under the influence of an external electric field.It is used in Protein separation, DNA migration studies, contaminant detection and separation.

Electroosmosis:- Movement of fluid under the influence of an external electric field. (Undesired in electrophoretic measurements)

OSMOTIC PRESSURE :

PYQ-2024-Solutions-Q1 , PYQ-2024-Solutions-Q6 , PYQ-2023- Solutions and colligative properties-Q13, PYQ-2023- Solutions and colligative properties-Q7, PYQ-2023- Solutions and colligative properties-Q4, PYQ-2023- Solutions and colligative properties-Q3

(i) $\quad \pi=\rho gh$ where, $\rho=$ density of solution, $\mathrm{h}=$ equilibrium height.

(ii) Van’t Hoff Formula (For calculation of O.P.)

$\quad \quad \pi=\mathrm{CRT}$

$\quad \quad \pi=\mathrm{CRT}=\frac{\mathrm{n}}{\mathrm{V}} \mathrm{RT}$ (just like ideal gas equation)

$\quad \quad \therefore \mathrm{C}=$ total conc. of all types of particles.

$\quad \quad = C_1 +C_2 +C_3 + \ldots \ldots \ $

$\quad \quad = \frac{(n_1 + n_2 +n_3 +\ldots\ldots)}{V}$

$If \quad V_1 mL \quad of \quad C_1 \quad conc.\quad + \quad V_2 mL\quad of\quad C_2 \quad conc.\quad are\quad mixed$

$\quad\quad \pi = (\frac{C_1V_1 +C_2 V_2}{V_1 +V_2})RT;$

$\quad \quad \pi = (\frac{\pi_1V_1 +\pi_2 V_2}{RT});$

Type of solutions :

(a) Isotonic solution - Two solutions having same O.P.

$\quad \quad\pi_{1}=\pi_{2} \text { (at same temp.) }$

(b) Hyper tonic- If $\pi_{1}>\pi_{2} \Rightarrow$ $1^{st}$ solution is hypertonic solution w.r.t. $2^{\text {nd }}$ solution.

(c) Hypotonic - II ${ }^{\text {nd }}$ solution is hypotonic w.r.t. $1^{st}$ solution.

Abnormal Colligative Properties : (In case of association or dissociation)

Van’t Hoff CORRECTION FACTOR (i) :

PYQ-2023- Solutions and colligative properties-Q7

PYQ-2023- Solutions and colligative properties-Q15

$\quad \quad i=\frac{\text { exp/observed / actual / abnormal value of colligative property }}{\text { Theoritical value of colligative property }}$

$\quad \quad =\frac{\text { exp./ observed no. of particles / conc. }}{\text { Theoritical no. of particles }}\quad =\frac{\text { observed molality }}{\text { Theoritical molality }}$

$\quad \quad =\frac{ \text{theoretical molar mass (formula mass)}}{\text{ experimental / observed molar mass (apparent molar mass)}}$

• $\mathrm{i}>1 \Rightarrow$ dissociation.

$\quad \quad \mathrm{i}<1 \Rightarrow$ association.

• $i =\frac{\pi_{exp.}}{\pi_{theor }}$

$\therefore \quad \pi =iCRT$

$ \quad \quad\pi =(i_{1} C_{1}+i_{2} C_{2}+i_{3} C_{3} \ldots . .){RT} $

Relation between i & $\alpha$ (degree of dissociation) :

$$ \mathrm{i}=1+(\mathrm{n}-1) \alpha \quad \text { Where, } \mathrm{n}=\mathrm{x}+\mathrm{y} \text { } $$

Relation b/w degree of association $\beta$ & $i$

$$ i=1+\left(\frac{1}{n}-1\right) \beta $$

RELATIVE LOWERING OF VAPOUR PRESSURE (RLVP):

Vapour pressure: $\mathrm{P}_{\text {Soln. }}<\mathrm{P}$

Lowering in $V P=P-P_{S}=\Delta P$

Relative lowering in vapour pressure $R L V P=\frac{\Delta P}{P}$

Raoult’s law : (For non - volatile solutes)

Experimentally relative lowering in V.P $=$ mole fraction of the non volatile solute in solutions.

$$ R L V P=\frac{P-P_{s}}{P}=X_{\text {solute }}=\frac{n}{n+N} $$

$$ \frac{P-P_{s}}{P_{s}}=\frac{n}{N} $$

$$ \frac{P-P_{s}}{P_{s}}=(\text { molality }) \times \frac{M}{1000} \quad \quad ( M = \text{molar mass of solvent}) $$

If solute gets associated or dissociated

$$ \begin{aligned} & \frac{P-P_{s}}{P_{s}}=\frac{i . n}{N} \\ & \frac{P-P_{s}}{P_{s}}=i \times(\text { molality }) \times \frac{M}{1000} \end{aligned} $$

According to Raoult’s law

PYQ-2024-Solutions-Q3 , PYQ-2024-Solutions-Q12

(i) $p_{1}=p_{1}^{0} X_{1}$. where $X_{1}$ is the mole fraction of the solvent (liquid).

(ii) An alternate form $\rightarrow \frac{p_{1}^{0}-p_{1}}{p_{1}^{0}}=x_{2}$.

Elevation in Boiling Point:

PYQ-2023- Solutions and colligative properties-Q9

$ \Delta T_{b}=i \times K_{b}m$

$K_{b}=\frac{RT_{b}^{2}}{1000 \times L_{vap}} C \text { or } \quad K_{b}=\frac{RT_{b}^{2}M}{1000 \times \Delta H_{vap}}$

$L_{vap}=(\frac{\Delta H_{vap}}{M}) $

Depression in Freezing Point

PYQ-2024-Solutions-Q2, PYQ-2024-Solutions-Q8, PYQ-2024-Solutions-Q11, PYQ-2023- Solutions and colligative properties-Q15, PYQ-2023- Solutions and colligative properties-Q11, PYQ-2023- Solutions and colligative properties-Q7, PYQ-2023- Solutions and colligative properties-Q6, PYQ-2023- Solutions and colligative properties-Q1

$\therefore \Delta T_{f}=i \times K_{f} . m$

$K_{f}=$ molal depression constant $=\frac{RT_f^{2}}{1000 \times L_{\text {fusion } }}$

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad=\frac{RT_f^{2}M}{1000 \times \Delta H_{\text {fusion } }}$

Raoult’s Law for Binary (Ideal) mixture of Volatile liquids :

PYQ-2023- Solutions and colligative properties-Q12

PYQ-2023- Solutions and colligative properties-Q2

$P_A = X_AP_A^{0} \quad \therefore P_B = X_B P_B^0$

$if\quad P_A^0 > P_B^0 \quad \therefore \quad A \quad is\quad more \quad volatile \quad than \quad B$

$\quad \quad \quad \quad \quad \quad\quad \therefore \quad$ B.P. of A $<$ B.P. of $B$

$\quad \quad \quad \quad \quad \quad\quad\therefore \quad$ According to Dalton’s law

$\quad \quad \quad\quad\quad \quad \quad P_T = P_A + P_B = X_AP_A^0 + X_BP_B^0$

$X_{A}{ }^{\prime}=$ mole fraction of $A$ in vapour above the liquid / solution.

$X_{B}{ }^{\prime}=$ mole fraction of $B$

$ P_{A}=X_{A} P_{A}{ }^{0}=X_{A}{ }^{\prime} P_{T}$

$P_{B}=X_{B}{ }^{\prime} P_{T}=X_{B} P_{B}{ }^{0}$

$\frac{1}{P_{T}}=\frac{X_{A}{ }^{\prime}}{P_{A}{ }^{0}}+\frac{X_{B}{ }^{\prime}}{P_{B}{ }^{0}} $

Graphical Representation :

A more volatile than $B\left(P_{A}{ }^{0}>P_{B}{ }^{\circ}\right)$

Ideal solutions (mixtures) :

Mixtures which follow Raoult’s law at all temperature.

$\quad \quad A$ —— A $\quad \Rightarrow \quad A$ —— $B$,

$\quad \quad$ B ——– B

$\quad \quad \Delta H_{mix}=0 \quad: \quad \Delta V_{mix}=0$

$\quad \quad \Delta S_{mix}=+$ ve as for process to proceed : $\Delta G_{mix}=-ve$

eg. $\quad $(1) Benzene + Toluene.

$\quad \quad $ (2) Hexane + heptane.

$\quad \quad$ (3) $C_2 H_5 Br + C_2 H_5 I$.

Non-Ideal solutions : Which do not obey Raoult’s law.

(a) Positive deviation :-

(i) $P_{T,exp} > (X_AP_A^0 + X_BP_B^0)$

(ii) $\mathrm{A}–\mathrm{A}>\mathrm{A}–\mathrm{B}$

$B–B>A–B$

$\quad\downarrow$

Force of attraction

(iii) $\Delta \mathrm{H}_{\text {mix }}=+\mathrm{ve}$ energy absorbed

(iv) $\Delta V_{mix}=+ve(1L+1L>2L)$

(v) $\Delta \mathrm{S}_{\text {mix }}=+\mathrm{ve}$

(vi) $\Delta \mathrm{G}_{\text {mix }}=-\mathrm{ve}$

e.g. $H_{2}O + CH_{3}OH$.

$H_{2}O + C_{2} H_{5} OH$

$C_{2} H_{5} OH + hexane$

$C_{2} H_{5} OH + cyclohexane$

$CHCI_3 + CCl_4 \rightarrow \text{dipole dipole interaction becomes weak}.$

$P^{0}A > P{^0} B$

(b) Negative deviation

(i) $P_{T}exp < X_A P_A^{0} + X_B P_B^{0}$

(ii) $\mathrm{A} —- \mathrm{A}>\mathrm{A} —- \mathrm{B}$

$B —- B>A —- B$

strength of force of attraction.

(iii) $\Delta \mathrm{H}_{\text {mix }}=-\mathrm{ve}$

(iv) $\Delta \mathrm{V}_{\text {mix }}=-\mathrm{ve} \quad $ $(1L + 1L < 2L)$

(v) $\Delta \mathrm{S}_{\text {mix }}=+\mathrm{ve}$

(vi) $\Delta \mathrm{G}_{\text {mix }}=-\mathrm{ve}$

e.g. $H_2O + HCOOH$

$H_2O + CH_3COOH$

$H_2O + HNO_3$

$CHCI_3 + CH_3OCH_3$

$P^{0}A > P{^0} B$

Immiscible Liquids :

(i) $P_{\text {total }}=P_{A}+P_{B}$

(ii) $P_{A}=P_{A}^{0} X_{A}=P_{A}^{0} \quad\left[\right.$ Since, $\left.X_{A}=1\right]$.

(iii) $P_{B}=P_{B}{ }^{0} X_{B}=P_{B}^{0} \quad\left[\right.$ Since, $\left.X_{B}=1\right]$.

(iv) $P_{\text {total }}=P_{A}^{0}+P_{B}^{0}$

(v) $\frac{P_{A}^{0}}{P_{B}^{0}}=\frac{n_{A}}{n_{B}}$

(vi) $\frac{P_{A}^{0}}{P_{B}^{0}}=\frac{W_{A} M_{B}}{M_{A} W_{B}}$

$P_{A}{ }^{0}=\frac{n_{A} R T}{V} ; \quad P_{B}{ }^{0}=\frac{n_{B} R T}{V}$

B.P. of solution is less than the individual B.P.’s of both the liquids.

Henry’s Law

This law deals with dissolution of gas in liquid i.e. mass of any gas dissolved in any solvent per unit volume is proportional to pressure of gas in equilibrium with liquid.

$m \propto p$

$\mathrm{m}=\mathrm{kp}$

$\mathrm{m} \rightarrow \frac{\text { weight of gas }}{\text { Volume of liquid }}$

Azeotropes

PYQ-2023- Solutions and colligative properties-Q7

PYQ-2023- Solutions and colligative properties-Q14

Azeotropes are binary mixtures having the same composition in liquid and vapour phase and boil at a constant temperature.In such cases, it is not possible to separate the components by fractional distillation.

Types of azeotropes:-

There are two types of azeotropes (i) Minimum boiling azeotrope :- Azeotropic mixtures with a higher boiling point in their constitutions are maximum boiling azeotropes. example:- Separation of water and isobutanol,Dehydration of ethanol etc.

(ii) Maximum boiling azeotrope:- An azeotropic mixture that has a boiling point lesser than its constituents is known as a minimum boiling azeotrope.

(iii) Heterogeneous azeotrope:- When azeotropes are present in mixture constitutions and are not fully miscible, they are called heterogeneous azeotropes

(iv)Homogeneous azeotropes:- Homogeneous azeotropes are azeotropes where a mixture’s constitutions are completely miscible.