Colligative Properties of Solutions PDF

## Colligative properties of solutions ### **Chapter 1** **Q.1.1** Derive Vant Hoff equation for osmotic pressure. - We have relation $Π = \frac {RT}{V} * P$ - But $P = \frac {1-N_2}{N_2}$ - Therefore, $Π = \frac {RT}{V} * \frac { 1-N_2}{N_2}$ - And $Π = -RT * \frac {1}{V} ln (1-N_2)$ - Macla...

## Colligative properties of solutions ### **Chapter 1** **Q.1.1** Derive Vant Hoff equation for osmotic pressure. - We have relation $Π = \frac {RT}{V} * P$ - But $P = \frac {1-N_2}{N_2}$ - Therefore, $Π = \frac {RT}{V} * \frac { 1-N_2}{N_2}$ - And $Π = -RT * \frac {1}{V} ln (1-N_2)$ - Maclaurins gives $-ln(1-N_2) = N_2$ - So, $Π = \frac {RT}{V} * N_2$ - For very dilute solution $N_1 >> N_2$, $N_2 ≈ \frac {D_2}{V_1}$ - Therefore $Π = \frac {RT}{V_1} * \frac {D_2}{V_1}$ - But $C = \frac {n_2}{V_1}$ - So, $Π = CRT$ **(Eq. 4) Vant Hoff equation** **Q.2.1** Show that depression in freezing point is a colligative property. **Q.2.2** Show that depression in freezing point depends on molality. **Q.2.3** Show that $ΔT_f = k_f * m$. - In the figure, curve $AB$ - sublimation curve, $EF$ - vapour curve of solution, $CD$ - vapour curve of solvent, $GC$ - Supercooled liquid. - And $ΔT_f = T_o - T = 0$ **Q.3.** Define lowering of v.p and relative lowering in v.p. - When a non-volatile solute is added in solvent then the vapour of solution is decreased, this phenomenon is called **lowering** of v.p. - Relative lowering of v.p = $\frac{ΔP}{P_o}$. ### **Chapter 2** **Q.4.1** Describe Berkeley - Hartley's method to determine osmotic pressure of a solution. - It consist of a porous tube with semipermeable membrane, one side reservoir of solvent, another side calibrated capillary, upper flower side of container with solution, and the solution side has a piston with p-gauge. - The solution enters filled in upper and lower part. - Solvent enters in solution chamber and solution side goes upward. - Mechanical pressure is applied on the piston to stop osmosis, which is osmotic pressure. **Q.5.1** Show that $ΔT_b= k_b * m.$ **Q.5.2** Show that elevation in B.P is a colligative property. - In the figure, $AB$ - for pure solvent, $CD$ - for solution - Where $P_o$ - v.p of pure solvent, $P$ - v.p of solution. - And $ΔT_b = T-T_o$ - Apply Clausius - Clayperon equation to curve $EF$. - $\frac{d ln P}{d p} = \frac{ΔH_v}{R} * \frac {1}{T_o - T}$ - Raoult's law gives: $P = P_o * (1-N_2)$ - And: $T-T_o = ΔT_b$. - For dilute solution $T_o . T ≈ T_o^2$. - So, $-ln(1-N_2) = \frac{ΔH_v * ΔT_b}{R * T_o^2}$ - Maclaurins gives: $N_2 = -ln(1-N_2)$. - Thus, $N_2= \frac{ΔT_b * R * T_o^2}{ΔH_v}$. - $N_2 = \frac{M_2}{M_1}$ - So, $ΔT_b = k_b * m$; where $k_b = \frac{R * T_o^2}{ΔH_v}$. - Eq. 5 shows that $ΔT_b$ is a colliagative property ### **Chapter 3** **Q.6.1** Define abnormal molecular weight. - The unexpected molecular weight of solute obtained in colligative study due to dissociation or association is called abnormal molecular weight. **Q.7.1** Define Vant Hoff factor. - It is defined as: - $i = \frac{Colligative \ effect \ of \ electrolyte}{Colligative \ effect \ of \ non \ electrolyte \ of \ same \ conc.}$ **Q.8.1** Define mole fraction. - Mole fraction $N_2 = \frac{n_2}{n_1 + n_2}$, where $n_2$ - number of moles of solute, $n_1$ - number of moles of solvent. **Q.9.1** Define osmosis and osmotic pressure. - The spontaneous unidirectional flow of solvent molecules through a semipermeable membrane from solvent side to solution side is called osmosis. - The mechanical pressure applied on solution side to stop osmosis is called osmotic pressure. - The membrane which allows only the flow of solvent molecules not solute particles, is called a semipermeable membrane. **Q.10.1** Define colligative properties. Give an example. - These properties depend on the number of solute particles, and are independent of nature of the solute and depend on the nature of the solvent. - E.g., Depression in freezing point. **Q.11.1** Define Normality, Molarity, and Molality. Give their unit. - **Normality:** number of gram equivalents of solute in 1 L of solution. Unit: $gm - equiv * L^{-1}$. - **Molarity:** number of moles of solute in 1 L of solution. Unit: $mol * L^{-1}$. - **Molality:** number of moles of solute in 1 kg of solvent. Unit: $mol * Kg^{-1}$. **Q.12.1** Give the statement of Raoult’s law of partial pressure. - Partial vapour pressure = vapour pressure of pure liquid * mole fraction of solvent. - $P = P_o * x_1$ **Q.13.1** Define ebullioscopic constant / molal elevation in B.P constant. How it is related with molar latent heat of vaporization? - It is defined as the elevation in B.P when 1 mole of solute is dissolved in 1000 gm solvent. - $Unit\ of \ k_b: K * Kg * mol^{-1}$ - $k_b = \frac{R * T_o^2}{ΔH_v * n_1}$ - $k_b = \frac{R * T_o^2}{1000 * L_v}$ - Where $T_o$ - B.P of solvent. - $n_1$ - number of moles of the solvent - $ΔH_v$ - heat of vaporization - $L_v$ - latent heat of vaporization **Q.14.1** Define cryoscopic constant / molal elevation in depression in freezing point constant. How it is related with heat of vaporization? - It is defined as the depression in freezing point when 1 mole of solute is dissolved in 1000 gm of solvent. - $Unit\ of \ k_f: K * Kg * mol^{-1}$ - $k_f = \frac {R * T_o^2}{ΔH_f * n_1} $ - $k_f = \frac {R * T_o^2}{1000 * L_f}$ - Where $T_o$ - freezing point of solvent. - $ΔH_f$ - heat of freezing. - $L_f$ - latent heat. **Q. 15.1** Show that lowering in v.p is a colligative property. Show that relative lowering in v.p. is equal to mole fraction of solute. - $ΔP = P -P’$. - But, $P = P_o * N_1$ - Therefore, $ΔP = P_o * N_2$ - Hence, lowering of v.p is a colligative property. - Relative lowering = $\frac{ΔP}{P_o} = N_2$ - Hence, relative lowering is equal to $N_2$. **Q.16.1** Derive relation between osmotic pressure $Π$ and vapour pressure $P$. - $G - G^o = ΔG$ - And $ΔG = RT * ln * a$ - $a = \frac{P}{P_o}$ - So, $ΔG = RT * ln \frac{P}{P_o}$ - And $ΔG = ΠV$ - $ΠV = RT * ln \frac{P_o}{P}$ - Therefore, $Π = \frac {RT}{V} * ln\frac{P_o}{P}$ - Eq. 15 is relation between Π and P. ## **Exercise** **Multiple Choice Questions:** 1. Colligative properties are mainly dependent on: - **(a) Number of solute particles** - (b) Number of solvent particles - (c) Amount of solvent - (d) Pressure of solute 2. Molality of the solution is number of moles of solute present in: - (a) 100 ml of solvent - (c) 1000 g of solvent - **(b) One lit of solution** - (d) 100 g of solvent 3. Relative lowering of vapour pressure of a solution is directly proportional to mole fraction of: - (a) Solvent - (b) Solute - (c) Solute minus solvent - **(d) Solute plus solvent** 4. Molal depression constant is also known as: - (a) Ebullioscopic constant - **(c) Cryoscopic constant** - (b) Molar gas constant - (d) Boltzmann constant 5. Addition of non-volatile solute _______ the vapour pressure: - (a) Enhances - **(b) Lowers** - (c) Diminishes - (d) Keep constant 6. When non-volatile solute is added in the solvent then its vapour pressure: - (a) Increases - (b) Decreases - **(c) Remains constant** - (d) Become zero 7. The vapour pressure of solvent is always: - **(a) Lesser than** - (b) Twice than - (c) Greater than - (d) Same as that of vapour pressure of solution 8. The term $ΔP$ is known as: - (a) Relative lowering of vapour pressure - (c) Average vapour pressure - **(b) Lowering of vapour pressure** - (d) Saturated vapour pressure 9. The relative lowering of vapour pressure is given by: - **(a) $(P°-P)/P_o$** - (b) $(P°-P)/P$ - (c) $(P°+P)/P_o$ - (d) $(P°-P)/P$ 10. Molal elevation constant $(K_b)$ is: - **(a) Directly proportional to heat of vaporization** - (b) Inversely proportional to heat of vaporization - (c) Equal to - (d) Independent on 11. The derivation of colligative properties are based on: - (a) Avogadro's - **(b) Ostwald law** - (c) Raoult's law - (d) Grahm's law 12. Elevation in boiling point is measured by: - (a) Beckmann's method - (c) Vant Hoff method - (b) Landberger method - (d) Berkley method 13. The elevation in boiling point is given by $ΔT = K_b * m$. The $K_b$ term is called as: - **(a) Molal elevation constant** - (b) Ebullioscopic constant - (c) Elevation in boiling point constant - (d) All of these 14. Molal elevation constant is the elevation in boiling point when the molality of the solution is: - (a) 1 - **(b) 2** - (c) 0.5 - (d) 1.5 15. The colligative effect of an electrolyte is always ______ that of a non-electrolyte of the same molar concentration. - (a) Greater - (b) Smaller - **(c) Equal to** - (d) Independent on 16. When non-volatile solute is added to solvent the freezing point of the solvent: - (a) Remains same - **(b) Decreases** - (c) Increases - (d) Becomes zero 17. An aqueous solution of potassium chloride has a boiling point: - (a) Equal to that of water - **(b) More than that of water** - (c) Less than that of water - (d) 1/10 of boiling point of water 18. Which of the following is not a colligative property? - (a) Relative lowering of vapour pressure - (c) Osmotic pressure - **(b) Depression in freezing point** - (d) Surface tension 19. The molar depression constant is given by: - (a) $ΔT * M$ - (b) $ΔT * m$ - (c) $ΔT / m$ - **(d) $ΔT * N$** 20. The flow of solvent molecules take place from: - (a) Dilute solution to concentrated solution - ** (b) Concentrated solution to dilute solution** - (c) Any solution to other - (d) None of these 21. The osmotic pressure of a solution at a given temperature is directly proportional to: - **(a) Osmotic pressure** - (b) Concentration - (c) Volume of the solution - (d) Internal energy 22. The osmotic pressure at a given concentration is directly proportional to: - (a) Room temperature - (c) Critical temperature - **(b) Atmospheric pressure** - (d) Absolute temperature 23. Semi permeable membrane allows to pass only: - (a) Molecules of solute - (c) Cation - **(b) Molecules of solvent** - (d) Anion 24. The method, which measures osmotic pressure, is: - (a) Beckmann method - (c) Vant Hoff method - **(b) Berkley Hartley method** - (d) Landsbergis method 25. The maximum colligative effect in boiling point is observed in: - (a) 0.1 M Cane sugar - **(b) 0.1 M NaCl** - (c) 0.1 M BaCl2 - (d) 0.1 M Urea 26. Abnormal molecular masses are obtained when there exists: - (a) Dissociation of molecule - (c) Dissociation as well as association - **(b) Association of molecule** - (d) No dissociation of solute 27. Osmotic pressure of the solution increases as: - **(a) Number of solution particles decreased** - (c) Number of solute particles increased - (b) Number of solute particles decreased - (d) Temperature is decreased. 28. An aqueous solution of sodium chloride in water has vapour pressure: - (a) Equal to that of water - (c) Less than that of water - **(b) More than that of water** - (d) 760 mm Hg 29. When solute dissociate in the solvent the molecular weight obtained by colligative studies is: - **(a) Greater than** - (b) Lower than - (c) Same as - (d) Double than formula molecular weight 30. The ratio of colligative effect produced by concentration (m) of electrolyte divided by the effect observed in non-electrolyte for the same concentration is known as: - (a) Depression in freezing point - (c) Abnormal molecular weight - **(b) Van't Hoff factor** - (d) Vapour pressure lowering 31. Properties which depend upon the number rather then the nature of the dissolved particles in a solution are called: - (a) Intensive property - (c) Extensive property - **(b) Colligative property** - (d) Constitutive property 32. A colligative property depends upon: - (a) Chemical nature of the particles - (c) Number of particles - **(b) Size of the particles** - (d) Temperature of the solution 33. The ratio of the cogitative effect produced by an electrolyte solution to the corresponding effect for the same concentration of a non-electrolyte solution is known as: - (a) Mole fraction - (c) Relative lowering of vapour pressure - **(b) Lowering of vapour pressure** - (d) Van't Hoff factor 34. Abnormal molecular masses are obtained when there exists: - **(à) Dissociation of molecules** - (c) Either of the two - (b) Association of molecules - (d) None of these 35. Which one of the following is true for the van't Hoff factor $i$? - (a) $i=ΔT/[ΔT]’$ - (b) $i = ΔT’/[ΔT]$ - (c) $i=ΔP / [ΔP]’$ - **(d) All of the above** 36. The value of van't Hoff factor is ______ for an electrolyte. - (a) Greater than one - **(b) Less than one** - (c) Equal to one - (d) Equal to $z$ 37. Benzoic acid, when dissolved in benzene, undergoes: - (a) Dissociation - (b) Association - (c) No change - **(d) Solvation** 38. Which of the following statements is true? - **(à) Osmosis can be reversed by application of a pressure on the solution.** - (b) Osmosis is not spontaneous - (c) Osmosis and diffusion are same in solutions. - (d) Barometer can be used to measure osmotic pressure 39. Select the one that is a colligative property. - (a) Osmotic pressure. - (b) Boiling point. - (c) Freezing point. - **(d) Sublimation** 40. When a solution is diluted, the colligative effect: - (a) Sometimes increases and some times decreases - **(b) Decreases always** - (c) Increases always - (d) Remains unchanged 41. Which of the following is a colligative property? - (a) Surface tension - (b) Viscosity - **(c) Osmotic pressure** - (d) Optical rotation 42. Which of the following is not a colligative property? - (a) Depression of freezing point - (c) Osmotic pressure - **(b) Elevation of boiling point** - (d) Сhange of refractive index 43. Colligative properties of a solution depend upon: - (a) Nature of solute. - (b) Nature of solvent. - **(c) The relative number of solute and solvent particles.** - (d) None of these 44. Which of the following is a colligative property? - (a) Change in free energy. - (c) Heat of vaporization - **(b) Change in pressure** - (d) Osmotic pressure 45. The order of osmotic pressure of equaimolar solutions, of $BaCl_2$, $NaCl$, and glucose will be: - **(a) $BaCl_2 > NaCl > glucose$** - (b) $NaCl > BaCl_2 > glucose$ - (c) $glucose > BaCl_2 > NaCl$ - (d) $glucose > NaCl > BaCl_2$ **Answer:** 1. A 2. C 3. B 4. C 5. B 6. B 7. C 8. B 9. A 10. A 11. B 12. B 13. D 14. B 15. C 16. D 17. B 18. D 19. D 20. B 21. A 22. B 23. B 24. D 25. B 26. C 27. C 28. B 29. A 30. A 31. B 32. C 33. D 34. A 35. D 36. B 37. D 38. A 39. D 40. B 41. C 42. D 43. C 44. D 45. A