Colligative properties

In a solvent S, a compound B is partially dissociated into C and D as given below:
$$\ce{B <=> 2C + 2D}$$
B, C and D are non-volatile in nature. The molar mass of B is 10 times the molar mass of S. The standard boiling point and the standard enthalpy of vaporization of S are 400 K and $10R$ J mol$^{-1}$, respectively ($R$ is the gas constant in J K$^{-1}$ mol$^{-1}$). A solution of B in S with an initial concentration of B as 0.25% (mass/mass) has a boiling point of 408 K at 1 bar pressure. In this solution, the mole percent of B that has been dissociated is ____.

19.5 g of fluoro acetic acid (molar mass = 78 g mol$^{-1}$) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1 °C. What is $K_a$ of fluoro acetic acid ? (For water, $K_f=1.86$ K kg mol$^{-1}$). Assume molarity and molality to have same values.

Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol$^{-1}$) in 0.5 L of water at 300 K. Its osmotic pressure is $x$ bar. Solution B is made by dissolving 2 g of same protein in 1 L of water at 300 K. Osmotic pressure of solution B is $y$ bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is $z$ bar. $x$, $y$ and $z$ respectively are :
($R=0.083$ L bar mol$^{-1}$ K$^{-1}$)

A non-volatile, non-electrolyte solid solute when dissolved in 40 g of a solvent, the vapour pressure of the solvent decreased from 760 mm Hg to 750 mm Hg. If the same solution boils at 320 K, then the number of moles of the solvent present in the solution is ________. (Nearest integer)
[Given: boiling point of the pure solvent = 319.5 K, $K_b$ of the solvent = 0.3 K kg mol$^{-1}$]

At 27 °C, 0.1 M, 1 L $\ce{K4[Fe(CN)6]}$ aqueous solution and 0.1 M, 1 L $\ce{FeCl3}$ aqueous solution are placed in a container separated by a semi permeable membrane AB. Assume complete dissociation of both the solutes. Which of the following statement is correct?

20 g hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a tube dipped in a solution (A) is found to be 80.0 mm higher than the tube dipped in water.

The molar mass of hemoglobin is ________ kg mol$^{-1}$. (Nearest integer)

(Given : $g=10$ m s$^{-2}$, $R=8.3$ kPa dm³ K$^{-1}$mol$^{-1}$, density of solution = 1000 kg m$^{-3}$)

Given below are two statements :

Statement I : $\ce{H2O}$ molecules move from the chamber 1 to chamber 2.

Statement II : The osmotic pressure of a solution prepared by dissolving 50 mg of potassium sulphate (molar mass = 174 g/mol) in 2 L of water (at 27 °C) is 0.0107 bar. (Given: R = 0.083 dm³ bar K$^{-1}$ mol$^{-1}$ and assume complete dissociation of electrolyte)

In the light of the above statements, choose the correct answer from the options given below :

Which of the following statements are not correct ?

A. For water, magnitude of $K_b$ is more than the magnitude of $K_f$.

B. The elevation in boiling point of water when a non-volatile solute is added to it is larger in magnitude than its depression in freezing point.

C. Osmotic pressure measurement is preferred over any other colligative property to determine molar mass of proteins and polymers.

D. The dimerised form of benzoic acid in benzene is $\ce{C6H5-C(=O)-OH\cdots O=C(OH)-C6H5}$

Choose the correct answer from the options given below :

At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density $= 1.00\ \mathrm{g\,cm^{-3}}$) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule is $2.00\ \mathrm{g\,dm^{-3}}$, the molar mass of the macromolecule is calculated to be $\boldsymbol{X}\times10^4\ \mathrm{g\,mol^{-1}}$. The value of $\boldsymbol{X}$ is _____.

Use: Universal gas constant (R) $= 8.3\ \mathrm{J\,K^{-1}\,mol^{-1}}$ and acceleration due to gravity ($g$) $= 10\ \mathrm{m\,s^{-2}}$

Vessel-1 contains $\mathbf{w_2}$ g of a non-volatile solute X dissolved in $\mathbf{w_1}$ g of water. Vessel-2 contains $\mathbf{w_2}$ g of another non-volatile solute Y dissolved in $\mathbf{w_1}$ g of water. Both the vessels are at the same temperature and pressure. The molar mass of X is 80% of that of Y. The van't Hoff factor for X is 1.2 times of that of Y for their respective concentrations.

The elevation of boiling point for solution in Vessel-1 is _____ % of the solution in Vessel-2.

50 mL of 0.2 molal urea solution (density $= 1.012\ \mathrm{g\,mL^{-1}}$ at 300 K) is mixed with 250 mL of a solution containing 0.06 g of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in Torr) of the resulting solution at 300 K is _____.

[Use: Molar mass of urea $= 60\ \mathrm{g\,mol^{-1}}$; gas constant, $R = 62\ \mathrm{L\,Torr\,K^{-1}\,mol^{-1}}$; Assume, $\Delta_\mathrm{mix}H = 0$, $\Delta_\mathrm{mix}V = 0$]

The osmotic pressure of blood is 7.47 bar at 300 K. To inject glucose to a patient intravenously, it has to be isotonic with blood. The concentration of glucose solution in $\mathrm{gL^{-1}}$ is ______.

(Molar mass of glucose $=180\ \mathrm{g\,mol^{-1}}$, $R=0.083\ \mathrm{L\,bar\,K^{-1}mol^{-1}}$) (Nearest integer)

Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 g of water, it depresses the freezing point by 0.2 °C. The percentage association of solute A in water, is :

[Given: Molar mass of A = 93 g mol$^{-1}$. Molal depression constant of water is 1.86 K kg mol$^{-1}$.]

A 0.5 percent solution of potassium chloride was found to freeze at $-0.24$°C. The percentage dissociation of potassium chloride is ______. (Nearest integer)

(Molal depression constant for water is 1.80 K kg mol$^{-1}$ and molar mass of KCl is 74.6 g mol$^{-1}$)

The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass 60 kg mol$^{-1}$ in 200 mL of water at 27°C is ______ Pa. [integer value]

(use $R=0.083$ L bar mol$^{-1}$ K$^{-1}$)

2 g of a non-volatile non-electrolyte solute is disolved in 200 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1 : 8. The elevation in boiling points of A and B are in the ratio $\dfrac xy$ $(x:y)$. The value of $y$ is ______. (Nearest Integer)

A solution containing $2.5\times10^{-3}$ kg of a solute dissolved in $75\times10^{-3}$ kg of water boils at 373.535 K. The molar mass of the solute is ______ g mol$^{-1}$. [nearest integer] (Given : $K_b(\mathrm{H_2O})=0.52$ K kg mol$^{-1}$ and boiling point of water = 373.15 K)

2.5 g of protein containing only glycine ($\mathrm{C_2H_5NO_2}$) is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found to be $5.03\times10^{-3}$ bar. The total number of glycine units present in the protein is ______.

(Given : R = 0.083 L bar K$^{-1}$ mol$^{-1}$)

1.2 mL of acetic acid is dissolved in water to make 2.0 L of solution. The depression in freezing point observed for this strength of acid is 0.0198°C. The percentage of dissociation of the acid is ______. (Nearest integer)

[Given : Density of acetic acid is 1.02 g mL$^{-1}$; Molar mass of acetic acid is 60 g mol$^{-1}$; $K_f(\mathrm{H_2O})=1.85$ K kg mol$^{-1}$]

Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant ($K_b/K_f$) is ______.