van't Hoff factor

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.

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?

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 :

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.

An aqueous solution is prepared by dissolving 0.1 mol of an ionic salt in 1.8 kg of water at 35 ºC. The salt remains 90% dissociated in the solution. The vapour pressure of the solution is 59.724 mm of Hg. Vapor pressure of water at 35 ºC is 60.000 mm of Hg. The number of ions present per formula unit of the ionic salt is ________.

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$^{-1}$)

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$^{-1}$]

The depression in freezing point observed for a formic acid solution of concentration 0.5 mL L$^{-1}$ is 0.0405°C. Density of formic acid is 1.05 g mL$^{-1}$. The Van't Hoff factor of the formic acid solution is nearly : (Given for water $k_f=1.86$ k kg mol$^{-1}$)

The value of $\mathbf x$ is ____.

The value of $|\mathbf y|$ is ____.

When 9.45 g of ClCH$_2$COOH is added to 500 mL of water, its freezing point drops by 0.5°C. The dissociation constant of ClCH$_2$COOH is $x\times10^{-3}$. The value of $x$ is _______. (Rounded off to the nearest integer)

[$K_{f(\mathrm{H_2O})}$ = 1.86 K kg mol$^{-1}$]

The plot given below shows $P-T$ curves (where $P$ is the pressure and $T$ is the temperature) for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents.

On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is ______.

The freezing point of benzene decreases by 0.45°C when 0.2 g of acetic acid is added to 20 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be :

($K_f$ for benzene = 5.12 K kg mol$^{-1}$)

5 g of $\ce{Na2SO4}$ was dissolved in $x$ g of $\ce{H2O}$. The change in freezing point was found to be 3.82°C. If $\ce{Na2SO4}$ is 81.5% ionised, the value of $x$ ($K_f$ for water = 1.86°C kg mol$^{-1}$) is approximately :

(molar mass of S = 32 g mol$^{-1}$ and that of Na = 23 g mol$^{-1}$)

An aqueous solution of a salt $\ce{MX2}$ at certain temperature has a van't Hoff factor of 2. The degree of dissociation for this solution of the salt is :

If the freezing point of a 0.01 molal aqueous solution of a cobalt(III) chloride-ammonia complex (which behaves as a strong electrolyte) is −0.0558 °C, the number of chloride(s) in the coordination sphere of the complex is

[$K_f$ of water = 1.86 K kg mol⁻¹]

Determination of the molar mass of acetic acid in benzene using freezing point depression is affected by :

$\ce{MX2}$ dissociates into $\ce{M^{2+}}$ and $\ce{X-}$ ions in an aqueous solution, with a degree of dissociation ($\alpha$) of 0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is