At $\mathrm{T}(\mathrm{K}), 2$ moles of liquid A and 3 moles of liquid B are mixed. The vapour pressure of ideal solution formed is 320 mm Hg . At this stage, one mole of A and one mole of B are added to the solution. The vapour pressure is now measured as 328.6 mm Hg . The vapour pressure (in mm Hg ) of A and B are respectively:

At 298 K , the mole percentage of $\mathrm{N}_2(\mathrm{~g})$ in air is $80 \%$. Water is in equilibrium with air at a pressure of 10 atm . What is the mole fraction of $\mathrm{N}_2(\mathrm{~g})$ in water at 298 K ? $\left(\mathrm{K}_{\mathrm{H}}\right.$ for $\mathrm{N}_2$ is $\left.6.5 \times 10^7 \mathrm{~mm} \mathrm{Hg}\right)$

Two liquids A and B form an ideal solution at temperature T K . At T K , the vapour pressures of pure A and B are 55 and $15 \mathrm{kN} \mathrm{m}^{-2}$ respectively. What is the mole fraction of A in solution of A and B in equilibrium with a vapour in which the mole fraction of A is 0.8?

A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute 'A' of molar mass $60 \mathrm{~g} \mathrm{~mol}^{-1}$ and 0.9 g of a non-volatile non-electrolyte solute ' B ' of molar mass $180 \mathrm{~g} \mathrm{~mol}^{-1}$ in $100 \mathrm{~mL} \mathrm{H}_2 \mathrm{O}$ at $27^{\circ} \mathrm{C}$. Osmotic pressure of the solution will be

[Given: $\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ ]

' W ' g of a non-volatile electrolyte solid solute of molar mass ' M ' $\mathrm{g} \mathrm{mol}^{-1}$ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg . If aqueous solution of the electrolyte boils at 375 K and $\mathrm{K}_{\mathrm{b}}$ for water is $0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$, then the mole fraction of the electrolyte solute $\left(x_2\right)$ in the solution can be expressed as

(Given : density of water $=1 \mathrm{~g} / \mathrm{mL}$ and boiling point of water $=373 \mathrm{~K}$ )

Which one of the following graphs accurately represents the plot of partial pressure of $\mathrm{CS}_2$ vs its mole fraction in a mixture of acetone and $\mathrm{CS}_2$ at constant temperature?

At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $49 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution. What is the mole fraction of $\mathrm{H}_2 \mathrm{SO}_4$ in the resultant solution?

(Given : Atomic mass $\mathrm{H}=1 \mathrm{u} ; \mathrm{S}=32 \mathrm{u} ; \mathrm{O}=16 \mathrm{u}$ ).

(Assume that temperature after mixing remains constant)

Consider a solution of $\mathrm{CO}_2(\mathrm{~g})$ dissolved in water in a closed container.

Which one of the following plots correctly represents variation of log (partial pressure of $\mathrm{CO}_2$ in vapour phase above water) $[y$-axis $]$ with $\log$ (mole fraction of $\mathrm{CO}_2$ in water) $[x$-axis $]$ at $25^{\circ} \mathrm{C}$ ?

Given below are two statements :

Statement I : The Henry's law constant $\mathrm{K}_{\mathrm{H}}$ is constant with respect to variations in solution's concentration over the range for which the solution is ideally dilute.

Statement II : $\mathrm{K}_{\mathrm{H}}$ does not differ for the same solute in different solvents.

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

Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and $\mathrm{PQ}_2$. When 1 g of $P Q$ is dissolved in 50 g of solvent ' $A^{\prime}, \Delta T_b$ was 1.176 K while when 1 g of $P Q_2$ is dissolved in 50 g of solvent ' $\mathrm{A}^{\prime}, \Delta \mathrm{T}_{\mathrm{b}}$ was 0.689 K . ( $\mathrm{K}_{\mathrm{b}}$ of ' $\mathrm{A}^{\prime}=5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ ). The molar masses of elements P and Q (in $\mathrm{g} \mathrm{mol}^{-1}$ ) respectively, are :

Given below are two statements :

Given : Molar mass of $\mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{Cl}$ are $12,1,16$ and $35.5 \mathrm{~g} \mathrm{~mol}^{-1}$, respectively

Statement I : In $30 \%(\mathrm{w} / \mathrm{w})$ solution of methanol in $\mathrm{CCl}_4($ at T K$)$, the mole fraction of $\mathrm{CCl}_4$ is equal to 0.33 .

Statement II : Mixture of methanol and $\mathrm{CCl}_4$ shows positive deviation from Raoult's law. 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 $\mathrm{K}_{\mathrm{b}}$ is more than the magnitude of $\mathrm{K}_{\mathrm{f}}$.

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.

$ \text { D. The dimerised form of benzoic acid in benzene is } $

Choose the correct answer from the options given below :

Given below are two statements :

Statement I : $\quad \mathrm{H}_2 \mathrm{O}$ 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 $=174 \mathrm{~g} / \mathrm{mol}$ ) in 2 L of water (at $27^{\circ} \mathrm{C}$ ) is 0.0107 bar. (Given: $\mathrm{R}=0.083 \mathrm{dm}^3$ bar $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$ and assume complete dissociation of electrolyte)

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

When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapor pressure of solution was $x \%$ of vapor pressure of pure solvent. What is $x \%$ ?

At $27^{\circ} \mathrm{C}, 0.1 \mathrm{M}, 1 \mathrm{~L} \mathrm{~K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ aqueous solution and $0.1 \mathrm{M}, 1 \mathrm{~L} \mathrm{FeCl}_3$ 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?

Solution A is prepared by dissolving 1 g of a protein (molar mass = 50,000 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 the 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 the 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)

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.

The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 °C. The dissociation constant for the acid is

Given: $K_f$(H₂O) = 1.8 K kg mol⁻¹, molality ≡ molarity

Which of the following binary mixture does not show the behaviour of minimum boiling azeotropes?

Liquid A and B form an ideal solution. The vapour pressures of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If $x_A$ and $x_B$ are the mole fraction of A and B in solution while $y_A$ and $y_B$ are the mole fraction of A and B in vapour phase, then,

Match List - I with List - II.

Choose the correct answer from the options given below :

Given below are two statements:

Statement (I) : Molal depression constant $\mathrm{K}_f$ is given by $\frac{\mathrm{M}_1 \mathrm{RT}_f}{\Delta \mathrm{~S}_{\mathrm{fus}}}$, where symbols have their usual meaning.

Statement (II) : $\mathrm{K}_f$ for benzene is less than the $\mathrm{K}_f$ for water.

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

$X Y$ is the membrane/partition between two chambers 1 and 2 containing sugar solutions of concentration $c_1$ and $c_2\left(c_1>c_2\right) \mathrm{mol} \mathrm{L}^{-1}$. For the reverse osmosis to take place identify the correct condition.

(Here $p_1$ and $p_2$ are pressures applied on chamber 1 and 2 ).

A. Membrane/Partition : Cellophane, $\mathrm{p}_1>\pi$

B. Membrane/Partition : Porous, $\mathrm{p}_2>\pi$

C. Membrane/Partition : Parchment paper, $p_1>\pi$

D. Membrane/Partition : Cellophane, $\mathrm{p}_2>\pi$

Choose the correct answer from the option given below:

Which of the following properties will change when system containing solution 1 will become solution 2 ?

' $x$ ' g of NaCl is added to water in a beaker with a lid. The temperature of the system is raised from $1^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. Which out of the following plots, is best suited for the change in the molarity $(\mathrm{M})$ of the solution with respect to temperature ?

[Consider the solubility of NaCl remains unchanged over the temperature range]

A solution is made by mixing one mole of volatile liquid $A$ with 3 moles of volatile liquid $B$. The vapour pressure of pure A is 200 mm Hg and that of the solution is 500 mm Hg . The vapour pressure of pure B and the least volatile component of the solution, respectively, are:

Which of the following graph correctly represents the plots of $\mathrm{K}_{\mathrm{H}}$ at 1 bar for gases in water versus temperature?

Given below are two statements :

Statement (I): NaCl is added to the ice at 0°C, present in the ice cream box to prevent the melting of ice cream.

Statement (II): On addition of NaCl to ice at 0°C, there is a depression in freezing point.

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

1.24 g of AX₂ (molar mass 124 g mol⁻¹) is dissolved in 1 kg of water to form a solution with boiling point of 100.015°C, while 25.4 g of AY₂ (molar mass 250 g mol⁻¹) in 2 kg of water constitutes a solution with a boiling point of 100.0260°C.

K_b(H₂O) = 0.52 kg mol⁻¹

Which of the following is correct?

Assume a living cell with 0.9% (w/w) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water.
(Consider the data upto first decimal place only)

The cell will :

What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non volatile solute (molar mass $256 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and the decrease in freezing point is 0.40 K ?

Consider the given plots of vapour pressure (VP) vs temperature(T/K). Which amongst the following options is correct graphical representation showing $\Delta \mathrm{T}_{\mathrm{f}}$, depression in the freezing point of a solvent in a solution?

When a non-volatile solute is added to the solvent, the vapour pressure of the solvent decreases by 10 mm of Hg . The mole fraction of the solute in the solution is 0.2 . What would be the mole fraction of the solvent if decrease in vapour pressure is 20 mm of Hg ?

Consider a binary solution of two volatile liquid components 1 and $2 . x_1$ and $y_1$ are the mole fractions of component 1 in liquid and vapour phase, respectively. The slope and intercept of the linear plot of $\frac{1}{x_1}$ vs $\frac{1}{y_1}$ are given respectively as :

Arrange the following solutions in order of their increasing boiling points.

(i) $10^{-4} \mathrm{M} \mathrm{NaCl}$

(ii) $10^{-4} \mathrm{M}$ Urea

(iii) $10^{-3} \mathrm{M} \mathrm{NaCl}$

(iv) $10^{-2} \mathrm{M} \mathrm{NaCl}$

$0.05 \mathrm{M} \mathrm{~CuSO}_4$ when treated with $0.01 \mathrm{M} \mathrm{~K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ gives green colour solution of $\mathrm{Cu}_2 \mathrm{Cr}_2 \mathrm{O}_7$. The two solutions are separated as shown below : [SPM : Semi Permeable Membrane]

Due to osmosis :

Identify the mixture that shows positive deviations from Raoult's Law

The solution from the following with highest depression in freezing point/lowest freezing point is

What happens to freezing point of benzene when small quantity of napthalene is added to benzene?

A solution of two miscible liquids showing negative deviation from Raoult's law will have :

What weight of glucose must be dissolved in $100 \mathrm{~g}$ of water to lower the vapour pressure by $0.20 \mathrm{~mm} ~\mathrm{Hg}$ ?

(Assume dilute solution is being formed)

Given : Vapour pressure of pure water is $54.2 \mathrm{~mm} ~\mathrm{Hg}$ at room temperature. Molar mass of glucose is $180 \mathrm{~g} \mathrm{~mol}^{-1}$

Match List I with List II

Choose the correct answer from the options given below :

In the depression of freezing point experiment

A. Vapour pressure of the solution is less than that of pure solvent

B. Vapour pressure of the solution is more than that of pure solvent

C. Only solute molecules solidify at the freezing point

D. Only solvent molecules solidify at the freezing point

Choose the most appropriate answer from the options given below :

Boiling point of a $2 \%$ aqueous solution of a non-volatile solute A is equal to the boiling point of $8 \%$ aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is

Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y, respectively in 1 kg of water. The ratio of depression in freezing points for A and B is found to be 1 : 4. The ratio of molar masses of X and Y is

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

For a solution of the gases A, B, C and D in water at 298 K, the values of Henry's law constant (K_H) are 30.40, 2.34, 1.56 $\times$ 10^$-$5 and 0.513 k bar respectively. In the given graph, the lines marked as 'p' and 's' correspond respectively to :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : At 10$^\circ$C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g mol^$-$1 respectively], is 'x' g ml^$-$1. The solution is cooled to $-$21$^\circ$C. The molality of the solution will remain unchanged.

Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.

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

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$^\circ$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.]