Solutions · JEE Main previous year questions

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. A.Both Statement I and Statement II are false
2. B.Statement I is true but Statement II is false
3. C.Both Statement I and Statement II are true
4. D.Statement I is false but Statement II is true

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

1. A.$4.43\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$
2. B.$3.72\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$
3. C.$5.12\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$
4. D.$1.86\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$

The large difference between the melting and boiling points of oxygen and sulphur may be explained on the basis of

1. A.Atomicity
2. B.Electron gain enthalpy
3. C.Atomic size
4. D.Electronegativity

1. A.
2. B.
3. C.
4. D.

Let us consider an endothermic reaction which is non-spontaneous at the freezing point of water. However, the reaction is spontaneous at boiling point of water. Choose the correct option.

1. A.Both $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ are (-ve)
2. B.$\Delta \mathrm{H}$ is (+ve) but $\Delta \mathrm{S}$ is (-ve)
3. C.$\Delta \mathrm{H}$ is (-ve) but $\Delta \mathrm{S}$ is (+ve)
4. D.Both $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ are (+ve)

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

1. A.(i) < (ii) < (iii) < (iv)
2. B.(ii) < (i) < (iii) < (iv)
3. C.(iv) < (iii) < (i) < (ii)
4. D.(ii) < (i) $\equiv$ (iii) < (iv)

The vapor pressure of pure benzene and methyl benzene at $27^{\circ }\mathrm{C}$ is given as $80\mathrm{Torr}$ and $24\mathrm{Torr}$, respectively. The mole fraction of methyl benzene in vapor phase, in equilibrium with an equimolar mixture of those two liquids (ideal solution) at the same temperature is ____ $\times 10^{-2}$ (nearest integer)

A solution containing $10\mathrm{g}$ of an electrolyte $\mathrm{A}{\mathrm{B}}_2$ in $100\mathrm{g}$ of water boils at $100.52^{\circ }\mathrm{C}$. The degree of ionization of the electrolyte $(\alpha )$ is ____ $\times 10^{-1}$. (nearest integer) $[\text{Given : Molar mass of }\mathrm{A}{\mathrm{B}}_2=200\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}\text{, }{\mathrm{K}}_{\mathrm{b}}\text{ (molal boiling point elevation const. of water)}=0.52\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}\text{, boiling point of water}=100^{\circ }\mathrm{C}\text{; }\mathrm{A}{\mathrm{B}}_2\text{ ionises as }\mathrm{A}{\mathrm{B}}_2\to {\mathrm{A}}^{2+}+2{\mathrm{B}}^{-}]$

$2.5\mathrm{g}$ of a non-volatile, non-electrolyte is dissolved in $100\mathrm{g}$ of water at $25^{\circ }\mathrm{C}$. The solution showed a boiling point elevation by $2^{\circ }\mathrm{C}$. Assuming the solute concentration is negligible with respect to the solvent concentration, the vapor pressure of the resulting aqueous solution is ____ $\mathrm{mm}\mathrm{of}\mathrm{Hg}$ (nearest integer) [Given : Molal boiling point elevation constant of water $({\mathrm{K}}_{\mathrm{b}})=0.52K.\mathrm{kgmo}{\mathrm{l}}^{-1}$, $1\mathrm{atm}$ pressure $=760\mathrm{mm}\mathrm{of}\mathrm{Hg}$, molar mass of water $=18\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$]

$2.7\text{ kg}$ of each of water and acetic acid are mixed. The freezing point of the solution will be $-x^{\circ }\text{C}$. Consider the acetic acid does not dimerise in water, nor dissociates in water. $x=$ ________ (nearest integer) [Given: Molar mass of water $=18{\text{ g mol}}^{-1}$, acetic acid $=60{\text{ g mol}}^{-1}$ ${\text{K}}_{\text{f}}{\text{H}}_2\text{O}:1.86{\text{ K kg mol}}^{-1}$ ${\text{K}}_{\text{f}}\text{ acetic acid}:3.90{\text{ K kg mol}}^{-1}$ freezing point: ${\text{H}}_2\text{O}=273\text{ K}$, acetic acid $=290\text{ K}$]

We have three aqueous solutions of $\mathrm{NaCl}$ labelled as ' $\mathrm{A}$ ', ' $\mathrm{B}$ ' and ' $\mathrm{C}$ ' with concentration $0.1\mathrm{M}$, $0.01\mathrm{M}$ and $0.001\mathrm{M}$, respectively. The value of van 't Hoff factor(i) for these solutions will be in the order :

1. A.${\mathrm{i}}_{\mathrm{A}}<{\mathrm{i}}_{\mathrm{C}}<{\mathrm{i}}_{\mathrm{B}}$
2. B.${\mathrm{i}}_{\mathrm{A}}<{\mathrm{i}}_{\mathrm{B}}<{\mathrm{i}}_{\mathrm{C}}$
3. C.${\mathrm{i}}_{\mathrm{A}}>{\mathrm{i}}_{\mathrm{B}}>{\mathrm{i}}_{\mathrm{C}}$
4. D.${\mathrm{i}}_{\mathrm{A}}={\mathrm{i}}_{\mathrm{B}}={\mathrm{i}}_{\mathrm{C}}$

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): $\mathrm{P}{\mathrm{H}}_3$ has lower boiling point than $\mathrm{N}{\mathrm{H}}_3$. Reason (R) : In liquid state $\mathrm{N}{\mathrm{H}}_3$ molecules are associated through van der Waals forces, but $\mathrm{P}{\mathrm{H}}_3$ molecules are associated through hydrogen bonding. In the light of the above statements, choose the most appropriate answer from the options given below :

1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. B.(A) is not correct but (R) is correct
3. C.(A) is correct but (R) is not correct
4. D.Both $(\mathbf{A})$ and $(\mathbf{R})$ are correct but $(\mathbf{R})$ is not the correct explanation of $(\mathbf{A})$

Which among the followng has highest boiling point?

1. A.$\mathrm{C}{\mathrm{H}}_3\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2-\mathrm{OH}$
2. B.$\mathrm{C}{\mathrm{H}}_3\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_3$
3. C.$\mathrm{C}{\mathrm{H}}_3\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{CHO}$
4. D.${\mathrm{H}}_5{\mathrm{C}}_2-\mathrm{O}-{\mathrm{C}}_2{\mathrm{H}}_5$

Mass of ethylene glycol (antifreeze) to be added to $18.6\text{ kg}$ of water to protect the freezing point at $-24^{\circ }\text{C}$ is ________ $\text{kg}$ (Molar mass in $\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ for ethylene glycol $62$, ${\mathrm{K}}_f$ of water $=1.86{\text{ K kg mol}}^{-1}$ )

Given below are two statements: Statement - I: Noble gases have very high boiling points. Statement - II: Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because of this they are liquefied at very low temperature. Hence, they have very high boiling points. In the light of the above statements, choose the correct answer from the options given below:

1. A.Both Statement I and Statement II are false.
2. B.Statement I is true but Statement II is false.
3. C.Statement I is false but Statement II is true.
4. D.Both Statement I and Statement II are true.

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

1. A.$(\mathrm{C}{\mathrm{H}}_3{)}_2\mathrm{CO}+\mathrm{C}{\mathrm{S}}_2$
2. B.$(\mathrm{C}{\mathrm{H}}_3{)}_2\mathrm{CO}+{\mathrm{C}}_6{\mathrm{H}}_5\mathrm{N}{\mathrm{H}}_2$
3. C.$\mathrm{CHC}{\mathrm{l}}_3+{\mathrm{C}}_6{\mathrm{H}}_6$
4. D.$\mathrm{CHC}{\mathrm{l}}_3+(\mathrm{C}{\mathrm{H}}_3{)}_2\mathrm{CO}$

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

1. A.Increases
2. B.Decreases
3. C.Remains unchanged
4. D.First decreases and then increases

The osmotic pressure of a dilute solution is $7\times 10^5\text{ Pa}$ at $273\text{ K}$. Osmotic pressure of the same solution at $283\text{ K}$ is _________ $\times 10^4\mathrm{N}{\mathrm{m}}^{-2}$.

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

1. A.increased vapour pressure, increased boiling point
2. B.increased vapour pressure, decreased boiling point
3. C.decreased vapour pressure, decreased boiling point
4. D.decreased vapour pressure, increased boiling point

Solution of $12\text{ g}$ of non-electrolyte (A) prepared by dissolving it in $1000\text{ mL}$ of water exerts the same osmotic pressure as that of $0.05\text{ M}$ glucose solution at the same temperature. The empirical formula of A is ${\mathrm{CH}}_2\mathrm{O}$. The molecular mass of A is ___________ g. (Nearest integer)

Sea water contains $29.25\%$ $\mathrm{NaCl}$ and $19\%$ ${\mathrm{MgCl}}_2$ by weight of solution. The normal boiling point of the sea water is ___________ ${}^{\circ }\mathrm{C}$ (Nearest integer) Assume $100\%$ ionization for both $\mathrm{NaCl}$ and ${\mathrm{MgCl}}_2$ Given : ${\mathrm{K}}_b({\mathrm{H}}_2\mathrm{O})=0.52{\text{ K kg mol}}^{-1}$ Molar mass of $\mathrm{NaCl}$ and ${\mathrm{MgCl}}_2$ is $58.5$ and $95{\text{ g mol}}^{-1}$ respectively.

Given below are two statements : Statement I : Boron is extremely hard indicating its high lattice energy. Statement II : Boron has highest melting and boiling point compared to its other group members. In the light of the above statements, choose the most appropriate answer from the options given below :

1. A.Both Statement I and Statement II are incorrect
2. B.Statement I is incorrect but Statement II is correct
3. C.Statement I is correct but Statement II is incorrect
4. D.Both statement I and Statement II are correct

If the degree of dissociation of aqueous solution of weak monobasic acid is determined to be 0.3, then the observed freezing point will be ___________% higher than the expected/theoretical freezing point. (Nearest integer)

An aqueous solution of volume $300{\text{ cm}}^3$ contains 0.63 g of protein. The osmotic pressure of the solution at 300 K is 1.29 mbar. The molar mass of the protein is _________ ${\text{g mol}}^{-1}$ Given : $\text{R}=0.083{\text{ L bar K}}^{-1}{\text{ mol}}^{-1}$