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Chemistry

At \( 300 \, \text{K} \), the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below:

The conductivity of a saturated aqueous solution of AgCl is \( 1.40 \times 10^{-6} \, \text{S cm}^{-1} \) at \( 300 \, \text{K} \). If the solubility of AgCl in water at \( 300 \, \text{K} \) is \( X \, \text{mol L}^{-1} \), then \( \log_{10}\!\left(X^{-1}\right) \) is
(Assume that AgCl dissolved in water ionizes completely and that the molar conductivity of saturated AgCl solution is equal to its limiting molar conductivity.)

20.

The correct order of ONO bond angle in the given species is:

21.

Natural rubber on complete ozonolysis \( \left(\mathrm{O_3/Zn - H_2O}\right) \) gives compound \( X \) as the major product. \( X \) gives positive iodoform and Tollen’s tests. \( X \) on heating with aqueous \( \mathrm{NaOH} \) gives \( Y \) as the major product. \( Y \) is:

22.

A known artificial sweetener \( X \) is composed of \( 4 \)-chloro-\( 4 \)-deoxy- \( \alpha \)-\( D \)-galactose and \( 1,6 \)-dichloro-\( 1,6 \)-dideoxy- \( \beta \)-\( D \)-fructose joined by a glycosidic linkage. Structure of \( D \)-galactose is given below:

The correct structure of \( X \) is:

23.

For a first-order reaction \( R \rightarrow P \) at a given temperature, \( k \) is the rate constant. For this reaction, at the given temperature, the concentrations of \( R \) and \( P \) at a time \( t \) are \( [R] \) and \( [P] \), respectively. The correct graphical representation(s) for this reaction is(are):

24.

Correct statement(s) about the compounds P, Q and R is(are)

25.

The correct statement(s) regarding the periodic properties of elements is(are):

26.

In the following reaction sequence, P, Q, S and T are the major products.

The correct statement(s) about P, Q, S and T is(are):

27.

The correct statement(s) regarding sugars is(are):
Given: Specific rotations of L–(−)–glucose and L–(+)–fructose are \( -52.5^\circ \) and \( +92.5^\circ \), respectively.

28.

\( \mathrm{X^{a+}} \) and \( \mathrm{Y^{b+}} \) are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers \( n = 1 \) and \( n = 2 \) of \( \mathrm{X^{a+}} \) is \( \lambda \). The wavelength of light absorbed during the transition between the states with principal quantum numbers \( n = 2 \) and \( n = 4 \) of \( \mathrm{Y^{b+}} \) is \( 9\lambda \). The lowest possible value of \( (a + b) \) is __________.

29.

At a given temperature, \( 0.45 \, \text{g} \) of acetic acid in \( 50 \, \text{mL} \) of water is shaken with \( 1.0 \, \text{g} \) of charcoal and the pH of the resulting solution is \( 3.0 \). Assume, the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich isotherm, \( \dfrac{x}{m} = k C^{1/n} \).
If the plot of \( \log_{10}\!\left(\dfrac{x}{m}\right) \) against \( \log_{10} C \) gives a straight line with slope \( 1 \), the value of \( k \) in \( \text{L mol}^{-1} \) is ________.
Given: The molar mass of acetic acid is \( 60 \, \text{g mol}^{-1} \).
The acid dissociation constant of acetic acid is \( 1.0 \times 10^{-5} \) at the given temperature.
\( x \) is the mass (in grams) of acetic acid adsorbed.
\( m \) is the mass (in grams) of charcoal.
\( C \) is the equilibrium concentration of acetic acid in the solution after the adsorption is complete.
\( k \) and \( n \) are constants for acetic acid-charcoal system at the given temperature.

30.

In a solvent \( S \), a compound \( B \) is partially dissociated into \( C \) and \( D \) as given below:
\( B \rightleftharpoons 2C + 2D \)
\( B, C \) 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 \( 400 \, \text{K} \) and \( 10R \, \text{J mol}^{-1} \), respectively \( (R \) is the gas constant in \( \text{J K}^{-1} \text{ mol}^{-1}) \). A solution of \( B \) in \( S \) with an initial concentration of \( B \) as \( 0.25\% \) (mass/mass) has a boiling point of \( 408 \, \text{K} \) at \( 1 \) bar pressure. In this solution, the mole percent of \( B \) that has been dissociated is ________.

31.

Consider that the coordinating atoms of the ligands in \( \text{cis-}[ \mathrm{Co(NH_3)_4Cl_2}] \mathrm{Cl} \) and \( \text{mer-}[ \mathrm{Co(NH_3)_3Cl_3}] \) octahedral complexes are at the vertices of an octahedron. The sum of total number of the triangular faces in both the complexes having one \( \mathrm{N} \) atom and two \( \mathrm{Cl} \) atoms at their corners is ________.

32.

In the following reaction sequence, major products \( X \) and \( Y \) are acyclic monomers.

\( 500 \) mol of \( X \) completely reacts with \( 500 \) mol of \( Y \) to give \( 1 \) mol of a single biodegradable acyclic copolymer \( Z \) as the only product. The amount of \( Z \) formed in grams is ________.
Given: Atomic mass (in amu): \( \mathrm{H:1, \; C:12, \; N:14, \; O:16, \; Br:80} \)

33.

Two volatile liquids \( A \) and \( B \) form an ideal solution. Consider a \( 5 \) molal solution of \( B \) in \( A \) inside a closed container having a total vapour pressure of \( 100 \, \text{mm Hg} \) at \( 300 \, \text{K} \). The vapour pressure of pure \( A \) at \( 300 \, \text{K} \) is \( 105 \, \text{mm Hg} \). Assume that \( A \) and \( B \) behave as ideal gases in the vapour phase.
Given:
The gas constant \( R = 0.08 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)
Molar mass of \( A \) is \( 50 \, \text{g mol}^{-1} \)
Molar mass of \( B \) is \( 57 \, \text{g mol}^{-1} \)
Density of liquid \( B \) at \( 300 \, \text{K} \) is \( 0.5 \, \text{g/mL} \)
\( 1 \, \text{atm} = 760 \, \text{mm Hg} \)
At \( 300 \, \text{K} \), the ratio of the molar volume of pure \( B \) in vapour phase to its molar volume in liquid phase is ________.

34.

Two volatile liquids \( A \) and \( B \) form an ideal solution. Consider a \( 5 \, \text{molal} \) solution of \( B \) in \( A \) inside a closed container having a total vapour pressure of \( 100 \, \text{mm Hg} \) at \( 300 \, \text{K} \). The vapour pressure of pure \( A \) at \( 300 \, \text{K} \) is \( 105 \, \text{mm Hg} \). Assume that \( A \) and \( B \) behave as ideal gases in the vapour phase.
Given:
The gas constant \( R = 0.08 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)
Molar mass of \( A \) is \( 50 \, \text{g mol}^{-1} \)
Molar mass of \( B \) is \( 57 \, \text{g mol}^{-1} \)
Density of liquid \( B \) at \( 300 \, \text{K} \) is \( 0.5 \, \text{g/mL} \)
\( 1 \, \text{atm} = 760 \, \text{mm Hg} \)
The mole fraction of \( B \) in vapour phase which is in equilibrium with this solution is ________.

35.

Consider the following reaction sequence in which \( J \), \( K \), \( L \) and \( M \) are the major products.

Given:
Atomic mass (in amu): \( \text{H} : 1 , \; \text{C} : 12 , \; \text{N} : 14 , \; \text{O} : 16 , \; \text{S} : 32 , \; \text{Br} : 80 , \; \text{Ba} : 137 \)
The volume of \( 1 \, \text{M} \) aqueous \( \text{H}_2\text{SO}_4 \) required to completely neutralize the ammonia evolved from \( 5.72 \, \text{g} \) of \( L \) in Kjeldahl's method of nitrogen estimation is _______ \( \text{mL} \).

36.

Consider the following reaction sequence in which \( J \), \( K \), \( L \) and \( M \) are the major products.

Given:
Atomic mass (in amu): \( \text{H} : 1 , \; \text{C} : 12 , \; \text{N} : 14 , \; \text{O} : 16 , \; \text{S} : 32 , \; \text{Br} : 80 , \; \text{Ba} : 137 \)
In sulphur estimation by Carius method, the amount of \( \text{BaSO}_4 \) formed from \( 3.79 \, \text{g} \) of \( M \) is _______ \( \text{g} \).

JEE Advanced 2026 Paper - 2

Physics Chemistry Mathematics

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The correct statement(s) regarding the periodic properties of elements is(are):

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