JEE (Advanced) 2023 Paper-2

In the following reactions, P, Q, R, and S are the major products.

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

H$$_2$$S (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is x, and the number of moles of electrons involved is y. The value of (x + y) is ____.

Among [I$$_3$$]$$^+$$, [SiO$$_4$$]$$^{4-}$$, SO$$_2$$Cl$$_2$$, XeF$$_2$$, SF$$_4$$, ClF$$_3$$, Ni(CO)$$_4$$, XeO$$_2$$F$$_2$$, [PtCl$$_4$$]$$^{2-}$$, XeF$$_4$$, and SOCl$$_2$$, the total number of species having $$sp^3$$ hybridised central atom is ____.

Consider the following molecules: Br$$_3$$O$$_8$$, F$$_2$$O, H$$_2$$S$$_4$$O$$_6$$, H$$_2$$S$$_5$$O$$_6$$, and C$$_3$$O$$_2$$.

Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is ____.

For He$$^+$$, a transition takes place from the orbit of radius 105.8 pm to the orbit of radius 26.45 pm. The wavelength (in nm) of the emitted photon during the transition is ____.

[Use: Bohr radius, $$a = 52.9$$ pm; Rydberg constant, $$R_H = 2.2 \times 10^{-18}$$ J; Planck's constant, $$h = 6.6 \times 10^{-34}$$ J s; Speed of light, $$c = 3 \times 10^8$$ m s$$^{-1}$$]

50 mL of 0.2 molal urea solution (density = 1.012 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 g mol$$^{-1}$$; gas constant, R = 62 L Torr K$$^{-1}$$ mol$$^{-1}$$; Assume, $$\Delta_{mix}H = 0$$, $$\Delta_{mix}V = 0$$]

The reaction of 4-methyloct-1-ene (P, 2.52 g) with HBr in the presence of (C$$_6$$H$$_5$$CO)$$_2$$O$$_2$$ gives two isomeric bromides in a 9 : 1 ratio, with combined yield of 50%. Of these, the entire amount of the primary alkyl bromide was reacted with an appropriate amount of diethylamine followed by treatment with eq. K$$_2$$CO$$_3$$ to give a non-ionic product S in 100% yield.

The mass (in mg) of S obtained is ____.

[Use molar mass (in g mol$$^{-1}$$): H = 1, C = 12, N = 14, Br = 80]

The value of entropy change, $$S_\beta - S_\alpha$$ (in J mol$$^{-1}$$ K$$^{-1}$$), at 300 K is ____.

[Use: ln 2 = 0.69]

[Given: $$S_\beta - S_\alpha = 0$$ at 0 K]

The value of enthalpy change, $$H_\beta - H_\alpha$$ (in J mol$$^{-1}$$), at 300 K is ____.

The number of heteroatoms present in one molecule of R is ____.

[Use: Molar mass (in g mol$$^{-1}$$): H = 1, C = 12, N = 14, O = 16, Br = 80, Cl = 35.5

Atoms other than C and H are considered as heteroatoms]