GATE 2026 Chemistry Question Paper with Solutions

"He often the numbers. False claims are not going to help. Honesty trust", said the manager.
Choose the option with the correct order of words to fill the blanks.

• (A) exaggerates; engenders
• (B) excels; encourages
• (C) aggravates; alleviates
• (D) diminishes; eliminates

In the sequence of tiles shown below, the missing tile indicated by the question mark should be

• (A)

• (B)

• (C)

• (D)

A school has 100 students distributed among 1^st to 10^th standards.
Based on this, which one of the following statements is always correct?

• (A) There are at least 10 students who belong to the same standard.
• (B) There is at least one student in each standard.
• (C) There are at most 10 students in 10^th standard.
• (D) The total number of students from 1^st to 5^th standards is at least 50.

How many 3-digit numbers can be formed using three distinct single digit prime numbers?

• (A) 64
• (B) 24
• (C) 12
• (D) 4

In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is

• (A) 18
• (B) 20
• (C) 24
• (D) 32

Charity : P :: Retaliation : Q
Choose the appropriate pair of words P and Q that fit the analogy.

• (A) P = Parsimonious; Q = Vengeful
• (B) P = Altruistic; Q = Amicable
• (C) P = Resentful; Q = Spiteful
• (D) P = Magnanimous; Q = Vindictive

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

• (A) Only (i) can correspond to the unfolded cube in Panel I.
• (B) Only (ii) can correspond to the unfolded cube in Panel I.
• (C) Both (i) and (ii) can correspond to the unfolded cube in Panel I.
• (D) Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is

• (A) 8
• (B) 4
• (C) 3
• (D) 2

Four hills \(H_1, H_2, H_3\), and \(H_4\) are present in an area. The following observations are made about them:
(i) Neither \(H_2\) nor \(H_3\) is the easternmost hill.
(ii) Neither \(H_2\) nor \(H_3\) is the westernmost hill.
(iii) Neither the easternmost hill nor the westernmost hill is the southernmost hill.
(iv) Two hills are located to the west of \(H_2\).
(v) The southernmost hill has at least two hills to its east.
The southernmost hill is .

• (A) \(H_1\)
• (B) \(H_2\)
• (C) \(H_3\)
• (D) \(H_4\)

As shown in the figure, circle \(C_1\) with center \(O_1\) and radius \(r_1\) touches the square \(VWXY\) at points \(P\) and \(Q\), while circle \(C_2\) with center \(O_2\) and radius \(r_2\) touches the square \(VWXY\) at points \(R\) and \(S\). The two circles touch each other at \(T\).
Given \(r_1 = 1\) cm and \(\overline{VY} = \overline{VW} = 4\) cm, \(r_2 =\) cm.

• (A) \(4 - 3\sqrt{2}\)
• (B) \(1 + 2\sqrt{2}\)
• (C) \(7 - 4\sqrt{2}\)
• (D) \(5 + 3\sqrt{2}\)

The major product formed in the following reaction is:

• (A)

• (B)

• (C)

• (D)

The correct statement about the following quaternary ammonium ion is:

• (A) It has only \(C_2\)-symmetry, hence chiral
• (B) It has \(S_4\)-symmetry, hence achiral
• (C) It has no symmetry, hence chiral
• (D) It has a centre of symmetry, hence achiral

The major product formed in the following reaction sequence is:
Step 1: \(\mathrm{C_6H_{13}{-}C{\equiv}CH}\) is treated with catecholborane, then heated.
Step 2: the product from Step 1 is treated with \(\mathrm{Br_2}\), then \(\mathrm{NaOMe}\).

• (A) \(\mathrm{C_6H_{13}{-}CH{=}CH{-}Br}\) (E-configured: the hexyl chain and \(\mathrm{Br}\) on opposite sides of the double bond)
• (B) \(\mathrm{C_6H_{13}{-}CH{=}CBr_2}\) (1,1-dibromoalkene: both \(\mathrm{Br}\) atoms on the terminal alkene carbon)
• (C) \(\mathrm{C_6H_{13}{-}CH{=}CH{-}Br}\) (Z-configured: the hexyl chain and \(\mathrm{Br}\) on the same side of the double bond)
• (D) \(\mathrm{C_6H_{13}{-}CBr{=}CH{-}Br}\) (1,2-dibromoalkene: one \(\mathrm{Br}\) on each alkene carbon)

The major product formed in the following reaction is:

• (A)

• (B)

• (C)

• (D)

The species that undergoes \(\beta\)-elimination is

• (A) \([\mathrm{Rh(C_5H_5)(P(CH_3)_3)(C_2H_5)}]^{+}\)
• (B) \([\mathrm{Rh(NH_3)_5(C_2H_5)}]^{2+}\)
• (C) \([\mathrm{Pt(P(C_6H_5)_3)_2(C_6H_5)I}]\)
• (D) \([\mathrm{Cr(CH_2Si(CH_3)_3)_4}]\)

According to molecular orbital theory, the correct ground state electronic configuration for \(\mathrm{[Co(NH_3)_6]^{3+}}\) ion is

• (A) \(a_{1g}^{2}\ t_{1u}^{6}\ e_g^{4}\ t_{2g}^{6}\ e_g^{*0}\)
• (B) \(a_{1g}^{2}\ t_{1u}^{6}\ t_{2g}^{6}\ e_g^{4}\ e_g^{*0}\)
• (C) \(t_{1u}^{6}\ a_{1g}^{2}\ e_g^{4}\ t_{2g}^{6}\ e_g^{*0}\)
• (D) \(a_{1g}^{2}\ t_{1u}^{6}\ e_g^{4}\ t_{2g}^{4}\ e_g^{*2}\)

The species which follows the 18-electron rule is
(\(en = \mathrm{ethylenediamine}\))

• (A) \(\mathrm{[Rh(PPh_3)_3Cl]}\)
• (B) \(\mathrm{[Co(NH_3)_6]^{2+}}\)
• (C) \(\mathrm{[V(CO)_6]^{-}}\)
• (D) \(\mathrm{[Ni(en)_3]^{2+}}\)

The point group of \(\mathrm{CH_2=C=CH_2}\) is

• (A) \(D_{2h}\)
• (B) \(C_{2h}\)
• (C) \(C_{2v}\)
• (D) \(D_{2d}\)

Among the following, the one for which the infrared active vibrational modes are Raman inactive and vice versa is

• (A) \(\mathrm{H_2O}\)
• (B) trans-planar conformer of \(\mathrm{H_2O_2}\)
• (C) eclipsed conformer of ethane
• (D) \(\mathrm{CH_4}\)

For the following reaction,
\(\mathrm{A + B \rightleftharpoons X^{\ddagger} \rightarrow product}\)
If the value of \(\Delta^{\ddagger}U^{o} = \dfrac{5}{2}RT\), then the value of \(\Delta^{\ddagger}H^{o}\) is
(\(X^{\ddagger}\) is an activated complex; \(\Delta^{\ddagger}U^{o}\) is the standard change in internal energy; \(\Delta^{\ddagger}H^{o}\) is the standard enthalpy of activation; \(R\) is the gas constant; \(T\) is the temperature)

• (A) \(\dfrac{1}{2}RT\)
• (B) \(\dfrac{3}{2}RT\)
• (C) \(\dfrac{7}{2}RT\)
• (D) \(\dfrac{5}{2}RT\)

The reagent(s) that will effect the following transformation is(are)

• (A) \(\mathrm{Pd/C, H_2}\)
• (B) \(\mathrm{ZnBr_2}\)
• (C) Pyridinium p-toluenesulfonate (PPTS), \(^t\mathrm{BuOH}\)
• (D) \(^{n}\mathrm{Bu_4NF}\)

The reaction(s) that give(s) meso-1,2-diphenylethane-1,2-diol as the major product is(are)

• (A)

• (B)

• (C)

• (D)

In the \(^1\mathrm{H}\) NMR spectrum of compound \(\mathbf{X}\), the coupling constant (\(J_{ab}\)) between \(H_a\) and \(H_b\) is 3 Hz. The amino alcohol(s) that give(s) \(\mathbf{X}\) on reaction with methyl iodide followed by heating is(are)

• (A)

• (B)

• (C)

• (D)

The correct statement(s) regarding plastocyanin is(are)

• (A) It is an electron transfer protein
• (B) It is intensely colored in its oxidised form
• (C) Its central metal ion has a distorted tetrahedral geometry
• (D) It contains \(S^{2-}\) bridged metal cluster

The correct statement(s) about Mossbauer spectroscopy of iron compounds is(are)

• (A) \(^{57}\mathrm{Co}\) is used as a source
• (B) Their Mossbauer spectra are obtained using \(\gamma\)-ray with resonance energy of 14.4 keV
• (C) \(\mathrm{K_2[Fe(CN)_5NO]}\) shows large quadrupole splitting
• (D) Isomer shift of \(\mathrm{FeSO_4 \cdot 7H_2O}\) is smaller than that of \(\mathrm{K_3[Fe(CN)_6]}\)

The interconversion of oxidation states of metal(s) observed in Wacker process is(are)

• (A) \(\mathrm{Pd(II)/Pd(0)}\)
• (B) \(\mathrm{Cu(II)/Cu(I)}\)
• (C) \(\mathrm{Pd(IV)/Pd(II)}\)
• (D) \(\mathrm{Cu(II)/Cu(0)}\)

For the wavefunction \(\Phi = x(a-x)\), where \(a\) is a constant, the correct statement(s) is(are)

• (A) It represents a stationary state
• (B) It is an odd function
• (C) It represents the wavefunction of a particle moving on a circular ring of radius \(a\)
• (D) It is an eigen function of the momentum operator

The correct statement(s) about spherical harmonics \((Y_l^m)\) is(are)

• (A) All spherical harmonics are complex functions
• (B) They are eigen functions of \(\hat{L}^2\)
• (C) They are eigen functions of \(\hat{L}_z\)
• (D) The spherical harmonics \(Y_1^1\) and \(Y_1^{-1}\) are degenerate

The difference in the number of gauche interactions present in diaxial and diequatorial chair conformations of trans-1,2-dimethylcyclohexane is (in integer).

The total number of symmetry operations (order, \(h\)) present in the point group of \([\mathrm{PdCl_6}]^{2-}\) is \(x\) and that in trans-\([\mathrm{PdBr_2Cl_4}]^{2-}\) is \(y\). The value of \(x-y\) is (in integer).

A 0.005 M solution of compound X transmits 80% of the incident light of wavelength (\(\lambda\)) 500 nm. The absorbance of 0.01 M solution of X is (rounded off to three decimal places).
(Given: path length = 1.0 cm)

The microwave spectrum of gaseous \(\mathrm{HF}\) consists of a series of lines separated by \(41.11\ \mathrm{cm^{-1}}\). The bond length (in \(\mathrm{\mathring{A}}\)) of \(\mathrm{HF}\) is (rounded off to two decimal places).

(Given: Atomic mass (in amu): \(\mathrm{H} = 1.008\), \(\mathrm{F} = 18.998\); \(1\ \mathrm{amu} = 1.661\times10^{-27}\ \mathrm{kg}\); \(h = 6.626\times10^{-34}\ \mathrm{J\,s}\); \(c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}\))

In a \(^1\mathrm{H}\) NMR spectrum obtained from a spectrometer operating at a magnetic field of \(14.1\ \mathrm{T}\), two resonances are observed at \(1.25\) ppm and \(5.75\) ppm. The separation between the two resonances (in Hz) is (rounded off to one decimal place).

(Given: gyromagnetic ratio (\(\gamma\)) of \(\mathrm{H} = 2.675\times10^{8}\ \mathrm{T^{-1}\,s^{-1}}\))

The maximum work (\(|W_{max}|\), in kJ) that can be obtained by complete combustion of \(1.0\) mol of \(\mathrm{CH_4}\) at constant pressure and \(25^{\circ}\mathrm{C}\) is (rounded off to one decimal place).

(Given: \(\Delta S = -241.60\ \mathrm{J\,K^{-1}\,mol^{-1}}\); \(\Delta H = -890.01\ \mathrm{kJ\,mol^{-1}}\); \(R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\))

If the ionic mobility of \(\mathrm{Ag^+}\) ion in a very dilute aqueous solution of \(\mathrm{AgNO_3}\) at \(298\ \mathrm{K}\) is \(y\times10^{-8}\ \mathrm{m^2\,V^{-1}\,s^{-1}}\), then the value of \(y\) is (rounded off to two decimal places).

(Given: viscosity of water at \(298\ \mathrm{K} = 8.94\times10^{-4}\ \mathrm{kg\,m^{-1}\,s^{-1}}\); \(k = 1.38\times10^{-23}\ \mathrm{J\,K^{-1}}\); \(F = 96500\ \mathrm{C\,mol^{-1}}\); \(R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\); Stokes radius of \(\mathrm{Ag^+} = 0.15\ \mathrm{nm}\))

The major product formed in the following reaction is

• (A)

• (B)

• (C)

• (D)

The correct match for the protons labeled in compound \(\mathrm{X}\) in Column M with the corresponding chemical shifts (\(\delta\), ppm) in Column N is

• (A) \(P\rightarrow II;\ Q\rightarrow III;\ R\rightarrow I;\ S\rightarrow IV\)
• (B) \(P\rightarrow I;\ Q\rightarrow IV;\ R\rightarrow II;\ S\rightarrow III\)
• (C) \(P\rightarrow II;\ Q\rightarrow IV;\ R\rightarrow I;\ S\rightarrow III\)
• (D) \(P\rightarrow I;\ Q\rightarrow III;\ R\rightarrow II;\ S\rightarrow IV\)

The correct statement about the intermediate formed in the following reaction is

• (A)
  is formed through conrotatory opening of \(\mathrm{X}\)
• (B)
  is formed through disrotatory opening of \(\mathrm{X}\)
• (C)
  is formed through conrotatory opening of \(\mathrm{X}\)
• (D)
  is formed through disrotatory opening of \(\mathrm{X}\)

The major product formed in the following reaction sequence is:

• (A)

• (B)

• (C)

• (D)

Consider the figure given below, where M is a metal and L is a monodentate ligand. The \(\sigma\)-bonding ligand group orbital (LGO) having same symmetry with \(d_{z^2}\) orbital of M in the octahedral coordination geometry is:

• (A) \(\dfrac{1}{\sqrt{12}}\left(2\sigma_1+2\sigma_2-\sigma_3-\sigma_4-\sigma_5-\sigma_6\right)\)
• (B) \(\dfrac{1}{\sqrt{12}}\left(2\sigma_1-2\sigma_2+\sigma_3-\sigma_4+\sigma_5-\sigma_6\right)\)
• (C) \(\dfrac{1}{\sqrt{6}}\left(\sigma_1+\sigma_2-\sigma_3-\sigma_4-\sigma_5-\sigma_6\right)\)
• (D) \(\dfrac{1}{\sqrt{6}}\left(\sigma_1+\sigma_2+\sigma_3+\sigma_4+\sigma_5+\sigma_6\right)\)

The correct electronic configuration of central metal ion in ferrocene with \(z\)-axis passing through the centre of two \(\mathrm{C_5H_5^-}\) rings and the metal ion is:

• (A) \(d_{xy}^2 = d_{x^2-y^2}^2 < d_{z^2}^2 < d_{xz}^0 = d_{yz}^0\)
• (B) \(d_{xz}^2 = d_{yz}^2 < d_{z^2}^2 < d_{x^2-y^2}^0 = d_{xy}^0\)
• (C) \(d_{xy}^2 = d_{xz}^2 = d_{yz}^2 < d_{x^2-y^2}^0 = d_{z^2}^0\)
• (D) \(d_{xy}^2 < d_{xz}^2 = d_{yz}^2 < d_{x^2-y^2}^0 < d_{z^2}^0\)

The pair of complex ions that exhibits the slowest outer-sphere electron-exchange reaction at 25 \(^{\circ}\mathrm{C}\) is:

• (A) \(\mathrm{[Co(NH_3)_6]^{3+}}\) and \(\mathrm{[Co(NH_3)_6]^{2+}}\)
• (B) \(\mathrm{[Fe(H_2O)_6]^{3+}}\) and \(\mathrm{[Fe(H_2O)_6]^{2+}}\)
• (C) \(\mathrm{[Ru(NH_3)_6]^{3+}}\) and \(\mathrm{[Ru(NH_3)_6]^{2+}}\)
• (D) \(\mathrm{[Mn(CN)_6]^{3-}}\) and \(\mathrm{[Mn(CN)_6]^{4-}}\)

The structure of \(\mathrm{B_4H_{10}}\) is given below. Its styx number is:

• (A) 4012
• (B) 4102
• (C) 2104
• (D) 2014

For the following reaction,
\[ 2\,\mathrm{Pb_3O_4(s)} \rightleftharpoons 6\,\mathrm{PbO(s)} + \mathrm{O_2(g)} \] The correct option showing the number of phases (P), number of components (C) and degrees of freedom (F) is:

• (A) P = 3, C = 2, F = 1
• (B) P = 3, C = 3, F = 2
• (C) P = 2, C = 3, F = 3
• (D) P = 2, C = 2, F = 2

The correct option for the average value of kinetic energy and the average value of potential energy of a one-dimensional harmonic oscillator with frequency \(\nu\) in its ground state is:

• (A) \(\dfrac{h\nu}{2}\) and \(\dfrac{h\nu}{4}\), respectively
• (B) \(\dfrac{h\nu}{2}\) and \(\dfrac{h\nu}{2}\), respectively
• (C) \(\dfrac{h\nu}{4}\) and \(\dfrac{h\nu}{4}\), respectively
• (D) \(\dfrac{h\nu}{4}\) and \(\dfrac{h\nu}{2}\), respectively

For a reaction between neutral molecules \(\mathrm{X}\) and \(\mathrm{Y}\) in a solution at temperature \(T\), the measured rate of reaction is equal to the rate of diffusion. Assume \(\mathrm{X}\) is stationary and \(\mathrm{Y}\) is moving. If the diameter of the molecule \(\mathrm{X}\) is five times that of \(\mathrm{Y}\), then the rate constant for the reaction is
(\(\eta\) is viscosity of the solvent; \(k\) is the Boltzmann constant)

• (A) \(\dfrac{8kT}{3\eta}\)
• (B) \(\dfrac{4kT}{\eta}\)
• (C) \(\dfrac{24kT}{5\eta}\)
• (D) \(\dfrac{15kT}{4\eta}\)

For the following electrochemical cells, liquid junction potentials affect the cell potential (\(E_{cell}\)).
I. \(\mathrm{Electrode\text{-}1 \mid 0.1\ M\ KCl \parallel 0.1\ M\ NaCl \mid Electrode\text{-}2}\)
II. \(\mathrm{Electrode\text{-}1 \mid 0.1\ M\ HCl \parallel 0.01\ M\ HCl \mid Electrode\text{-}2}\)
III. \(\mathrm{Electrode\text{-}1 \mid 0.01\ M\ KCl \parallel 0.01\ M\ HCl \mid Electrode\text{-}2}\)
The correct order of their \(E_{cell}\) at \(25^{\circ}\mathrm{C}\) is

• (A) I > II > III
• (B) II > I > III
• (C) III = I > II
• (D) II > I = III

The set(s) of reagents that will effect the following conversion is(are)

• (A) i) \(\mathrm{Ph_3P{=}CHOMe}\); ii) \(\mathrm{H_3O^+}\)
• (B) i) \(\mathrm{TsNHNH_2}\); ii) \(^{n}\mathrm{BuLi}\) (2 equiv) then \(\mathrm{DMF}\)
• (C) i) 1,3-dithiane, \(^{n}\mathrm{BuLi}\); ii) \(\mathrm{HgSO_4}\), dil. \(\mathrm{H_2SO_4}\)
• (D) i) \(\mathrm{Me_3SI}\), \(\mathrm{NaH}\); ii) \(\mathrm{BF_3\cdot OEt_2}\)

The reaction(s) that produce(s) the following compound is(are)

• (A)

• (B)

• (C)

• (D)

The reaction(s) that produce(s) 2-methylindole as the major product is(are)

• (A)

• (B)

• (C)

• (D)

Chymotrypsin selectively cleaves a peptide at the carboxyl side of the amino acids having an aryl sidechain. The tripeptide(s) formed on hydrolysis of the peptide, \(\mathrm{Val\text{-}Phe\text{-}Leu\text{-}Met\text{-}Tyr\text{-}Pro\text{-}Gly\text{-}Trp\text{-}Cys}\), with chymotrypsin is(are)

• (A) Leu-Met-Tyr
• (B) Phe-Leu-Met
• (C) Pro-Gly-Trp
• (D) Tyr-Pro-Gly

Consider the given pairs of complex ions. The correct pair(s) in which each complex ion exhibits three spin-allowed \(d\text{-}d\) transitions (excluding those arising due to distortions) is(are)

• (A) \(\mathrm{[V(H_2O)_6]^{3+}}\) and \(\mathrm{[Ni(H_2O)_6]^{2+}}\)
• (B) \(\mathrm{[Cr(H_2O)_6]^{3+}}\) and \(\mathrm{[NiCl_4]^{2-}}\)
• (C) \(\mathrm{[Ti(H_2O)_6]^{3+}}\) and \(\mathrm{[Mn(H_2O)_6]^{2+}}\)
• (D) \(\mathrm{[FeF_6]^{3-}}\) and \(\mathrm{[FeCl_4]^{2-}}\)

The correct statement(s) about the structure of metal oxides is(are)

• (A) Spinel has 8 tetrahedral sites and 4 octahedral sites per formula unit
• (B) \(\mathrm{BaTiO_3}\) has a perovskite structure
• (C) In \(\mathrm{Fe_3O_4}\), \(\mathrm{Fe^{2+}}\) occupies both tetrahedral and octahedral sites in the unit cell
• (D) \(\gamma\text{-}\mathrm{Al_2O_3}\) is a defect spinel

The pair(s) of lanthanide ions whose ground state term symbols have same spin multiplicity \((2S+1)\) and orbital angular momentum \((L)\), but different spin-orbit coupling \((J)\) is(are)
(Given: Atomic number: \(\mathrm{Nd}=60\); \(\mathrm{Pm}=61\); \(\mathrm{Ho}=67\); \(\mathrm{Er}=68\))

• (A) \(\mathrm{Pm^{3+}}\) and \(\mathrm{Ho^{3+}}\)
• (B) \(\mathrm{Nd^{3+}}\) and \(\mathrm{Er^{3+}}\)
• (C) \(\mathrm{Pm^{3+}}\) and \(\mathrm{Nd^{3+}}\)
• (D) \(\mathrm{Ho^{3+}}\) and \(\mathrm{Er^{3+}}\)

The correct statement(s) about enterobactin (ent) is(are)

• (A) It has three catechol moieties
• (B) It has a serine-trilactone backbone
• (C) It binds with \(\mathrm{Fe^{3+}}\) ion to form \(\mathrm{[Fe(ent)]^{3-}}\) ion
• (D) It has three hydroxamic acid groups

The correct statement(s) for a surface catalyzed unimolecular gaseous reaction is(are)

• (A) It follows Freundlich adsorption isotherm
• (B) Zero order kinetics is followed at sufficiently high pressure of the reacting molecules
• (C) First order kinetics is followed at very low pressure of the reacting molecules
• (D) Rate of the reaction is proportional to the fraction of surface covered by the reacting molecules

Consider the following reaction sequence, where \(\mathrm{A}\) and \(\mathrm{B}\) are the major products.

On heating, the compound \(\mathrm{Z}\) undergoes a series of 1,5-H/D shifts to give a mixture of its isomers.

The sum of bond orders of metal-metal bonds in \([\mathrm{Os_2Cl_8}]^{2-}\), \([\mathrm{Re_2Cl_8}]^{2-}\), \([\mathrm{W_2(NMe_2)_6}]\) and \([\mathrm{Mo(C_5H_5)(CO)_2}]_2\) is (in integer).

The sum of the number of \(\alpha\)-particles and \(\beta\)-particles emitted in the nuclear decay process, \(^{238}_{92}\mathrm{U} \rightarrow\, ^{206}_{82}\mathrm{Pb}\), is (in integer).

The positions of two atoms in spherical polar coordinates \((r, \theta, \Phi)\) are \((1, \frac{\pi}{2}, \frac{\pi}{2})\) and \((1, \frac{\pi}{4}, \frac{3\pi}{2})\), where the distance is in \(\overset{\circ}{\mathrm{A}}\) and the angles are in radian. The interatomic distance (in \(\overset{\circ}{\mathrm{A}}\)) is (rounded off to two decimal places).

If the translational partition function for \(\mathrm{H_2}\) confined in a 1 L vessel at 300 K is \(y \times 10^{27}\), then the value of \(y\) is (rounded off to one decimal place).
(Given: Atomic mass (in amu): H = 1.008; 1 amu = \(1.661 \times 10^{-27}\) kg; \(h = 6.626 \times 10^{-34}\) J s; \(k = 1.381 \times 10^{-23}\) J K\(^{-1}\))

In a calibrated pH meter comprising of glass electrode-standard calomel electrode, the potential for a buffer solution of pH 4.01 is measured as 0.814 V at 25\(^{\circ}\)C. For a \(4.0 \times 10^{-3}\) M solution of acetic acid, the measured potential (in V) is (rounded off to three decimal places).
(Given: \(K_a\) of acetic acid at 25\(^{\circ}\)C = \(1.75 \times 10^{-5}\); \(2.303RT/F = 0.059\); Assume: \(a_{H^+} = [H^+]\))

The Brunauer-Emmett-Teller (BET) surface area measurement data for adsorption of \(\mathrm{N_2}\) gas at 77 K on 1.0 g of an adsorbent fits into a straight line, when \(\dfrac{z}{(1-z)V}\) is plotted against \(z\). The slope and intercept of the straight line are \(6 \times 10^{-4}\) mm\(^{-3}\) and \(4 \times 10^{-6}\) mm\(^{-3}\), respectively. The surface area (in m\(^2\) g\(^{-1}\)) of the adsorbent is (rounded off to one decimal place).
(Given: 1 mm\(^3\) of \(\mathrm{N_2}\) gas corresponds to \(2.7 \times 10^{16}\) molecules and each molecule occupies 0.16 nm\(^2\). \(V\) is the volume of gas adsorbed in mm\(^3\), \(z\) is \(p/p_o\), where \(p\) is the pressure of the \(\mathrm{N_2}\) gas and \(p_o\) is equilibrium vapour pressure of liquid \(\mathrm{N_2}\))

The orbital angular momentum (\(\mathbf{L}\)) of an electron is \(\sqrt{12}\,\hbar\). The minimum angle between \(\mathbf{L}\) and its \(z\)-component (in degrees) is (rounded off to one decimal place).