The biological functions of cytochrome $\text{P}_{450}$ and myoglobin are, respectively
a.
oxidation of alkene and $\text{O}_2$ storage
Correct Answer
b.
$\text{O}_2$ trasnport and $\text{O}_2$ storage
c.
$\text{O}_2$ storage and electron carrier
d.
electron carrier and $\text{O}_2$ transport
Step-by-Step AI Explanation
Verified Method
Cytochrome $\text{P}_{450}$ is a monooxygenase enzyme that catalyzes the insertion of an oxygen atom into unactivated C-H bonds as well as the epoxidation (oxidation) of alkenes. Myoglobin is a hemoprotein found in muscle tissue responsible for the storage of dioxygen ($\text{O}_2$). Therefore, the correct pair of biological functions is oxidation of alkene and $\text{O}_2$ storage, matching option A.
Q22mcq
Deoxy-hemocyanin is
a.
heme protein and paramagnetic
b.
colorless and diamagnetic
Correct Answer
c.
$\text{O}_2$ transporter and paramagnetic
d.
blue colored and diamagnetic
Step-by-Step AI Explanation
Verified Method
Hemocyanin is a non-heme copper protein. In the deoxy form (deoxy-hemocyanin), both copper centers are present as $\text{Cu(I)}$ ($d^{10}$ configuration). Because all electrons are paired ($d^{10}$), it is diamagnetic. Furthermore, without any $d$-$d$ transitions or low-energy charge-transfer bands, deoxy-hemocyanin is colorless. (In contrast, oxy-hemocyanin contains two $\text{Cu(II)}$ centers bridged by a peroxo group and is blue in color and diamagnetic due to strong antiferromagnetic coupling).
Q23mcq
The oxidizing power of $[\text{CrO}_4]^{2-}$, $[\text{MnO}_4]^{2-}$, and $[\text{FeO}_4]^{2-}$ follows the order
In all three tetrahedral oxoanions, $[\text{CrO}_4]^{2-}$, $[\text{MnO}_4]^{2-}$, and $[\text{FeO}_4]^{2-}$, the metal is in the $+6$ oxidation state: $\text{Cr(VI)}$, $\text{Mn(VI)}$, and $\text{Fe(VI)}$. As we move across the 3d transition series from left to right ($ ext{Cr} \to \text{Mn} \to \text{Fe}$), the effective nuclear charge ($Z_{\text{eff}}$) increases, making high oxidation states increasingly unstable and easier to reduce. Consequently, the tendency to gain electrons (oxidizing power) increases in the order: $$[\text{CrO}_4]^{2-} < [\text{MnO}_4]^{2-} < [\text{FeO}_4]^{2-}$$
Q24mcq
Using crystal field theory, identify from the following complex ions that shows same $\mu_{\text{eff}}$ (spin only) values
(A) $[\text{CoF}_6]^{3-}$
(B) $[\text{IrCl}_6]^{3-}$
(C) $[\text{Fe}(\text{H}_2\text{O})_6]^{2+}$
a.
A and B
b.
B and C
c.
A and C
Correct Answer
d.
A, B and C
Step-by-Step AI Explanation
Verified Method
To find which complexes have the same $\mu_{\text{eff}}$ (spin-only) value, determine the number of unpaired electrons ($n$) for each complex using crystal field theory:
1. **$[\text{CoF}_6]^{3-}$**:
- Oxidation state of $\text{Co}$ is $+3$, which corresponds to a $3d^6$ configuration.
- $\text{F}^-$ is a weak-field ligand, giving a high-spin octahedral arrangement: $t_{2g}^4 e_g^2$.
- Number of unpaired electrons, $n = 4$.
2. **$[\text{IrCl}_6]^{3-}$**:
- Oxidation state of $\text{Ir}$ is $+3$, corresponding to a $5d^6$ configuration.
- Since $\text{Ir}^{3+}$ is a $5d$ transition metal, the crystal field splitting parameter $\Delta_o$ is very large, so it is always low-spin, regardless of ligand: $t_{2g}^6 e_g^0$.
- Number of unpaired electrons, $n = 0$.
3. **$[\text{Fe}(\text{H}_2\text{O})_6]^{2+}$**:
- Oxidation state of $\text{Fe}$ is $+2$, corresponding to a $3d^6$ configuration.
- $\text{H}_2\text{O}$ is a weak-field ligand, giving a high-spin octahedral arrangement: $t_{2g}^4 e_g^2$.
- Number of unpaired electrons, $n = 4$.
Since both (A) and (C) have $n = 4$ unpaired electrons, they exhibit the same spin-only magnetic moment: $\mu_{\text{eff}} = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90\text{ BM}$. Therefore, the correct pair is A and C.
Q25mcq
The W-W bond order in $[\text{W}(\eta^5-\text{C}_5\text{H}_5)(\mu-\text{Cl})(\text{CO})_2]_2$ is
a.
three
b.
two
c.
one
Correct Answer
d.
zero
Step-by-Step AI Explanation
Verified Method
To determine the $\text{W}-\text{W}$ bond order, we apply the 18-electron rule to the dimer $[\text{W}(\eta^5-\text{C}_5\text{H}_5)(\mu-\text{Cl})(\text{CO})_2]_2$:
1. **Total valence electron count ($VEC$) for the dimer**:
- Each $\text{W}$ (Group 6) contributes: $2 \times 6 = 12\, e^-$
- Two $\eta^5-\text{C}_5\text{H}_5$ ligands contribute: $2 \times 5 = 10\, e^-$
- Two bridging $\mu-\text{Cl}$ ligands contribute: $2 \times 3 = 6\, e^-$
- Four terminal $\text{CO}$ ligands contribute: $4 \times 2 = 8\, e^-$
$$\text{Total } VEC = 12 + 10 + 6 + 8 = 36\, e^-$$
2. **Number of metal-metal bonds ($n$)**:
$$n = \frac{18 \times 2 - VEC}{2} = \frac{36 - 36}{2} = 0$$
Wait, let's check the valence electron contribution of bridging chloride in neutral counting:
A neutral bridging halogen ($\mu_2-\text{Cl}$) provides 3 electrons in total (one covalent single bond contributing 1 electron to one metal, and a dative lone pair contributing 2 electrons to the other metal, totaling 3 electrons per bridging $\text{Cl}$). Two $\mu-\text{Cl}$ ligands contribute $2 \times 3 = 6\, e^-$. That gives 36 electrons, leading to 0 metal-metal bonds.
However, let's verify if $\mu-\text{Cl}$ is 3-electron or if the question considers a single bond:
Is $[\text{W}(\eta^5-\text{C}_5\text{H}_5)(\mu-\text{Cl})(\text{CO})_2]_2$ possessing a $\text{W}-\text{W}$ single bond? Wait, $\text{W}$ has 6 electrons, $\text{Cp}$ has 5, $2\,\text{CO}$ have 4, one bridging $\text{Cl}$ contributes 3/2 = 1.5 per metal (or one $\mu-\text{Cl}$ gives 3 electrons shared between two metals). Total electrons per tungsten atom without M-M bond:
$6 + 5 + 4 + 3 = 18\, e^-$ (if each bridging Cl donates 3 electrons to the dimer, total from two bridging chlorines is 6 electrons, so each W receives 3 electrons from the two chlorines).
Thus, each $\text{W}$ has:
$6 (\text{W}) + 5 (\text{Cp}) + 4 (2\,\text{CO}) + 3 (\text{two } \mu-\text{Cl}) = 18\, e^-$.
Since each tungsten already achieves an 18-electron configuration without any $\text{W}-\text{W}$ bond, the $\text{W}-\text{W}$ bond order is zero.
Q26mcq
The correct statement for Mn–O bond lengths in $[\text{Mn}(\text{H}_2\text{O})_6]^{2+}$ is
a.
all bonds are equal
Correct Answer
b.
four bonds are longer than two others
c.
two bonds are longer than four others
d.
they are shorter than the Mn-O bond in $[\text{MnO}_4]^-$
Step-by-Step AI Explanation
Verified Method
In $[ ext{Mn}( ext{H}_2 ext{O})_6]^{2+}$, manganese is in the $+2$ oxidation state with a $d^5$ high-spin electronic configuration: $t_{2 ext{g}}^3 e_{ ext{g}}^2$. Because both the $t_{2 ext{g}}$ and $e_{ ext{g}}$ subshells are symmetrically (singly) occupied, there is no electronic degeneracy and hence no Jahn-Teller distortion. Consequently, the complex adopts a regular octahedral geometry where all six $\text{Mn}-\text{O}$ bond lengths are equal. (Option D is incorrect because $\text{Mn}^{2+}$ has a much larger ionic radius and weaker bonding than $\text{Mn}^{7+}$ in $[\text{MnO}_4]^-$, so its bonds are longer, not shorter).
Q27mcq
For the reaction of $[\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\text{CH}_3)(\text{CO})_2]$ with $\text{PMe}_3$, the main intermediate is
The reaction of $[\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\text{CH}_3)(\text{CO})_2]$ with a Lewis base such as $\text{PMe}_3$ is a classic alkyl migratory insertion reaction (carbonylation).
1. The starting 18-electron complex $[\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\text{CH}_3)(\text{CO})_2]$ undergoes intramolecular migration of the methyl group onto an adjacent coordinated $\text{CO}$ ligand to form a 16-electron acyl intermediate:
$$[\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\text{CH}_3)(\text{CO})_2] \rightleftharpoons [\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\text{COCH}_3)(\text{CO})]$$
2. The incoming nucleophile ($\text{PMe}_3$) then rapidly attacks the vacant coordination site of this 16-electron intermediate to yield the 18-electron product $[\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\text{COCH}_3)(\text{CO})(\text{PMe}_3)]$.
Therefore, the main intermediate is the coordinatively unsaturated acyl complex $[\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\text{COCH}_3)(\text{CO})]$, which corresponds to option B.
Q28mcq
Identify the complex ions in sequential order when ferroin is used as an indicator in the titration of iron(II) with potassium dichromate, (phen = 1, 10-phenathroline)
a.
$[\text{Fe}(\text{phen})_3]^{2+}$ and $[\text{Fe}(\text{phen})_3]^{3+}$
Correct Answer
b.
$[\text{Fe}(\text{phen})_3]^{3+}$ and $[\text{Fe}(\text{phen})_3]^{2+}$
c.
$[\text{Fe}(\text{CN})_6]^{4-}$ and $[\text{Fe}(\text{CN})_6]^{3-}$
d.
$[\text{Fe}(\text{CN})_6]^{3-}$ and $[\text{Fe}(\text{CN})_6]^{4-}$
Step-by-Step AI Explanation
Verified Method
Ferroin is the complex tris(1,10-phenanthroline)iron(II), which has the formula $[\text{Fe}(\text{phen})_3]^{2+}$ and displays an intense red color. During redox titration of $\text{Fe}^{2+}$ with an oxidizing agent like potassium dichromate ($\text{K}_2\text{Cr}_2\text{O}_7$), ferroin initially exists in its reduced form, $[\text{Fe}(\text{phen})_3]^{2+}$. At the end point, the excess oxidant oxidizes ferroin to ferriin, which is the pale blue iron(III) complex $[\text{Fe}(\text{phen})_3]^{3+}$. Therefore, the complex ions in sequential order are $[\text{Fe}(\text{phen})_3]^{2+}$ followed by $[\text{Fe}(\text{phen})_3]^{3+}$, making option A correct.
Q29mcq
The structures of $\text{XeF}_2$ and $\text{XeO}_2\text{F}_2$ respectively are
a.
bent, tetrahedral
b.
linear, square planar
c.
linear, see-saw
Correct Answer
d.
bent, see-saw
Step-by-Step AI Explanation
Verified Method
For $\text{XeF}_2$, Xe has 8 valence electrons, forms 2 single bonds with fluorine, leaving 3 lone pairs. The steric number is $2 + 3 = 5$ (trigonal bipyramidal electron geometry with 3 equatorial lone pairs), giving a **linear** molecular geometry.
For $\text{XeO}_2\text{F}_2$, Xe has 8 valence electrons. It forms 2 double bonds to O atoms and 2 single bonds to F atoms, leaving 1 lone pair ($8 - 4 - 2 = 2$ electrons = 1 lone pair). The steric number is $4 \text{ bonded atoms} + 1 \text{ lone pair} = 5$ (trigonal bipyramidal electron geometry with 1 equatorial lone pair), giving a **see-saw** molecular geometry.
Q30mcq
Spin motion of which of the following gives magnetic moment
(A) electron, (B) proton (C) neutron
Correct answer is
a.
A and B
b.
B and C
c.
A and C
d.
A, B and C
Correct Answer
Step-by-Step AI Explanation
Verified Method
All three subatomic particles possess an intrinsic spin angular momentum ($S = 1/2$) and a non-zero magnetic moment:
- **Electron:** As a charged fundamental particle with spin, it has a significant magnetic moment (approximately $-1\ \mu_B$).
- **Proton:** As a charged composite baryon consisting of quarks with spin, it has a magnetic moment of approximately $+2.79\ \mu_N$.
- **Neutron:** Although electrically neutral overall, the neutron is composed of charged quarks (one up quark and two down quarks). The spin motion of these constituent charged quarks gives the neutron an intrinsic magnetic dipole moment of approximately $-1.91\ \mu_N$.
Thus, spin motion gives a magnetic moment to all three: electron, proton, and neutron (A, B, and C).
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Among the following, species expected to show fluxional behaviour are
(A) $[\text{NiCl}_4]^{2-}$ (tetrahedral)
(B) $\text{IF}_7$ (pentagonal bipyramidal)
(C) $[\text{CoF}_6]^{3-}$ (octahedral)
(D) $\text{Fe(CO)}_5$ (trigonal bipyramidal)
a.
B and C
b.
B and D
c.
C and D
d.
A and D
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The concentration of a reactant R varies with time for two different reactions as shown in the following plots :
The orders of these two reactions I and II, respectively are
a.
zero and one
b.
one and zero
c.
zero and two
d.
two and zero
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For the following reaction,
$$\text{A} \xrightleftharpoons[k_{-1}]{k_1} 2\text{B} ; \quad \text{B} \xrightarrow{k_2} \text{C}$$
$\frac{\mathrm{d}[\text{B}]}{\mathrm{dt}}$ is given by
The value of $\Delta\text{U} - \Delta\text{H}$ for the reaction $\text{Fe}_2\text{O}_3(\text{s}) + 3\text{C}(\text{s}) \longrightarrow 2\text{Fe}(\text{s}) + 3\text{CO}(\text{g})$ is
a.
-3RT
b.
+3RT
c.
+RT
d.
-RT
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The correct expression for the product $((\overline{\text{M}}_{\text{n}}) \cdot (\overline{\text{M}}_{\text{w}}))$ [ $\overline{\text{M}}_{\text{n}}$ and $\overline{\text{M}}_{\text{w}}$ are the number-average and weight average molar masses, respectively, of a polymer] is
a.
$\text{N}^{-1}\sum_i \text{N}_i\text{M}_i$
b.
$\text{N}^{-1}\sum_i \text{N}_i\text{M}_i^2$
c.
$\text{N}/\sum_i \text{N}_i\text{M}_i$
d.
$\text{N}/\sum_i \text{N}_i\text{M}_i^2$
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$\text{sp}$ hybrid orbitals are of the form $\text{C}_1 2\text{s} + \text{C}_2 2\text{p}_{\text{z}}$ ($2\text{s}$ and $2\text{p}_{\text{z}}$ are normalised individually). The coefficients of the normalized form fo the above sp hybrid orbitals are
The formation constant for the complexation of $\text{M}^+$ ($\text{M} = \text{Li}, \text{Na}, \text{K}$ and $\text{Cs}$) with cryptand, C222 follows the order
The correct match for the compounds in column A with the description in column B is
**Column - A**
(P)
(Q)
(R)
**Column - B**
(X) Oil of Wintergreen
(Y) Aspirin
(Z) Ibuprofen
a.
P-Y, Q-Z, R-X
b.
P-Z, Q-X, R-Y
c.
P-Z, Q-Y, R-X
d.
P-X, Q-Z, R-Y
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The resonance Raman stretching frequency ($v_{\text{O}-\text{O}}$, in $\text{cm}^{-1}$) of $\text{O}_2$ is 1580. The $v_{\text{O}-\text{O}}$ for $\text{O}_2$ in bound oxy-hemoglobin is close to
a.
1600
b.
1900
c.
800
d.
1100
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Match the metalloprotein in Column-A with its biological function and metal centre in Column-B.
**Column-A**
(A) hemoglobin
(B) cytochrome b
(C) vitamin $\text{B}_{12}$
(D) hemocyanin
**Column-B**
(I) electron carrier and iron
(II) electron carrier and copper
(III) $\text{O}_2$ transport and copper
(IV) Group transfer reactions and cobalt
(V) $\text{O}_2$ storage and cobalt
(VI) $\text{O}_2$ transport and iron
The correct match is
a.
A-VI, B-I, C-IV and D-III
b.
A-V, B-I, C-IV and D-III
c.
A-VI, B-V, C-I and D-II
d.
A-V, B-VI, C-II and D-IV
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Pick the correct statements about Atomic Absorption Spectrometry (AAS) from the following
(A) Hg lamp is not a suitable source for AAS
(B) Graphite furnace is the best atomizer for AAS
(C) Non-metals cannot be determined with AAS
(d) AAS is better than ICP-AES for simultaneous determination of metal ions.
Correct answer is
a.
A, B and C
b.
B, C and D
c.
C, D and A
d.
D, A and B
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$[(\eta^3-\text{C}_3\text{H}_5)\text{Mn}(\text{CO})_4]$ shows fluxional behavior. The $^1\text{H}$ NMR spectrum of this compound when it is in the non-fluxional state shows
a.
one signal
b.
two signals in the intensity ratio of $4 : 1$
c.
three signals in the intensity ratio of $2 : 2 : 1$
d.
five signals of equal intensity.
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Consider the following reaction :
$$\text{N}_3\text{P}_3\text{Cl}_6 + 6\text{HNMe}_2 \rightarrow \underset{\text{[A]}}{\text{N}_3\text{P}_3\text{Cl}_3(\text{NMe}_2)_3} + 3\text{Me}_2\text{NH}\cdot\text{HCl}$$
The number of possible isomers for [A] is
a.
4
b.
3
c.
2
d.
5
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Among the following complexes
(A) $[\text{Co}(\text{ox})_3]^{3-}$
(B) $\text{trans}-[\text{CoCl}_2(\text{en})_2]^+$
(C) $[\text{Cr}(\text{EDTA})]^-$ the chiral one(s) is/are
a.
A and B
b.
C and B
c.
C only
d.
A and C
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Mössbauer spectrum of a metal complex gives information about
(A) oxidation state and spin state of metal
(B) types of ligands coordinated to metal
(C) nuclear spin state of metal
(D) geometrey of metal
Correct answer is
a.
A and C
b.
B and C
c.
A, B and D
d.
B and D
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For uranocene, the correct statement(s) is/are
(A) oxidation state of uranium is '$+4$'
(B) it has cyclooctatetraenide ligands
(C) it is bent sandwich compound
(D) it has '$-2$' charge
Correct answer is
a.
A and B
b.
B and C
c.
A and D
d.
B only
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The final products of the reaction of carbonyl metalates $\left[\mathrm{V}(\mathrm{CO})_6\right]^-$ and $\left[\mathrm{Co}(\mathrm{CO})_4\right]^-$ with $\mathrm{H}_3\mathrm{PO}_4$, respectaively, are
a.
$\mathrm{V}(\mathrm{CO})_6$ and $\mathrm{HCo}(\mathrm{CO})_4$
b.
$\mathrm{HV}(\mathrm{CO})_6$ and $\mathrm{Co}_2(\mathrm{CO})_8$
c.
$\left[\mathrm{H}_2\mathrm{V}(\mathrm{CO})_6\right]^+$ and $\mathrm{HCo}(\mathrm{CO})_4$
d.
$\mathrm{V}(\mathrm{CO})_6$ and $\mathrm{Co}_2(\mathrm{CO})_8$
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The correct statement about the substitution reaction of $\left[\mathrm{Co}(\mathrm{CN})_5 \mathrm{Cl}\right]^{3-}$ with $\mathrm{OH}^-$ to give $\left[\mathrm{Co}(\mathrm{CN})_5(\mathrm{OH})\right]^{3-}$ is,
a.
it obeys first order kinetics
b.
its rate is proportional to the concentration of both the the reactants
c.
it follows the $\mathrm{S}_\mathrm{N}^1\mathrm{CB}$ mechanism
d.
its rate is dependent only on the concentration of $[\mathrm{OH}]^-$
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Aqueous $\mathrm{Cr}^{2+}$ effects one electron reduction of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}\right]^{2+}$ giving compound Y. Compound Y undergoes rapid hydrolysis. Y is ,
The reaction of $\mathrm{BCl}_3$ with $\mathrm{NH}_4 \mathrm{Cl}$ gives product A which upon reduction by $\mathrm{NaBH}_4$ gives product B. Product B upon reacting with $\mathrm{HCl}$ affords compound C, which is
Choose the correct statements about Tanabe-Sugano diagrams
(A) $\mathrm{E/B}$ is plotted against $\Delta_0 / \mathrm{B}$
(B) The zero energy is taken as that of the lowest term
(C) Terms of the same symmetry cross each other
(D) Two terms of the same symmetry upon increases of ligand field strength bend apart from each other.
Correct answer is
a.
A and B
b.
A and C
c.
A, B and D
d.
A, B, C and D
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Which of the following statements are TRUE for the lanthanides?
(A) the observed magnetic moment of $\mathrm{Eu}^{3+}$ at room temperature is higher than that calculated from spin-orbit coupling
(B) Lanthanide oxides are predominantly acidic in nature
(C) The stability of $\mathrm{Sm(II)}$ is due to its half-filled sub-shell.
(D) Lanthanide (III) ions can be separated by ion exchange chromatography
Correct answer is
a.
A and D
b.
A and B
c.
A and C
d.
B and C
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Reaction of $[\text{Mn}_2(\text{CO})_{10}]$ with $\text{I}_2$ results in A without loss of CO. Compound A, on heating ot $120^\circ\text{C}$ loses a CO ligand to give B, which does not have a Mn–Mn bond. Compound B reacts with pyridine to give 2 equivalents of C. Compounds A, B and C from the following respectively, are
a.
II, V anad IV
b.
II, III and IV
c.
V, III and IV
d.
II, V and III
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The approximate positions of $\nu_{\text{CO}}$ bands ($\text{cm}^{-1}$) in the solid-state infrared spectrum and the Fe-Fe bond order in $[\text{Fe}(\eta^5-\text{C}_5\text{H}_5)(\mu-\text{CO})(\text{CO})]_2$ (non-centrosymmetric) respectively, are
a.
(2020, 1980, 1800) and one
b.
(2020, 1980, 1800) and two
c.
(2020, 1980) and one
d.
(2143) and one
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Three electronic transitions at 14900, 22700 and $34400\text{ cm}^{-1}$ are observed in the absorption spectrum of $[\text{CrF}_6]^{3-}$. The $\Delta_0$ value (in $\text{cm}^{-1}$) and the corresponding transition are
a.
7800 and ${^4\text{A}_{2\text{g}}} \rightarrow {^4\text{T}_{2\text{g}}}$
b.
14900 and ${^4\text{A}_{2\text{g}}} \rightarrow {^4\text{T}_{2\text{g}}}$
c.
14900 and ${^4\text{T}_{2\text{g}}} \rightarrow {^4\text{T}_{1\text{g}}}\text{ (F)}$
d.
7800 and ${^4\text{T}_{2\text{g}}} \rightarrow {^4\text{T}_{1\text{g}}}\text{ (F)}$
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According to the transition state theory, one of the vibrations in the activated complex is a loose vibration. The partition function for this loose vibration is equal to ($k_B$ is the Boltzmann's constant and $h$ is the Planck's constant)
a.
$\frac{k_B T}{h}$
b.
$\frac{h\nu}{k_B T}$
c.
$k_B T$
d.
$\frac{k_B T}{h\nu}$
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For a simple cubic crystal, X-ray diffraction shows intense reflections for angles $\theta_1$ and $\theta_2$ which are assigned to $\left[1\ 0\ 1\right]$ and $\left[1\ 1\ 1\right]$ planes, respectively. The ratio $\frac{\sin\theta_1}{\sin\theta_2}$ is
a.
$1.5$
b.
$1.22$
c.
$0.82$
d.
$0.67$
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A certain 2-level system has stationary state energies $E_1$ and $E_2$ ($E_1 < E_2$) with normalized wave functions $\varphi_1$ and $\varphi_2$ respectively. In the presence of a perturbation V, the second-order correction to the energy for the first state ($\varphi_1$) will be
The $^{1}\text{H}$ NMR frequency at $1.0\text{ T}$ is $42.4\text{ MHz}$. If the gyromagnetic ratios of $^{1}\text{H}$ and $^{13}\text{C}$ are $27\times 10^7$ and $6.75\times 10^7\text{ T}^{-1}\text{S}^{-1}$, respectively, what will be the $^{13}\text{C}$ frequency at $1.0\text{ T}$?
a.
$10.6\text{ MHz}$
b.
$169.9\text{ MHz}$
c.
$42.6\text{ MHz}$
d.
$21.3\text{ MHz}$
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$10\text{ mL}$ aliquots of a mixture of $\text{HCl}$ and $\text{HNO}_3$ are titrated conductometrically using a $0.1\text{M } \text{NaOH}$ and a $0.1\text{M } \text{AgNO}_3$ separately. The titre volumes are $\text{V}_1$ and $\text{V}_2\text{ mL}$, respectively. The concentration of $\text{HNO}_3$ in the mixture is obtained from the combination.
a.
$V_1 - V_2$
b.
$2V_1 - V_2$
c.
$V_2 - V_1$
d.
$2V_2 - V_1$
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Given that $E^0\left(\text{Cl}_2 / \text{Cl}^-\right) = 1.35\text{ V}$ and $K_{sp}\left(\text{AgCl}\right) = 10^{-10}$ at $25^\circ\text{C}$, $\text{E}^0$ corresponding to the electrode reaction
$$\frac{1}{2}\text{Cl}_2(g) + \text{Ag}^+(soln.) + e^- \rightarrow \text{AgCl}(s)$$
is $\left[\frac{2.303RT}{F} = 0.06\text{V}\right]$
a.
$0.75\text{V}$
b.
$1.05\text{V}$
c.
$1.65\text{V}$
d.
$1.95\text{V}$
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The spectroscopic technique that can distinguish unambiguously between trans-1, 2-dichloroethylene and cis-1, 2-dichloroethylene without any numerical calculation is
a.
microwave spectroscopy
b.
UV-visible spectroscopy
c.
X-ray photoelectron spectroscopy
d.
$\gamma$-ray spectroscopy
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$v_{\max}$ and $K_m$ for an enzyme catalyzed reaction are $2.0\times 10^{-3}\text{ Ms}^{-1}$ and $1.0\times 10^{-6}\text{M}$, respectively. The rate of the reaction when the substrate concentration is $1.0\times 10^{-6}\text{M}$ is
a.
$3.0\times 10^{-3}\text{ s}^{-1}$
b.
$1.0\times 10^{-3}\text{ s}^{-1}$
c.
$2.0\times 10^{-3}\text{ s}^{-1}$
d.
$0.5\text{ s}^{-1}$
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The first order rate constant for a unimolecular gas phase reaction $A \rightarrow \text{products}$ that follows Lindemann mechanism is $2.0\text{ s}^{-1}$ at $p_A = 1\text{ atm}$ and $4.0\text{ s}^{-1}$ at $p_A = 2\text{ atm}$. The rate constant for the activation step is
a.
$1.0\text{ atm}^{-1}\text{s}^{-1}$
b.
$2.0\text{ atm}^{-1}\text{s}^{-1}$
c.
$4.0\text{ atm}^{-1}\text{s}^{-1}$
d.
$8.0\text{ atm}^{-1}\text{s}^{-1}$
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The vibrational frequency of a homo-nuclear diatomic molecule is $\nu$. The temperature at which the population of the first excited state will be half that of the ground state is given by
a.
$h\nu \cdot \ln 2 / k_B$
b.
$h\nu / (\ln 2 \cdot k_B)$
c.
$\ln 2 / (h\nu \cdot k_B)$
d.
$h\nu \cdot \log 2 / k_B$
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The irreducible representations of $C_{2h}$ are $\text{A}_g$, $\text{B}_g$, $\text{A}_u$ and $\text{B}_u$. The Raman active modes of trans-1, 3-butadiene belong to the irreducible representations
a.
$\text{A}_g$ and $\text{B}_g$
b.
$\text{A}_g$ and $\text{A}_u$
c.
$\text{A}_u$ and $\text{B}_g$
d.
$\text{B}_g$ and $\text{B}_u$
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A reversible expansion of $1.0\text{ mol}$ of an ideal gas is carried out from $1.0\text{ L}$ to $4.0\text{ L}$ under isothermal condition at $300\text{K}$. $\Delta G$ for this process is
a.
$300R \cdot \ln 2$
b.
$600R \cdot \ln 2$
c.
$-600R \cdot \ln 2$
d.
$-300R \cdot \ln 2$
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The temperature-dependence of the vapour pressurse of solid A can be represented by $\log p = 10.0 - \frac{1800}{T}$, and that of liquid A by $\log p = 8.0 - \frac{1400}{T}$. The temperature of the triple point of $A$ is
a.
$200\text{ K}$
b.
$300\text{ K}$
c.
$400\text{ K}$
d.
$500\text{ K}$
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The radial part of a hydrogenic wave function is given as $r(\alpha - r)e^{-\beta r}$ ($\alpha, \beta$ are constants). This function is then indentifiable as
a.
$2\text{s}$
b.
$3\text{p}$
c.
$4\text{d}$
d.
$5\text{f}$
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A normalised state $\phi$ is constructed as a linear combination of the ground state ($\psi_0$) and the first excited state ($\psi_1$) of some harmonic oscillator with energies $1/2$ and $3/2$ units, respectively. If the average energy of the state $\phi$ is $7/6$, the probability of finding $\psi_0$ in $\phi$ will be
a.
$1/2$
b.
$1/3$
c.
$1/4$
d.
$1/5$
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