Hydrocarbons - Class 11 Part 2

An acid-catalyzed thermodynamic equilibration is established between the \textit{cis} and \textit{trans} diastereomers of 2-methoxy-4-\textit{tert}-butyltetrahydropyran in anhydrous \ce{CCl4} at 298 K. Which of the following correctly identifies the major diastereomer present at equilibrium and the primary electronic interaction responsible for its stability?

Consider the stereoisomer (2S, 3R)-2-bromo-3-phenylbutane. When treated with \ce{NaOEt} in \ce{EtOH} at 350 K, it undergoes a stereospecific E2 elimination. Which of the following correctly identifies the major product and the stereoelectronic rationale governing the transition state?

Consider the synthesis of three biphenyl derivatives via the Ullmann coupling reaction (heating the respective aryl halide with Cu powder):

Reaction 1: \ce{1-bromo-2,4-dinitrobenzene ->[Cu, \Delta]} Compound \textbf{X} Reaction 2: \ce{2-bromo-1-methyl-3-nitrobenzene ->[Cu, \Delta]} Compound \textbf{Y} Reaction 3: \ce{2-bromo-1,3-dimethylbenzene ->[Cu, \Delta]} Compound \textbf{Z}

Which of the compounds \textbf{X}, \textbf{Y}, and \textbf{Z} can be resolved into stable enantiomers at 298 K?

The conformational landscapes of 1,2-difluoroethane (Molecule A) and $N$-methylacetamide (Molecule B) exhibit significant deviations from simple steric models. Consider the following statements regarding their structural and thermodynamic properties at 298 K:

I. The global energy minimum of A corresponds to a F-C-C-F dihedral angle $\theta \approx 60^\circ$, primarily stabilized by two antiperiplanar $\sigma_{C-H} \rightarrow \sigma^*_{C-F}$ hyperconjugative interactions. II. The global energy minimum of B corresponds to a C-C-N-C dihedral angle $\omega \approx 180^\circ$, dictated by $n_N \rightarrow \pi^*_{C=O}$ delocalization and minimization of steric strain. III. In highly polar solvents, the anti conformer of A becomes the global energy minimum because its zero dipole moment minimizes unfavorable solvent interactions. IV. The activation energy for rotation around the C-N bond in B is approximately $85 \text{ kJ/mol}$, which is significantly higher than the C-C rotational barrier in A.

Which of the following combinations of statements is correct?

Consider the gas-phase photochemical chlorination of 2,2,3-trimethylbutane at $298\text{ K}$ using 1 equivalent of $\ce{Cl2}$. The major monochlorinated product $\mathbf{P}$ is isolated. $\mathbf{P}$ is then treated with aqueous $\ce{AgNO3}$ at elevated temperature to yield the major organic product $\mathbf{Q}$. Identify the IUPAC name of $\mathbf{Q}$.

Compound \textbf{P}, (-)-menthyl 2-phenylethanoate, is subjected to free-radical monobromination using 1 equivalent of \ce{NBS} in \ce{CCl4 (l)} under UV irradiation ($h\nu$) at 298 K. The reaction yields a mixture of monobrominated products at the benzylic position. What is the stereochemical relationship between these newly formed products, and what is their expected relative molar ratio?

Consider the following reaction sequence starting from 1,1,1-trifluoro-2-methylpropane (Compound \textbf{X}): $\textbf{X} \xrightarrow{Cl_2,\ h\nu,\ 298\text{ K}} \textbf{Y} \text{ (Major monochlorinated product)}$ $\textbf{Y} \xrightarrow{NaCN,\ \text{DMF}} \textbf{Z}$ $\textbf{Z} \xrightarrow{H_3O^+,\ \Delta} \textbf{W}$ Identify the IUPAC name of the major product \textbf{W}.

A $140 \text{ mmol}$ sample of propane ($\ce{CH3-CH2-CH3}$) undergoes photochemical monochlorination at $298 \text{ K}$. The relative reactivity of $1^{\circ}$ and $2^{\circ}$ C-H bonds towards chlorine radicals is $1 : 4$. The major monochlorinated product (A) is isolated based strictly on its theoretical kinetic yield. Compound (A) is then treated with $\ce{Mg}$ in dry ether, followed by bubbling $\ce{CO2(g)}$ and subsequent acidic workup ($\ce{H3O+}$) to yield compound (B). The entire quantity of (B) produced is dissolved in $1.0 \text{ kg}$ of a non-polar solvent (dielectric constant $\epsilon \approx 2.2$) having a cryoscopic constant $K_f = 5.0 \text{ K kg mol}^{-1}$. Assuming (B) undergoes complete dimerization in this solvent due to intermolecular hydrogen bonding, what is the freezing point depression ($\Delta T_f$) of the resulting solution?

Consider the following reaction sequence starting from hept-6-enoic acid (\textbf{X}):

1. \textbf{X} $\xrightarrow{\text{i) } \ce{SOCl2} \text{, ii) sodium salt of N-hydroxypyridine-2-thione}}$ \textbf{Y}
2. \textbf{Y} $\xrightarrow{h\nu,\ \ce{[Co(NH3)5(NO2)]Cl2} \text{ (0.5 M)}}$ \textbf{Z} (Major organic product)
3. \textbf{Z} $\xrightarrow{\ce{H3O+},\ \Delta}$ \textbf{W} (Major organic product)

Given: $k_{\text{cyclization}}$ of the intermediate radical $\approx 1 \times 10^5 \text{ s}^{-1}$; $k_{\text{trapping}}$ by the Co(III) complex $\approx 1 \times 10^8 \text{ M}^{-1}\text{s}^{-1}$.

Identify \textbf{W} and the linkage of the ambidentate ligand in \textbf{Z}.

An organic compound \textbf{X} (\ce{C7H15Br}), specifically 2-bromo-3,4-dimethylpentane, is treated with potassium \textit{tert}-butoxide (\ce{t-BuOK}) in \textit{tert}-butanol (\ce{t-BuOH}) at 350 K to yield a major hydrocarbon product \textbf{Y}. Compound \textbf{Y} is then subjected to hydroboration-oxidation using \ce{B2H6} in THF followed by alkaline \ce{H2O2}, producing compound \textbf{Z}. Finally, \textbf{Z} is treated with Jones reagent (\ce{CrO3} / \ce{H2SO4} / \ce{H2O}) to give the final major product \textbf{W}. Identify the correct IUPAC name of \textbf{W}.

Consider the electrophilic addition of $\ce{HCl}$ (1 equivalent) to optically pure (1R, 4S)-1-methylbicyclo[2.2.1]hept-2-ene in an inert solvent ($\ce{CCl4}$) at 298 K. The reaction proceeds via a carbocation intermediate to yield a major optically active product $\mathbf{P}$. Assuming thermodynamic and kinetic control align due to the stability of the intermediate, identify the correct IUPAC name and stereochemistry of product $\mathbf{P}$.

A straight-chain alkene $\ce{A}$ ($\ce{C8H16}$) undergoes syn-hydroxylation with cold, dilute alkaline $\ce{KMnO4}$ (Baeyer's reagent) to yield a single stereoisomer $\ce{B}$ which is a meso-diol. Let $x$ be the number of moles of $\ce{KMnO4}$ required to completely oxidize 1 mole of $\ce{A}$ to $\ce{B}$ under cold, dilute alkaline conditions. Let $y$ be the number of moles of $\ce{KMnO4}$ required to completely cleave 1 mole of $\ce{A}$ into carboxylic acids under hot, acidic conditions. Identify the correct values of $x$ and $y$, and the IUPAC name of $\ce{A}$.

Consider the thermal gas-phase bromination of $(S)$-1-chloro-2-methylbutane ($\ce{RH}$) at $400\text{ K}$ to yield 2-bromo-1-chloro-2-methylbutane ($\ce{RBr}$). The reaction proceeds via a radical chain mechanism with the following elementary steps:

Initiation: $\ce{Br2 ->[k_i] 2Br^\bullet}$ (Rate $= k_i[\ce{Br2}]$) Propagation 1: $\ce{RH + Br^\bullet ->[k_1] R^\bullet + HBr}$ Propagation 2: $\ce{R^\bullet + Br2 ->[k_2] RBr + Br^\bullet}$ Termination: $\ce{2Br^\bullet ->[k_t] Br2}$

Assuming the Steady State Approximation (SSA) applies to all radical intermediates, let $k_{inv}$ represent the first-order rate constant for the conformational inversion of the intermediate carbon radical $\ce{R^\bullet}$. Which of the following correctly expresses the overall rate of formation of $\ce{RBr}$ and the kinetic condition required to obtain a predominantly racemic product mixture?

The electrophilic addition of \ce{Br2} to 4-\textit{tert}-butylcyclohexene in \ce{CCl4} at $300\text{ K}$ yields two possible \textit{trans}-dibromide stereoisomers: the diaxial product (A) and the diequatorial product (B). The thermodynamic parameters for the respective reaction pathways are given below:

\textbf{Pathway A (Diaxial):} $\Delta H^\ddagger = 35.0\text{ kJ/mol}$, $\Delta S^\ddagger = -20.0\text{ J K}^{-1}\text{mol}^{-1}$ $\Delta H^\circ = -110.0\text{ kJ/mol}$, $\Delta S^\circ = -100.0\text{ J K}^{-1}\text{mol}^{-1}$

\textbf{Pathway B (Diequatorial):} $\Delta H^\ddagger = 55.0\text{ kJ/mol}$, $\Delta S^\ddagger = -15.0\text{ J K}^{-1}\text{mol}^{-1}$ $\Delta H^\circ = -130.0\text{ kJ/mol}$, $\Delta S^\circ = -100.0\text{ J K}^{-1}\text{mol}^{-1}$

Determine the standard Gibbs free energy of reaction ($\Delta G^\circ$) for the formation of the major product at $300\text{ K}$.

Consider the stoichiometric halogenation of (Z)-2-butene using the neutral octahedral complex $[PtCl_4(bipy)]$ (where bipy = 2,2'-bipyridine) in $\ce{CH_2Cl_2}$ at 298 K. Due to the strong d-orbital contraction of the high-valent metal center, the electrophilicity of the coordinated chlorides is significantly enhanced. The reaction proceeds via alkene coordination followed by a locked, concerted cyclic transition state involving the transfer of two mutually \textit{cis} chloride ligands to the alkene. Identify the stereochemical nature of the major organic product and the final oxidation state of the transition metal.

The monoterpene (+)-limonene (\ce{1-methyl-4-(prop-1-en-2-yl)cyclohex-1-ene}) is subjected to reductive ozonolysis (\ce{O3} followed by \ce{Zn/H2O}) to yield an acyclic tricarbonyl compound \textbf{X}. Compound \textbf{X} is then treated with a catalytic amount of \ce{KOH} in ethanol and heated under reflux for 24 hours to yield \textbf{Y} as the major product. Identify the IUPAC name of \textbf{Y}.

An equimolar mixture of (2E)-1-chloro-4-fluorobut-2-ene and (3E)-5-methoxypent-3-enenitrile is subjected to exhaustive ozonolysis followed by an oxidative workup using $\ce{H2O2}$. The reaction yields four distinct substituted acetic acid derivatives: $\textbf{P}$ (chloro-substituted), $\textbf{Q}$ (fluoro-substituted), $\textbf{R}$ (methoxy-substituted), and $\textbf{S}$ (cyano-substituted). Which of the following represents the correct decreasing order of their acid dissociation constants ($K_a$) in aqueous solution at 298 K?

Consider the following reaction sequence starting from 1-methylcyclohex-1-ene (\textbf{A}):

\textbf{A} $\xrightarrow[\text{2. } \ce{Me2S}]{\text{1. } \ce{O3}, \ce{CH2Cl2}, 196\text{ K}}$ \textbf{B}

\textbf{B} $\xrightarrow[\text{2. } \ce{H3O^+}]{\text{1. } \ce{Mg(Hg)}, \text{THF}}$ \textbf{C}

\textbf{C} $\xrightarrow{\ce{HIO4}, \text{aq. THF}, 298\text{ K}}$ \textbf{D}

Identify the major product \textbf{D}.

An organic compound, 1,2-dimethylcyclohex-1-ene, is subjected to ozonolysis by passing a stream of $O_3$ gas through its solution in anhydrous methanol ($CH_3OH$) at $-78^\circ C$. The reaction mixture is then carefully warmed to room temperature without the addition of any reductive or oxidative workup reagents. Which of the following is the major organic product isolated?

An unknown alkene $\textbf{X}$ undergoes oxidative ozonolysis ($\ce{O3}$ at $298\text{ K}$ followed by $\ce{H2O2}$) to yield a single organic product $\textbf{Y}$. When $2.44\text{ g}$ of $\textbf{Y}$ is dissolved in $50\text{ g}$ of benzene (a non-polar solvent), the freezing point of the solution is depressed by $1.024\text{ K}$. Assuming $\textbf{Y}$ undergoes complete intermolecular hydrogen bonding to form dimers in benzene ($K_f = 5.12\text{ K kg mol}^{-1}$), identify the structure of alkene $\textbf{X}$.

Acetylene ($\ce{HC \equiv CH}$) exhibits terminal acidity due to its sp-hybridized carbon atoms. It reacts with Tollens' reagent to form a highly insoluble silver acetylide ($\ce{Ag2C2}$) precipitate. To utilize $\ce{Ag2C2}$ as a controlled source of the $\ce{C2^{2-}}$ nucleophile, excess solid $\ce{Ag2C2(s)}$ is added to $500 \text{ mL}$ of pure water, and the system is allowed to reach equilibrium. Subsequently, $500 \text{ mL}$ of a $0.04 \text{ M}$ $\ce{AgNO3(aq)}$ solution is added to this suspension at $298 \text{ K}$. Given that the solubility product ($K_{sp}$) of $\ce{Ag2C2}$ is $4.0 \times 10^{-24}$ at $298 \text{ K}$, calculate the new equilibrium concentration of the acetylide ion ($\ce{C2^{2-}}$) in the final mixture. (Assume the volume is strictly additive and no hydrolysis of $\ce{C2^{2-}}$ occurs).

An organic compound $\textbf{X}$ (1,2-dibromopropane, $1.0 \text{ mol}$) is treated with exactly $2.0 \text{ mol}$ of sodium amide ($\ce{NaNH2}$) in liquid ammonia at $195 \text{ K}$. The reaction is allowed to proceed until no further chemical change occurs, after which the reaction mixture is quenched with excess water. Given that the rate of the first dehydrohalogenation step is significantly greater than the second ($k_1 \gg k_2$), and the acid-base reaction is instantaneous, determine the final organic product composition.

An organic compound $\textbf{P}$ ($C_4H_6$) exhibits terminal acidity. Two separate experiments are performed on 1 mole of $\textbf{P}$:

\textbf{Experiment 1:} $\textbf{P}$ is subjected to vigorous oxidation with hot acidic $KMnO_4$, yielding a carboxylic acid $\textbf{Q}$ and a gas. The reaction consumes $x$ moles of $KMnO_4$.

\textbf{Experiment 2:} $\textbf{P}$ is treated with $HgSO_4 / H_2SO_4$ to undergo complete hydration, forming a stable tautomer $\textbf{R}$. Compound $\textbf{R}$ is then subjected to vigorous oxidation with hot acidic $KMnO_4$, yielding exclusively the major product $\textbf{S}$ as dictated by Popoff's rule. This oxidation step consumes $y$ moles of $KMnO_4$.

Assuming complete conversion in all steps, what are the values of $x$ and $y$, and the identity of $\textbf{S}$?

Compound $\mathbf{X}$, \ce{1-(but-2-yn-1-yl)-4-isopropylbenzene}, is treated with a large excess of sodium metal in liquid ammonia containing ethanol at $195\text{ K}$ until complete reduction of all reducible functional groups occurs. The reaction yields $\mathbf{Y}$ as the major organic product. Which of the following represents the correct IUPAC name and stereochemistry of $\mathbf{Y}$?

Consider the following multistep synthesis starting from Compound \textbf{X} (Methyl 7-((tetrahydro-2H-pyran-2-yl)oxy)hept-4-ynoate):

$\text{Compound \textbf{X}} \xrightarrow[2. \text{ Cat. } p\text{-TsOH, MeOH, } 25^\circ\text{C}]{1. \text{ Na, NH}_3(l), -78^\circ\text{C}} \textbf{Y}$

$\textbf{Y} \xrightarrow{PBr_3, \text{ pyridine, } 0^\circ\text{C}} \textbf{Z}$

$\textbf{Z} \xrightarrow[2. \text{ Excess } D_2O]{1. \text{ Rieke Mg, THF, } -78^\circ\text{C, high dilution}} \textbf{Major Product (P)}$

Identify the major product \textbf{P}.

An organic compound $\mathbf{X}$, (4-nitrophenyl)(phenyl)methane, is subjected to Friedel-Crafts alkylation using 1-chloro-2,2-dimethylpropane in the presence of a stoichiometric excess of anhydrous $\ce{AlCl3}$ at $298\text{ K}$. Assuming thermodynamic and kinetic factors strongly favor a single major product $\mathbf{Y}$, identify the correct IUPAC name of $\mathbf{Y}$.

An organic compound \textbf{X} ($\ce{C_{14}H_{22}}$) is synthesized by the reaction of benzene with an excess of 2-chloro-2-methylpropane in the presence of anhydrous $\ce{AlCl3}$ at 298 K. Compound \textbf{X} is subsequently subjected to Friedel-Crafts acylation using 1 equivalent of acetyl chloride ($\ce{CH3COCl}$) and anhydrous $\ce{AlCl3}$ in $\ce{CH2Cl2}$ at 298 K, followed by aqueous workup, to yield compound \textbf{Y} as the major organic product. Which of the following represents the correct IUPAC name of compound \textbf{Y}?

Consider the following reaction sequence: $\ce{1-Bromo-4-phenylbutane} \xrightarrow[\text{dry ether}]{\ce{Mg}} \textbf{P} \xrightarrow[\text{2. } \ce{H3O+}]{\text{1. } \ce{AlCl3} \text{ (anhydrous, 1 eq)}} \textbf{Q}$ Which of the following represents the major organic product \textbf{Q}?

Compound \textbf{P} (1-chloro-4-nitrobenzene) is subjected to the following sequence of reactions: \begin{enumerate} \item \ce{CH3Cl} (1 equiv.), Anhydrous \ce{AlCl3}, $\Delta$ $\rightarrow$ \textbf{Q} \item \ce{CH3ONa} (1 equiv.), \ce{CH3OH}, $\Delta$ $\rightarrow$ \textbf{R} \item \ce{Sn / HCl}, $\Delta$, followed by neutralization with \ce{NaOH(aq)} $\rightarrow$ \textbf{S} \item \ce{NaNO2 / HCl}, $273-278\text{ K}$, followed by \ce{CuCN / KCN}, $\Delta$ $\rightarrow$ \textbf{T} \end{enumerate} Identify the major organic product \textbf{T}.

In the Friedel-Crafts alkylation of benzene (used as solvent in large excess) with 1-chloropropane and anhydrous \ce{AlCl3} at $300\text{ K}$, the initial Lewis acid-base complex undergoes two competing pseudo-first-order processes:

\textbf{Path A:} Direct electrophilic aromatic substitution to form n-propylbenzene, with an activation energy $E_{a,\text{direct}}$. \textbf{Path B:} A 1,2-hydride shift to form a secondary carbocation complex, which rapidly reacts with benzene to form isopropylbenzene (Product $P$). The activation energy for the hydride shift is $E_{a,\text{shift}}$.

Given $E_{a,\text{direct}} - E_{a,\text{shift}} = 11.5\text{ kJ mol}^{-1}$ and assuming identical pre-exponential factors for both pathways, $P$ is isolated as the major product.

$P$ is oxidized with \ce{O2} at $400\text{ K}$ followed by acid hydrolysis to yield an aromatic compound $Q$ and an aliphatic compound $R$. $Q$ is then treated with \ce{CHCl3} and aqueous \ce{NaOH} at $340\text{ K}$, followed by acidification, to yield $S$ as the major product.

Identify the structure of $S$ and the approximate initial molar ratio of $P$ to n-propylbenzene. (Given: $R = 8.314\text{ J K}^{-1}\text{ mol}^{-1}$, $\ln(10) = 2.30$)

Consider the electrophilic mononitration of 4-chloro-1,1'-biphenyl ($\textbf{X}$) using a standard nitrating mixture ($\ce{HNO3}$/$\ce{H2SO4}$) at 298 K to form the major product $\textbf{Y}$. Let $E_{a,A}$ and $E_{a,B}$ represent the activation energies for the formation of the arenium ion intermediate via para-attack on the chlorinated ring (Ring A) and the unsubstituted ring (Ring B), respectively. Which of the following statements correctly identifies $\textbf{Y}$ and accurately describes the kinetic and electronic factors governing its formation?

When 3-(2-chloropropan-2-yl)cycloprop-1-ene is dissolved in a superacidic medium ($\ce{SbCl5}$ in liquid $\ce{SO2}$ at $223\text{ K}$), a highly stable carbocation $\mathbf{X}$ is observed via NMR spectroscopy. Which of the following best describes the structure of $\mathbf{X}$ and the dominant thermodynamic driving force for its formation?

Consider the transition metal complexes $\ce{[Cr(H2O)6]^{2+}}$ (Complex I) and the pseudo-octahedral piano-stool complex $\ce{[W(\eta^5-C5H5)(NH3)3]^+}$ (Complex II). Both contain the metal center in a $d^4$ electronic configuration. Which of the following statements correctly describes the magnetic behavior and structural distortion of these complexes at $298\text{ K}$?

The acidity of 1,3-cyclopentadiene (\ce{C5H6}) is governed by the formation of the aromatic cyclopentadienyl anion (\ce{C5H5^-}). However, its $pK_a$ is highly solvent-dependent due to solvation effects. At 298 K, the $pK_a$ of \ce{C5H6} is 15.0 in water and 18.0 in dimethyl sulfoxide (DMSO).

Given the following standard Gibbs free energies of transfer ($\Delta G^\circ_{tr}$) from water to DMSO at 298 K: $\Delta G^\circ_{tr}(\ce{H^+}) = -19.0 \text{ kJ mol}^{-1}$ $\Delta G^\circ_{tr}(\ce{C5H6}) = -11.1 \text{ kJ mol}^{-1}$

Calculate the standard Gibbs free energy of transfer of the cyclopentadienyl anion, $\Delta G^\circ_{tr}(\ce{C5H5^-})$, from water to DMSO at 298 K. (Take $2.303 RT = 5.7 \text{ kJ mol}^{-1}$)

Aniline is treated with a nitrating mixture (conc. \ce{HNO3} and conc. \ce{H2SO4}) at $288\text{ K}$ to yield three mononitrated products $P$, $Q$, and $R$ in $51\%$, $47\%$, and $2\%$ yields, respectively. Product $P$ is isolated, diazotized at $273\text{ K}$, and treated with \ce{CuCN/KCN} followed by complete acidic hydrolysis to yield compound $W$. Products $Q$ and $R$ are subjected to the identical sequence of reactions to yield compounds $T$ and $V$, respectively. Which of the following represents the correct decreasing order of acidic strength ($K_a$) of the compounds $W$, $T$, and $V$ in aqueous medium?

Consider the following reaction sequence starting from $m$-xylene:

1. $m$-Xylene $\xrightarrow{t-BuCl, \text{ anhydrous } AlCl_3, 298\text{ K}}$ $\mathbf{P}$ (Major product)
2. $\mathbf{P} \xrightarrow[\text{2. } H_3O^+]{\text{1. } KMnO_4, KOH, \Delta}$ $\mathbf{Q}$
3. $\mathbf{Q} \xrightarrow[\text{2. excess } NH_3]{\text{1. } SOCl_2, \Delta}$ $\mathbf{R}$
4. $\mathbf{R} \xrightarrow{Br_2, NaOH, \Delta}$ $\mathbf{S}$

Identify the final product $\mathbf{S}$.

Consider the following reaction sequence starting from 6-methoxy-3,4-dihydronaphthalen-2(1H)-one (\textbf{SM}):

Step 1: \textbf{SM} $\xrightarrow[2. \text{ CH}_3\text{I}]{\text{1. LDA (1.05 eq), THF, } -78^\circ\text{C}}$ \textbf{P} (Major)

Step 2: \textbf{P} $\xrightarrow[2. \text{ H}_2\text{O}]{\text{1. POCl}_3\text{, DMF, } 0^\circ\text{C} \rightarrow 80^\circ\text{C}}$ \textbf{Q} (Major)

Step 3: \textbf{Q} $\xrightarrow{\text{NaOMe, MeOH, } \Delta}$ \textbf{R} (Major)

Identify the correct IUPAC names for the major products \textbf{P} and \textbf{R}.

The reversible electrophilic aromatic substitution (e.g., sulfonation) of a monosubstituted benzene yields ortho ($O$) and para ($P$) products, exhibiting a classic kinetic vs. thermodynamic control dichotomy.

At $T_1 = 300\text{ K}$ (under strict kinetic control), the initial rate of formation of $O$ is $2e^2$ times that of $P$. At $T_2 = 600\text{ K}$ (under strict thermodynamic control), the equilibrium concentration of $P$ is $\frac{e^4}{2}$ times that of $O$.

The pre-exponential factors for the forward reactions satisfy $A_o = 2A_p$. The difference in standard entropy of reaction is $\Delta S^\circ_p - \Delta S^\circ_o = -R \ln 2$ (accounting for the statistical factor of two ortho positions vs. one para position).

Assuming activation energies and standard enthalpies are temperature-independent, what is the difference in the activation energies of the reverse reactions, $(E_{a,-o} - E_{a,-p})$?

An organic compound $\textbf{P}$ is formed by the reaction of ethanol with excess $Cl_2(g)$. $\textbf{P}$ is then reacted with two equivalents of chlorobenzene in the presence of concentrated $H_2SO_4$ to yield a major product $\textbf{Q}$. Subsequent treatment of $\textbf{Q}$ with strong alcoholic $KOH$ under heating yields compound $\textbf{R}$. Which of the following represents the correct IUPAC name of $\textbf{R}$?

Consider the following reaction sequence for 1-methylcyclohex-1-ene (Compound \textbf{A}): $\textbf{A} \xrightarrow[0^\circ\text{C}]{\text{BH}_3 \cdot \text{THF}} \textbf{B} \xrightarrow[\text{diglyme}]{\Delta, 160^\circ\text{C}} \textbf{C} \xrightarrow[\text{H}_2\text{O}]{\text{H}_2\text{O}_2, \text{NaOH}} \textbf{D}$ Identify the major product \textbf{D}.

Consider the reaction of 2-methylbut-1-en-3-yne with one equivalent of disiamylborane (\ce{Sia2BH}) in THF at 273 K, followed by treatment with alkaline hydrogen peroxide (\ce{H2O2} / \ce{NaOH}) at 298 K. What is the major organic product isolated at the end of the reaction?

Consider the following two independent reactions performed on (Z)-3-methylpent-2-ene (Compound X):\Reaction 1: X is treated with $\ce{BH3 \cdot THF}$ followed by alkaline $\ce{H2O2}$ to yield the major product Y.\Reaction 2: X is treated with $\ce{Br2}$ in $\ce{CCl4}$ to yield the major product Z.\Which of the following correctly describes the stereochemistry of the major products Y and Z?

An alkene $X$ ($\ce{C6H12}$) on reductive ozonolysis yields methanal and 2,2-dimethylpropanal. $X$ is subjected to three distinct hydration protocols at 298 K:

I. Catalytic hydration with dilute $\ce{H2SO4}$ yields $P$ as the major product. II. Hydroboration-oxidation ($\ce{B2H6}$ in THF, followed by $\ce{H2O2}$/$\ce{NaOH}$) yields $Q$ as the major product. III. Oxymercuration-demercuration ($\ce{Hg(OAc)2}$/$\ce{H2O}$, followed by $\ce{NaBH4}$/$\ce{NaOH}$) yields $R$ as the major product.

Identify the IUPAC names of $P$, $Q$, and $R$ respectively.

Consider the following two reactions of 1-methylcyclohexene:

Reaction I: $\ce{1-methylcyclohexene + DBr ->[R_2O_2, h\nu] P}$

Reaction II: $\ce{1-methylcyclohexene + BD_3 \cdot THF ->[1. \text{ THF}][2. \ce{H_2O_2}, \ce{NaOH}] Q}$

Let $x$ be the total number of stereoisomers formed in product $P$, and $y$ be the total number of stereoisomers formed in product $Q$. Determine the values of $x$ and $y$.

In an attempt to synthesize 2,5-hexanedione, a student subjects an aqueous solution of potassium 3-oxobutanoate to Kolbe electrolysis using smooth platinum electrodes at 298 K. However, the expected Kolbe dimerization product is obtained in negligible yield. Instead, the reaction is diverted through an alternative anodic process. Which of the following statements correctly identifies the primary reason for the failure of the standard Kolbe radical decarboxylation in this system?

An aqueous solution of potassium 2,2-dimethylpropanoate ($\ce{(CH3)3C-COOK}$) is subjected to Kolbe electrolysis using platinum electrodes at 298 K. Which of the following represents the major hydrocarbon product(s) formed at the anode?

An aqueous solution of potassium butanoate (\ce{CH3CH2CH2COOK}) is subjected to Kolbe's electrolysis using inert platinum electrodes. The electrolysis is carried out until exactly $4.30 \text{ g}$ of the major hydrocarbon product is formed at the anode. Assuming $100\%$ current efficiency and standard temperature and pressure (STP: $273 \text{ K}, 1 \text{ atm}$), what is the total volume and the total mass of all gases evolved at both electrodes?\n\n(Given: Molar volume of an ideal gas at STP = $22.4 \text{ L mol}^{-1}$, Molar masses in $\text{g mol}^{-1}$: $\ce{C}=12, \ce{H}=1, \ce{O}=16$)

A concentrated aqueous solution of potassium $(E)$-pent-3-enoate is subjected to Kolbe's electrolysis using platinum electrodes. Assuming the reaction proceeds exclusively via radical dimerization (with complete stereochemical scrambling of the intermediate radical), a mixture of hydrocarbon products is formed. Let $X$ be the total number of structural isomers of the diene products, and $Y$ be the total number of stereoisomers (accounting for all stereocenters and double bond geometries) among these products. Find the value of $X + Y$.

An electrochemical cell is constructed using Platinum electrodes in an aqueous buffer solution at $298\text{ K}$ and $\text{pH} = 4.0$. The solution contains $2.0\text{ M } \ce{CH3COOK}$ and $10^{-3}\text{ M } \ce{Mn(CH3COO)2}$. The applied voltage is gradually increased from $0\text{ V}$.

Given the following standard reduction potentials at $298\text{ K}$: $E^\circ(\ce{C2H6(g)}, \ce{CO2(g)} / \ce{CH3COO^-}) = +2.15\text{ V}$ $E^\circ(\ce{O2(g)} / \ce{H2O(l)}) = +1.23\text{ V}$ $E^\circ(\ce{MnO2(s)} / \ce{Mn^{2+}}, \ce{H^+}) = +1.23\text{ V}$

Assume the overpotential for Kolbe electrolysis on Pt is $0.10\text{ V}$, for $\ce{O2}$ evolution is $0.60\text{ V}$, and for $\ce{MnO2}$ deposition is negligible. Identify the first major product formed at the anode and the minimum anodic potential (vs SHE) required for its formation. (Take $\frac{2.303 RT}{F} = 0.06\text{ V}$ and assume partial pressures of all gases to be $1\text{ bar}$)

An alkene $\mathbf{X}$, 2-methyl-1-phenylprop-1-ene, is subjected to the following reaction sequence: \begin{enumerate} \item $\mathbf{X} \xrightarrow{\ce{HBr}, \text{ benzoyl peroxide}, \Delta} \mathbf{P} \text{ (Major Product)}$ \item $\mathbf{P} \xrightarrow{\ce{Mg}, \text{ dry ether}} \text{Grignard Reagent}$ \item $\text{Grignard Reagent} \xrightarrow{1. \ce{CO_2} (s) \quad 2. \ce{H_3O^+}} \mathbf{Q}$ \end{enumerate} Identify the correct IUPAC name of product $\mathbf{Q}$.