Redox Reactions - Class 11 Part 2

An acidified aqueous solution of $\ce{K2Cr2O7}$ reacts with $\ce{H2O2}$ in the presence of diethyl ether at $273\text{ K}$ to yield a deep blue colored compound $\mathbf{X}$, which is extracted into the organic layer. Consider two other compounds: $\mathbf{Y}$ is sodium tetrathionate ($\ce{Na2S4O6}$) and $\mathbf{Z}$ is tribromooctaoxide ($\ce{Br3O8}$). Let $p$ be the actual oxidation state of the central metal atom in $\mathbf{X}$, $q$ be the number of peroxy linkages ($\ce{-O-O-}$) present in one molecule of $\mathbf{X}$, $r$ be the magnitude of the difference between the highest and lowest formal oxidation states of the sulfur atoms in $\mathbf{Y}$, and $s$ be the average oxidation state of the bromine atoms in $\mathbf{Z}$. Evaluate the expression: $\Omega = (p \times q) + r + 3s$.

An aqueous solution of a yellow transition metal oxoanion $\mathbf{P}$ is acidified with dilute $\ce{H2SO4}$ at $298\text{ K}$, yielding an orange oxoanion $\mathbf{Q}$. Both $\mathbf{P}$ and $\mathbf{Q}$ are diamagnetic and exhibit intense color due to Ligand-to-Metal Charge Transfer (LMCT). Let $x$ and $y$ be the oxidation states of the central metal in $\mathbf{P}$ and $\mathbf{Q}$ respectively, as represented in their IUPAC Stock notations. Which of the following correctly identifies the Stock notations $(x, y)$ and the fundamental nature of the $\mathbf{P} \rightleftharpoons \mathbf{Q}$ transformation?

Consider the aqueous uranium species: $U^{3+}(aq)$, $U^{4+}(aq)$, $UO_2^{+}(aq)$, and $UO_2^{2+}(aq)$ at $298\text{ K}$. Their corresponding hydroxides exhibit varying degrees of basic character. Which of the following options correctly identifies the Stock notation of Uranium in the least basic species, and provides the accurate structural rationale for this chemical behavior?

A coordination compound has the empirical formula \ce{CoCl3 \cdot 2en} (where \ce{en} = ethane-1,2-diamine). When $0.1\text{ mol}$ of this compound is dissolved in water and treated with excess \ce{AgNO3(aq)} at $298\text{ K}$, exactly $14.35\text{ g}$ of a white precipitate is formed. The complex cation is known to exhibit optical isomerism. (Given: Molar mass of \ce{AgCl} = $143.5\text{ g/mol}$)

According to Werner's Coordination Theory, let: $P$ = Primary valency of the central metal atom (magnitude of the oxidation state used in Stock notation). $S$ = Secondary valency of the central metal atom. $N$ = Total number of stereoisomers possible for the complex cation.

Calculate the value of the expression $(P^2 + S^2 + N^2)$.

Gold(I) ions are thermodynamically unstable in aqueous solution and undergo disproportionation to Gold(III) and solid gold. Given the standard reduction potentials at $298 \text{ K}$:

$E^\circ_{\ce{Au^{3+}/Au}} = +1.36 \text{ V}$ $E^\circ_{\ce{Au^{+}/Au}} = +1.68 \text{ V}$

If a hypothetical aqueous solution is prepared with an initial concentration of $0.03 \text{ M}$ $\ce{Au^+_{(aq)}}$, what will be the equilibrium concentration of $\ce{Au^+_{(aq)}}$ remaining in the solution?

(Assume $\frac{2.303RT}{F} = 0.06 \text{ V}$ at $298 \text{ K}$)

A $100 \text{ mL}$ of $0.2 \text{ M}$ $MnSO_4$ aqueous solution is completely oxidized to a deeply purple-colored species by exactly $x$ moles of $NaBiO_3(s)$ in dilute $HNO_3$ at $298 \text{ K}$. The resulting purple species is then completely reduced by exactly $y$ moles of Mohr's salt, $\ce{FeSO4.(NH4)2SO4.6H2O}$, in an acidic medium.

Determine the values of $x$ and $y$, and identify the primary quantum mechanical phenomenon responsible for the exceptional oxidizing power of $NaBiO_3$ compared to its lighter group 15 congeners.

An electrochemical cell contains $1.0\text{ L}$ of an aqueous solution comprising $2.0\text{ M } \ce{NaCl}$ and $0.1\text{ M } \ce{Na2SO4}$ at $298\text{ K}$. Electrolysis is performed using inert platinum electrodes by passing a constant current of $9.65\text{ A}$ for $10,000\text{ s}$. The primary gas evolved at the anode is collected and completely reacted with an excess of hot, concentrated $\ce{NaOH}(aq)$.

Assuming $100\%$ current efficiency for the kinetically favored anodic process, identify the major chlorine-containing oxyanion formed in the final solution and calculate its amount.

(Given: $1\text{ F} = 96500\text{ C mol}^{-1}$; Standard oxidation potentials: $E^\circ_{\ce{Cl-}/\ce{Cl2}} = -1.36\text{ V}$, $E^\circ_{\ce{H2O}/\ce{O2}} = -1.23\text{ V}$, $E^\circ_{\ce{SO4^{2-}}/\ce{S2O8^{2-}}} = -2.01\text{ V}$)

Consider the following species at standard conditions: Tribromooctoxide (\ce{Br3O8}), Tetrathionate ion (\ce{S4O6^{2-}}), and Carbon suboxide (\ce{C3O2}). Let $x_1, x_2,$ and $x_3$ be the actual oxidation state of an individual central atom in the homonuclear chains of \ce{Br3O8}, \ce{S4O6^{2-}}, and \ce{C3O2}, respectively. Let $y_1, y_2,$ and $y_3$ be the actual oxidation state of an individual terminal atom in the homonuclear chains of the same respective species. Calculate the value of $(x_1 + x_2 + x_3) \times (y_1 + y_2 + y_3)$.

Chromium(VI) oxide (\ce{CrO3}) is a powerful oxidizing agent that undergoes thermal decomposition to chromium(III) oxide (\ce{Cr2O3}) and oxygen gas. Consider the balanced chemical equation for the decomposition of 2 moles of \ce{CrO3(s)}: $\ce{2CrO3(s) -> Cr2O3(s) + 3/2 O2(g)}$ Given the following thermodynamic data at $298 \text{ K}$: $\Delta H_f^\circ(\ce{CrO3}, s) = -590 \text{ kJ mol}^{-1}$ $\Delta H_f^\circ(\ce{Cr2O3}, s) = -1060 \text{ kJ mol}^{-1}$ $S^\circ(\ce{CrO3}, s) = 70 \text{ J K}^{-1}\text{mol}^{-1}$ $S^\circ(\ce{Cr2O3}, s) = 65 \text{ J K}^{-1}\text{mol}^{-1}$ $S^\circ(\ce{O2}, g) = 210 \text{ J K}^{-1}\text{mol}^{-1}$ Assuming $\Delta H^\circ$ and $\Delta S^\circ$ are independent of temperature, calculate the standard Gibbs free energy change ($\Delta G^\circ$) for this reaction at $600 \text{ K}$ and identify the primary thermodynamic driving force for the decomposition.

In an acidic aqueous medium, the comproportionation of $\ce{MnO4^-}$ and $\ce{Mn^{2+}}$ yields $\ce{Mn^{3+}}$, which is highly unstable and undergoes rapid disproportionation into $\ce{Mn^{2+}}$ and $\ce{MnO2(s)}$.

Given standard reduction potentials at 298 K: $E^\circ(\ce{Mn^{3+}/Mn^{2+}}) = 1.51\text{ V}$ $E^\circ(\ce{MnO2(s)/Mn^{3+}}) = 0.95\text{ V}$

To stabilize the $\ce{Mn^{3+}}$ oxidation state, a neutral ligand $L$ is added, forming octahedral complexes $\ce{MnL6^{3+}}$ and $\ce{MnL6^{2+}}$ with overall formation constants $\beta_{III}$ and $\beta_{II}$, respectively. The disproportionation reaction in the presence of $L$ is:

$2\ce{MnL6^{3+}} + 2\ce{H2O(l)} \rightleftharpoons \ce{MnL6^{2+}} + \ce{MnO2(s)} + 4\ce{H^+} + 6L$

Assume standard conditions for all species ($[\ce{MnL6^{3+}}] = [\ce{MnL6^{2+}}] = [L] = 1\text{ M}$) except for $\ce{H^+}$. If the solution is buffered at $\text{pH} = 2.0$, what is the minimum value of $\log_{10}\left(\frac{\beta_{III}^2}{\beta_{II}}\right)$ required to thermodynamically prevent the disproportionation of $\ce{MnL6^{3+}}$?

(Take $\frac{2.303 RT}{F} = 0.056\text{ V}$ at 298 K)

An actinoid oxide, \ce{M_xO_y} (Compound \textbf{P}), exhibits an average oxidation state of $+5.33$ for the metal \ce{M}. Upon fluorination with excess \ce{F2(g)} at $700\text{ K}$, \textbf{P} is completely converted into a volatile, diamagnetic, octahedral fluoride, \ce{MF6} (Compound \textbf{Q}). Compound \textbf{Q} is known to be a covalent molecule rather than an ionic solid.

Which of the following correctly identifies the actual oxidation states of \ce{M} in \textbf{P}, and the primary quantum mechanical reason for the stability of the $+6$ oxidation state in \textbf{Q}?

A $1.0 \text{ L}$ aqueous solution at $298 \text{ K}$ contains a mixture of \ce{Na2S2O3} and \ce{Na2S4O6}. A $100 \text{ mL}$ aliquot of this solution requires $30 \text{ mL}$ of $0.05 \text{ M}$ \ce{I2} solution for complete reaction in a mildly acidic medium. Another $100 \text{ mL}$ aliquot of the original solution is made strongly alkaline (pH = 14) and subjected to exhaustive anodic electrolysis at a constant current of $9.65 \text{ A}$. The electrolysis requires $380 \text{ seconds}$ for the complete oxidation of all sulfur species to sulfate (\ce{SO4^{2-}}). Assuming 100% current efficiency, what is the molarity of \ce{Na2S4O6} in the original solution?

An electrochemical cell is constructed at $298 \text{ K}$ by coupling a Standard Hydrogen Electrode (SHE) as the anode with a cathode half-cell. The cathode half-cell consists of a platinum wire dipped into a $1.0 \text{ L}$ aqueous solution prepared by completely dissolving $0.05 \text{ moles}$ of pure magnetite ($\ce{Fe3O4(s)}$) in excess dilute $\ce{HClO4(aq)}$ under an inert atmosphere. The final concentration of $\ce{H+(aq)}$ in the solution is adjusted to $1.0 \text{ M}$.

Given: Standard reduction potential $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.770 \text{ V}$ $\frac{2.303RT}{F} = 0.060 \text{ V}$ $\log 2 = 0.30$

Assuming ideal behavior and no hydrolysis of metal ions, what is the electromotive force (EMF) of the cell?

Hydrogen peroxide (\ce{H2O2}) contains a peroxy linkage and can act as both an oxidizing and reducing agent. Consider the following non-standard electrochemical cell at $298\text{ K}$:

$\ce{Pt(s) | O2(g, 1 bar) | H2O2(aq, 0.1 M), pH = 5 || pH = 1, H2O2(aq, 0.1 M) | Pt(s)}$

Given the standard reduction potentials: $E^\circ_{\ce{O2/H2O2}} = +0.68\text{ V}$ $E^\circ_{\ce{H2O2/H2O}} = +1.77\text{ V}$

Calculate the cell potential ($E_{\text{cell}}$) at $298\text{ K}$. (Assume $\frac{2.303RT}{F} = 0.059\text{ V}$)

Consider the following reaction sequence:

$\ce{4-vinylbenzonitrile ->[1. 9-BBN, THF, 0^{\circ}C][2. H_2O_2 (excess), NaOH (aq), 50^{\circ}C] P}$

Identify the major organic product $P$.

Compound $\textbf{X}$ is synthesized by the stoichiometric reaction of $1\text{ equivalent}$ of phthalic anhydride with $1\text{ equivalent}$ of anhydrous $\ce{H2O2}$ in ether. After isolation, $3.64\text{ g}$ of $\textbf{X}$ is dissolved in $100\text{ g}$ of benzene at $298\text{ K}$. The freezing point of the solution is depressed by $0.6144\text{ K}$. Assuming $\textbf{X}$ undergoes partial dimerization in benzene via intermolecular hydrogen bonding, determine the van't Hoff factor ($i$) and the dimerization equilibrium constant ($K_d$) of $\textbf{X}$. \ (Given: $K_f(\text{benzene}) = 5.12\text{ K kg mol}^{-1}$; Atomic masses: $\ce{C}=12, \ce{H}=1, \ce{O}=16$)

An aqueous solution of cold $50\% \text{ w/w } \ce{H2SO4}$ is electrolyzed at $273 \text{ K}$ using inert $\ce{Pt}$ electrodes. During the process, a total of $12.32 \text{ L}$ of gas (measured at STP, where $1 \text{ mol} = 22.4 \text{ L}$) is collected from both electrodes combined. The current efficiency for the formation of peroxydisulfate ($\ce{S2O8^{2-}}$) at the anode is $80\%$, with the remaining anodic current resulting in the evolution of $\ce{O2}$ gas. The cathodic current efficiency for $\ce{H2}$ evolution is $100\%$. The entire anodic solution is subsequently subjected to complete hydrolysis. What is the mass of $\ce{H2O2}$ produced?

The standard reduction potentials $E^\circ(\ce{M^{2+}/M})$ for \ce{Mn} and \ce{Zn} at $298\text{ K}$ are $-1.18\text{ V}$ and $-0.76\text{ V}$, respectively. The thermodynamic parameters for these metals are given below: Enthalpy of atomization ($\Delta_{a}H^\circ$): \ce{Mn} = $281\text{ kJ mol}^{-1}$, \ce{Zn} = $130\text{ kJ mol}^{-1}$. Sum of first and second ionization enthalpies ($IE_1 + IE_2$): \ce{Mn} = $2226\text{ kJ mol}^{-1}$, \ce{Zn} = $2639\text{ kJ mol}^{-1}$. Assuming that the standard entropy change ($\Delta S^\circ$) for the reduction half-reaction $\ce{M^{2+}(aq) + 2e^- -> M(s)}$ is identical for both metals, calculate the difference in their standard hydration enthalpies, $\Delta_{hyd}H^\circ(\ce{Zn^{2+}}) - \Delta_{hyd}H^\circ(\ce{Mn^{2+}})$. (Use $F = 96500\text{ C mol}^{-1}$)

Consider the compound $\ce{X}$ = 4-nitrophenylglyoxal ($\ce{C8H5NO4}$). $\ce{X}$ undergoes the following reaction sequence:

1. $\ce{X} \xrightarrow[2. \text{ H}_3\text{O}^+]{1. \text{ conc. NaOH, } \Delta} \ce{Y}$ (Major organic product)
2. $1 \text{ mole of } \ce{Y} \xrightarrow{\text{excess Sn/HCl}} \ce{Z1}$
3. $1 \text{ mole of } \ce{Y} \xrightarrow[2. \text{ H}_2\text{O}]{1. \text{ excess LiAlH}_4\text{, THF, } \Delta} \ce{Z2}$

Let $n_1$ be the total decrease in the oxidation state of the substrate per molecule of $\ce{Y}$ in the formation of $\ce{Z1}$. Let $n_2$ be the total decrease in the oxidation state of the substrate per molecule of $\ce{Y}$ in the formation of $\ce{Z2}$.

Calculate the value of $n_1 + n_2$.

An octahedral complex $X$ of a 3d transition metal $M$ in aqueous solution at $298 \text{ K}$ has a spin-only magnetic moment of $3.87 \text{ B.M.}$ and exhibits a characteristic visible absorption band at $\lambda_1$ due to a spin-allowed d-d transition. When excess $\ce{KCN(aq)}$ is added to the solution of $X$ under aerobic conditions (bubbling $\ce{O_2}$), a rapid electron transfer occurs, yielding a highly stable, diamagnetic octahedral complex $Y$. Complex $Y$ exhibits its lowest-energy spin-allowed d-d transition at $\lambda_2$. Assuming no charge transfer bands obscure the relevant spectra, which of the following correctly identifies $M$, the relationship between the absorption wavelengths, and the dominant physical cause?

2,6-Dimethylbenzoic acid ($\mathbf{A}$) and benzoic acid ($\mathbf{B}$) are subjected to esterification studies. Under standard Fischer esterification conditions (excess \ce{EtOH}, catalytic \ce{H2SO4}, 298 K), $\mathbf{A}$ fails to react due to severe steric hindrance. To achieve the esterification of $\mathbf{A}$, it is first dissolved in 100% \ce{H2SO4} to generate a reactive intermediate $\mathbf{X}$, which is subsequently treated with cold ethanol. When $\mathbf{A}$ and $\mathbf{B}$ are dissolved in 100% \ce{H2SO4}, their cryoscopic van't Hoff factors are observed to be $i_A$ and $i_B$, respectively. Identify the correct values of $i_A$ and $i_B$, the hybridization of the electrophilic carbon in $\mathbf{X}$, and the primary thermodynamic driving force for the formation of $\mathbf{X}$ over a standard protonated species.

Consider an equimolar mixture of 2,4,6-tri-\textit{tert}-butylbenzaldehyde ($\textbf{X}$) and formaldehyde ($\ce{HCHO}$). The mixture is treated with an excess of 50% aqueous $\ce{NaOH}$ at 373 K for several hours. The resulting mixture is then cooled, diluted with water, and carefully acidified with dilute $\ce{HCl}$. Which of the following best represents the major organic species present in the final acidified mixture?

The Inert Pair Effect typically renders the +5 oxidation state of Bismuth highly unstable, favoring Bi(III). However, in the presence of strong, highly electronegative ligands like $\ce{F^-}$, the 'd/f-orbital contraction' increases the effective nuclear charge, contracting the empty 6s/6p orbitals of Bi(V). This maximizes covalent overlap and bond enthalpy, making the high-valent state unexpectedly stable and reversing the expected direction of disproportionation.

Consider the spontaneous disproportionation of the transient Bismuth(IV) fluoro-complex at $300\text{ K}$: $2 \ce{[BiF6]^{2-}} \rightleftharpoons \ce{[BiF6]^{-}} + \ce{[BiF6]^{3-}}$

Given the thermodynamic parameters for the reaction: $\Delta H^\circ = -120\text{ kJ mol}^{-1}$ $\Delta S^\circ = -150\text{ J K}^{-1}\text{ mol}^{-1}$

Let $X$ be the magnitude of the standard free energy change ($\Delta G^\circ$) in $\text{kJ mol}^{-1}$. Let $Y$ be the total number of electrons residing in the $e_g$ (d-orbital derived) set of the central metal ions across both product complexes. Let $Z$ be the number of unpaired electrons in the central metal of the reactant complex.

Calculate the numerical value of $(X \times Z) + Y$.

Consider an aqueous solution containing dissolved $\ce{Cl2(aq)}$, $\ce{Cl-(aq)}$, and $\ce{ClO3-(aq)}$, all maintained at an identical concentration $C$. The solution is buffered at $pH = 1.0$ at $298\text{ K}$.

Given the standard reduction potentials: $E^\circ_{\ce{Cl2}/\ce{Cl-}} = 1.36\text{ V}$ $E^\circ_{\ce{ClO3-}/\ce{Cl2}} = 1.47\text{ V}$

(Assume $\frac{2.303 RT}{F} = 0.06\text{ V}$)

Which of the following statements correctly describes the thermodynamic stability of $\ce{Cl2(aq)}$ against disproportionation into $\ce{Cl-}$ and $\ce{ClO3-}$?

Consider the central atoms in the following species: (I) \ce{CrO5} (II) \ce{H2SO5} (III) \ce{XeF6} (IV) \ce{ClO2}

Which of the following statements correctly describes the ability of the central atom in these species to undergo disproportionation (for III, specifically into other binary fluorides) under standard conditions, and identifies the underlying structural reasons?

In an aqueous acidic medium at $298\text{ K}$, the $\ce{Mn^{3+}_{(aq)}}$ ion is thermodynamically unstable and undergoes spontaneous disproportionation into $\ce{Mn^{2+}_{(aq)}}$ and $\ce{MnO2_{(s)}}$. However, when excess ethylenediamine ($en$) is added to the solution, the disproportionation reaction is completely suppressed, yielding a stable octahedral complex $\ce{[Mn(en)3]^{3+}}$.

Which of the following statements correctly identifies the primary thermodynamic reason for the suppression of disproportionation, and what is the spin-only magnetic moment ($\mu$) of the resulting complex?

Consider the Latimer diagram for a hypothetical actinide element $\ce{An}$ in aqueous acidic medium ($\text{pH} = 0$) at $298\text{ K}$:

$\ce{AnO2^+} \xrightarrow{0.55\text{ V}} \ce{AnO^{2+}} \xrightarrow{0.35\text{ V}} \ce{An^{3+}} \xrightarrow{1.25\text{ V}} \ce{An^{2+}}$

Calculate the standard Gibbs free energy change ($\Delta G^\circ$) for the following balanced comproportionation reaction:

$\ce{AnO2^+(aq) + 2An^{2+}(aq) + 4H+(aq) \rightleftharpoons 3An^{3+}(aq) + 2H2O(l)}$

(Given: Faraday's constant $F = 96500\text{ C mol}^{-1}$)

Consider the redox chemistry of manganese in aqueous media at 298 K. The standard reduction potentials are given as: $E^\circ(\ce{MnO4- / Mn^2+}) = +1.51\text{ V}$ $E^\circ(\ce{MnO2 / Mn^2+}) = +1.23\text{ V}$ $E^\circ(\ce{Mn^{3+} / Mn^2+}) = +1.51\text{ V}$

A student investigates the comproportionation of $\ce{MnO4-}$ and $\ce{Mn^2+}$ to form $\ce{MnO2(s)}$ (Reaction I) and the disproportionation of $\ce{Mn^{3+}(aq)}$ to $\ce{MnO2(s)}$ and $\ce{Mn^2+}$ (Reaction II): Reaction I: $2\ce{MnO4-} + 3\ce{Mn^2+} + 2\ce{H2O} \rightleftharpoons 5\ce{MnO2(s)} + 4\ce{H+}$ Reaction II: $2\ce{Mn^{3+}} + 2\ce{H2O} \rightleftharpoons \ce{MnO2(s)} + \ce{Mn^2+} + 4\ce{H+}$

Determine the standard cell potentials $E^\circ_{\text{I}}$ and $E^\circ_{\text{II}}$ for Reactions I and II, respectively. Furthermore, identify the effect of increasing the pH from 0 to 6 on the thermodynamic stability of $\ce{Mn^{3+}(aq)}$ against disproportionation.

A galvanic cell is constructed at $298 \text{ K}$ with the following cell representation:

$\ce{Sn(s) | Sn^{2+}(aq, 1.0 M) || Sn^{4+}(aq, 1.0 M), Sn^{2+}(aq, 1.0 M) | Pt(s)}$

The standard reduction potentials are $E^\circ_{\ce{Sn^{4+}/Sn^{2+}}} = 0.15 \text{ V}$ and $E^\circ_{\ce{Sn^{2+}/Sn}} = -0.14 \text{ V}$. Initially, the cell operates spontaneously. A ligand $\ce{L^-}$ is then added to the cathode compartment, which selectively forms the highly stable complex $\ce{[SnL_6]^{2-}}$ with $\ce{Sn^{4+}}$ (Formation constant $\beta_6 = 10^{22}$). The concentration of free $\ce{L^-}$ is maintained at $0.1 \text{ M}$, and the volume change is negligible.

What is the magnitude of the new cell potential, and what is the spontaneous cell reaction after the addition of the ligand? (Assume $\frac{2.303RT}{F} = 0.06 \text{ V}$)

Consider the standard reduction potentials for Neptunium (\ce{Np}) species in aqueous acidic medium ($pH = 0$) at $298\ \text{K}$: \begin{align*} \ce{Np^{4+}{(aq)} + e^-} &\rightleftharpoons \ce{Np^{3+}{(aq)}} \quad &E^\circ = +0.14\ \text{V} \ \ce{NpO2^{+}{(aq)} + 4H^+{(aq)} + e^-} &\rightleftharpoons \ce{Np^{4+}{(aq)} + 2H2O{(l)}} \quad &E^\circ = +0.74\ \text{V} \ \ce{NpO2^{2+}{(aq)} + e^-} &\rightleftharpoons \ce{NpO2^{+}{(aq)}} \quad &E^\circ = +1.13\ \text{V} \end{align*} Three distinct redox reactions involving pairs of these Neptunium species as reactants can occur. Among them, identify the reaction that is both thermodynamically spontaneous and kinetically the fastest (characterized by the lowest activation energy barrier due to the preservation of the actinyl core and hydration spheres). What is the standard cell potential ($E^\circ_{\text{cell}}$) of this specific reaction?

A $500 \text{ mL}$ aqueous solution containing $40 \text{ mmol}$ of $\ce{KMnO4}$ and $50 \text{ mmol}$ of $\ce{MnSO4}$ is allowed to react at $298 \text{ K}$ in the presence of an excess of $\ce{ZnO}$ (to maintain a neutral pH). The mixture undergoes a complete comproportionation reaction to yield a dark brown precipitate of $\ce{MnO2(s)}$.\n\nOnce the reaction is complete, the suspension is filtered. The precipitate is washed thoroughly and then treated with an excess of acidified $\ce{KI}$ solution. The liberated iodine requires $V_1 \text{ mL}$ of $0.1 \text{ M } \ce{Na2S2O3}$ for complete titration.\n\nThe filtrate is similarly treated with an excess of acidified $\ce{KI}$ solution, and the liberated iodine requires $V_2 \text{ mL}$ of $0.1 \text{ M } \ce{Na2S2O3}$.\n\nAssuming no other side reactions occur, what is the integer value of the ratio $V_1 / V_2$?

The standard reduction potentials for the permanganate ion at $298 \text{ K}$ are given as:

$\ce{MnO4^- (aq) + 8H^+ (aq) + 5e^- -> Mn^{2+} (aq) + 4H2O (l)}$, $E^\circ = 1.51 \text{ V}$ $\ce{MnO4^- (aq) + 4H^+ (aq) + 3e^- -> MnO2 (s) + 2H2O (l)}$, $E^\circ = 1.69 \text{ V}$

A student constructs two half-cells at $298 \text{ K}$: Half-cell 1: $0.01 \text{ M } \ce{KMnO4}$ and $0.1 \text{ M } \ce{MnSO4}$ in an acidic buffer of $\text{pH} = 2$. Half-cell 2: $0.1 \text{ M } \ce{KMnO4}$ and excess solid $\ce{MnO2}$ in a neutral buffer of $\text{pH} = 7$.

Assuming the specified half-reactions are the sole determinants of the electrode potentials, what is the difference in the reduction potentials ($E_1 - E_2$) of the two half-cells? (Take $\frac{2.303 RT}{F} = 0.06 \text{ V}$)

A $100 \text{ mL}$ aqueous solution of $\ce{NaBH4}$ of unknown molarity $x$ is divided into two equal $50 \text{ mL}$ aliquots, A and B.

Aliquot A is adjusted to $\text{pH} = 12$. $50 \text{ mL}$ of $0.1 \text{ M}$ $\ce{KIO3}$ is added, and the mixture is heated to ensure complete reaction. The solution is then cooled, acidified, and treated with excess $\ce{KI}$. The liberated $\ce{I2}$ requires $100 \text{ mL}$ of $0.1 \text{ M}$ $\ce{Na2S2O3}$ for complete titration.

Aliquot B is adjusted to $\text{pH} = 2$ and allowed to stand for 30 minutes in an open flask. Then, $50 \text{ mL}$ of the same $0.1 \text{ M}$ $\ce{KIO3}$ and excess $\ce{KI}$ are added. The liberated $\ce{I2}$ requires $V \text{ mL}$ of $0.1 \text{ M}$ $\ce{Na2S2O3}$ for complete titration.

Assuming no evaporation losses, what are the values of $x$ and $V$?

A galvanic cell is constructed at $298\text{ K}$ with the following representation:

$\ce{Co}(s) | \ce{Co^{2+}}(10^{-3}\text{ M}) || \ce{[Co(NH_3)_6]^{3+}}(0.1\text{ M}), \ce{[Co(NH_3)_6]^{2+}}(0.01\text{ M}), \ce{NH_3}(1\text{ M}) | Pt(s)$

Given the following standard thermodynamic and electrochemical data at $298\text{ K}$: $E^\circ_{\ce{Co^{2+}/Co}} = -0.28\text{ V}$ $E^\circ_{\ce{Co^{3+}/Co^{2+}}} = +1.81\text{ V}$ Overall formation constant ($\beta_6$) for $\ce{[Co(NH_3)_6]^{3+}} = 10^{35}$ Overall formation constant ($\beta_6$) for $\ce{[Co(NH_3)_6]^{2+}} = 10^5$

Assuming $\frac{2.303RT}{F} = 0.06\text{ V}$, calculate the electromotive force ($E_{\text{cell}}$) of the cell.

An electrochemical cell is constructed at 298 K using two Nickel half-cells. Compartment A consists of a $\ce{Ni(s)}$ electrode immersed in a solution containing $0.10\text{ M } \ce{[NiCl4]^{2-}}$ and $1.0\text{ M } \ce{Cl-}$. Compartment B consists of a $\ce{Ni(s)}$ electrode immersed in a solution containing $0.01\text{ M } \ce{[Ni(CN)4]^{2-}}$ and $0.10\text{ M } \ce{CN-}$. The overall formation constants are $\beta_4(\ce{[NiCl4]^{2-}}) = 10^2$ and $\beta_4(\ce{[Ni(CN)4]^{2-}}) = 10^{30}$. Assume $\frac{2.303 RT}{F} = 0.06\text{ V}$. Determine the spontaneous EMF of the cell, and identify the coordination geometry and hybridization of the nickel complex present in the \textbf{anodic} compartment.

A half-cell is prepared by dissolving $0.055\text{ mol}$ of \ce{Na2CrO4} and $0.050\text{ mol}$ of \ce{CrCl3} in $1.0\text{ L}$ of a buffer solution at $298\text{ K}$. The buffer is formulated such that its pH is exactly equal to the pH of a $1.0 \times 10^{-8}\text{ M}$ \ce{HCl} aqueous solution.

Given: $\bullet$ $E^\circ_{\ce{Cr2O7^{2-}}/\ce{Cr^{3+}}} = 1.33\text{ V}$ $\bullet$ $K_{eq}$ for $2\ce{CrO4^{2-}} + 2\ce{H+} \rightleftharpoons \ce{Cr2O7^{2-}} + \ce{H2O}$ is $9.07 \times 10^{13}$ $\bullet$ $\frac{2.303 RT}{F} = 0.059\text{ V}$ at $298\text{ K}$ $\bullet$ $K_w = 1.0 \times 10^{-14}$ $\bullet$ $\sqrt{401} \approx 20.0$, $\log(1.05) \approx 0.02$

Calculate the reduction potential of this half-cell. (Assume the buffer capacity is sufficient to maintain the pH constant).

A concentration cell is constructed at $298 \text{ K}$ using copper electrodes dipping into two aqueous solutions of copper(II) sulfate ($\ce{CuSO4}$):

$\ce{Cu(s) | CuSO4 (aq, c_1) || CuSO4 (aq, c_2) | Cu(s)}$

Due to significant ion pairing at higher concentrations, the salt does not behave ideally. The Van't Hoff factor ($i$) for the left half-cell ($c_1 = 0.05 \text{ M}$) is experimentally determined to be $1.80$, while for the right half-cell ($c_2 = 0.40 \text{ M}$) it is $1.40$.

Assuming the effective concentration of $\ce{Cu^{2+}}$ ions is determined by the degree of dissociation ($\alpha$) derived from the Van't Hoff factor, calculate the cell potential ($E_{\text{cell}}$) in millivolts (mV).

(Given: $\frac{2.303 RT}{F} = 0.06 \text{ V}$, $\log 2 = 0.30$, $\log 3 = 0.48$, $\log 7 = 0.84$)

Given the standard reduction potential of the aqueous cobalt couple $E^\circ(\ce{Co^{3+}}/\ce{Co^{2+}}) = +1.82\text{ V}$ at $298\text{ K}$. The overall formation constants ($\beta_3$) for the ethylenediamine (en) complexes $[\ce{Co(en)_3}]^{3+}$ and $[\ce{Co(en)_3}]^{2+}$ are $10^{33}$ and $10^5$, respectively. Consider the redox reaction where $[\ce{Co(en)_3}]^{2+}$ is oxidized by $\ce{Sn^{4+}}$ to form $[\ce{Co(en)_3}]^{3+}$ and $\ce{Sn^{2+}}$ under standard conditions. Given $E^\circ(\ce{Sn^{4+}}/\ce{Sn^{2+}}) = +0.15\text{ V}$ and $\frac{2.303 RT}{F} = 0.06\text{ V}$ at $298\text{ K}$. Assuming $[\ce{Co(en)_3}]^{2+}$ is a high-spin complex and $[\ce{Co(en)_3}]^{3+}$ is a low-spin complex, what is the standard cell potential ($E^\circ_{\text{cell}}$) for this reaction, and what is the change in the number of unpaired electrons ($\Delta n = n_{\text{product}} - n_{\text{reactant}}$) on the cobalt center?

Consider a transition metal $M$ that forms coordination complexes with a tetradentate Schiff-base ligand $H_2L$. The standard reduction potentials and formation constants ($K_f$) at 298 K are given below:

$E^\circ(M^{3+}/M^{2+}) = +0.40$ V $E^\circ(M^{2+}/M) = -0.20$ V $M^{3+} + L^{2-} \rightleftharpoons ML^+$ $\log K_{f,III} = 30$ $M^{2+} + L^{2-} \rightleftharpoons ML$ $\log K_{f,II} = 16$

The ligand $H_2L$ has acid dissociation constants $pK_{a1} = 4.0$ and $pK_{a2} = 6.0$. An electrochemical cell is set up where the activities of the complexes $ML^+$ and $ML$ are maintained at $1.0$ M, and the total concentration of the uncomplexed ligand species ($[H_2L] + [HL^-] + [L^{2-}]$) is $1.0$ M. At what pH does the disproportionation of $ML$ into $ML^+$ and $M(s)$ just become thermodynamically favorable? (Given: $\frac{2.303 RT}{F} = 0.06$ V. Assume no other side reactions occur.)

A hydrogen-oxygen fuel cell operates at $300 \text{ K}$ with non-standard partial pressures: $P_{\ce{H2}} = 10 \text{ bar}$ and $P_{\ce{O2}} = 100 \text{ bar}$. The standard enthalpy of formation of liquid water is $\Delta H^\circ_f(\ce{H2O}, l) = -300 \text{ kJ mol}^{-1}$. The absolute molar entropies at $300 \text{ K}$ are $S^\circ(\ce{H2}, g) = 150 \text{ J K}^{-1}\text{mol}^{-1}$, $S^\circ(\ce{O2}, g) = 300 \text{ J K}^{-1}\text{mol}^{-1}$, and $S^\circ(\ce{H2O}, l) = 60 \text{ J K}^{-1}\text{mol}^{-1}$.

Assume Faraday's constant $F = 100,000 \text{ C mol}^{-1}$ and the Nernst factor $\frac{2.303 RT}{F} = 0.06 \text{ V}$ at $300 \text{ K}$.

Determine the operating cell potential ($E_{\text{cell}}$) and the thermodynamic efficiency ($\eta = \frac{\Delta G_{\text{operating}}}{\Delta H^\circ} \times 100$) of the fuel cell under these conditions.

Consider the following electrochemical cell at $298 \text{ K}$:

$\ce{Zn(s) | [Zn(NH_3)_4]^{2+}(aq, 0.10 M), NH_3(aq, 1.0 M) || OH^{-}(aq, 0.10 M) | Zn(OH)_2(s) | Zn(s)}$