Search This Blog

JEE advanced problems on S block elements

25 Ultra-Challenging JEE Advanced Problems on s-Block Elements & Hydrogen | Chemca

Masterclass: 25 Ultra-Challenging JEE Advanced Problems on s-Block Elements & Hydrogen

From the extreme hydration enthalpies of Lithium to the quantum spin isomers of Hydrogen. Master the chemistry of Groups 1 and 2.

Problem 1: Volume Strength of Hydrogen Peroxide
A bottle of aqueous Hydrogen Peroxide ($H_2O_2$) is labeled as "20 V". Calculate the Molarity, Normality, and Percentage Strength ($\text{w/v}$) of this solution.
View Solution
Strategy: "Volume Strength" means the volume of oxygen gas (at STP) liberated by 1 volume of the $H_2O_2$ solution. Use the decomposition stoichiometry to relate this to moles.

Step 1: Decode "Volume Strength"
A label of "20 V" means that $1.0 \text{ Liter}$ of this $H_2O_2$ solution will decompose to yield exactly $20.0 \text{ Liters}$ of Oxygen gas ($O_2$) at STP.

Step 2: Reaction Stoichiometry
$2H_2O_2 \rightarrow 2H_2O + O_2 \uparrow$
According to the balanced equation, $2 \text{ moles}$ of $H_2O_2$ produce $1 \text{ mole}$ of $O_2$.
At STP, $1 \text{ mole}$ of $O_2$ occupies $22.4 \text{ Liters}$.
Since $1 \text{ L}$ of our solution produced $20.0 \text{ L}$ of $O_2$, the moles of $O_2$ produced = $\frac{20.0}{22.4} \approx 0.893 \text{ moles}$.
Therefore, moles of $H_2O_2$ present in $1 \text{ L}$ of solution = $2 \times 0.893 = 1.786 \text{ moles}$.
Molarity ($M$) = $1.786 \text{ M}$.

Step 3: Calculate Normality
The n-factor for $H_2O_2$ in its disproportionation (or redox reactions) is $2$.
Normality ($N$) = Molarity $\times$ n-factor = $1.786 \times 2 = 3.57 \text{ N}$.

Step 4: Calculate Percentage Strength ($\text{w/v}$)
Molar mass of $H_2O_2 = 34 \text{ g/mol}$.
Mass of $H_2O_2$ in $1 \text{ Liter}$ ($1000 \text{ mL}$) = Moles $\times$ Molar mass = $1.786 \text{ mol} \times 34 \text{ g/mol} \approx 60.7 \text{ g}$.
Percentage strength is mass per $100 \text{ mL}$.
$\% \text{ w/v} = \frac{60.7 \text{ g}}{1000 \text{ mL}} \times 100 = 6.07\%$.

Final Answer: Molarity = $1.786 \text{ M}$; Normality = $3.57 \text{ N}$; Strength = $6.07\% \text{ (w/v)}$.
Problem 2: Thermodynamics of Alkali Metal Solutions in Liquid Ammonia
When a small amount of Sodium is dissolved in pure liquid Ammonia ($NH_3$), the solution is deep blue and highly paramagnetic. However, if the concentration of Sodium is heavily increased ($> 3 \text{ M}$), the solution turns a bronze/copper color and becomes diamagnetic. Explain the quantum/thermodynamic interactions dictating this transition.
View Solution
Strategy: Evaluate the fate of the valence electron when an alkali metal dissolves in ammonia, and how increasing concentration affects the distance between these solvated species.

Step 1: The Dilute Solution (Blue & Paramagnetic)
Alkali metals dissolve easily in liquid ammonia without reacting to form amide (initially). The metal ejects its valence electron, becoming a solvated cation. The electron is trapped in a cavity of ammonia molecules, becoming an ammoniated electron.
$Na + (x+y)NH_3 \rightarrow [Na(NH_3)_x]^+ + [e(NH_3)_y]^-$
The deep blue color arises from $s \rightarrow p$ like transitions of these free solvated electrons absorbing visible light (red region). Because these electrons are unpaired and moving independently, the solution is strongly paramagnetic.

Step 2: The Concentrated Solution (Bronze & Diamagnetic)
As the concentration of Sodium exceeds $\approx 3 \text{ M}$, the density of ammoniated electrons and cations becomes massive. The individual solvent cavities around the electrons overlap. The unpaired electrons are forced into close proximity and pair up with opposite spins.
Because the electrons are paired, the magnetic moment drops to zero, rendering the solution diamagnetic.

Step 3: The Mott Transition
This massive overlap of electron clouds creates a delocalized "sea of electrons" similar to a liquid metal. The solution undergoes a non-metal to metal transition (the Mott transition), reflecting light like a metal and turning a metallic bronze/copper color with dramatically higher electrical conductivity.

Final Answer: In dilute solutions, unpaired ammoniated electrons cause blue color and paramagnetism. In concentrated solutions, the electron cavities overlap, causing electrons to pair up (diamagnetic) and creating a metallic "sea of electrons" that reflects a bronze color.
Problem 3: Quantitative Hardness of Water (EDTA Titration)
$50 \text{ mL}$ of a hard water sample required $15.0 \text{ mL}$ of $0.01 \text{ M}$ EDTA solution for titration using Eriochrome Black T indicator at pH 10. Calculate the total hardness of the water sample in parts per million (ppm) of $CaCO_3$.
View Solution
Strategy: EDTA forms a 1:1 complex with $Ca^{2+}$ and $Mg^{2+}$ ions regardless of their charge. Hardness is universally expressed as the equivalent mass of $CaCO_3$.

Step 1: Calculate Moles of EDTA Used
Moles of EDTA = Molarity $\times$ Volume (in Liters)
Moles = $0.01 \text{ mol L}^{-1} \times 0.015 \text{ L} = 1.5 \times 10^{-4} \text{ moles}$.

Step 2: Apply 1:1 Stoichiometry
Since EDTA forms a 1:1 complex with hardness-causing ions ($Ca^{2+}, Mg^{2+}$):
Total moles of $Ca^{2+}/Mg^{2+}$ in $50 \text{ mL}$ = $1.5 \times 10^{-4} \text{ moles}$.

Step 3: Convert to $CaCO_3$ Equivalents
To express hardness in terms of $CaCO_3$, we treat all the metal ions as if they were $CaCO_3$.
Molar mass of $CaCO_3 = 100 \text{ g/mol}$.
Mass of $CaCO_3$ equivalent = $1.5 \times 10^{-4} \text{ moles} \times 100 \text{ g/mol} = 1.5 \times 10^{-2} \text{ g} = 15 \text{ mg}$.

Step 4: Calculate ppm (mg/L)
We have $15 \text{ mg}$ of hardness in $50 \text{ mL}$ ($0.050 \text{ L}$) of water. ppm is effectively milligrams per liter (mg/L).
Hardness = $\frac{15 \text{ mg}}{0.050 \text{ L}} = 300 \text{ mg/L} = 300 \text{ ppm}$.

Final Answer: The total hardness of the water is $300 \text{ ppm}$.
Problem 4: Solubility Trends of Alkaline Earth Sulfates
The solubility of alkaline earth metal sulfates in water rapidly decreases down the group ($BeSO_4 > MgSO_4 > CaSO_4 > SrSO_4 > BaSO_4$). Conversely, the solubility of their hydroxides increases down the group. Justify this complete reversal in solubility trends utilizing Lattice Enthalpy ($\Delta H_{lat}$) and Hydration Enthalpy ($\Delta H_{hyd}$).
View Solution
Strategy: Solubility depends on whether the energy gained from hydrating the ions ($\Delta H_{hyd}$) is sufficient to overcome the energy required to break the crystal lattice ($\Delta H_{lat}$). Analyze the size mismatch between cations and anions.

Step 1: The Size Mismatch Principle
Lattice energy is highest when the cation and anion are of similar size, allowing for incredibly tight and efficient packing in the crystal structure. A large mismatch in size leads to poor packing and significantly lower lattice energy.

Step 2: Analyze Sulfates (Massive Anion)
The sulfate ion ($SO_4^{2-}$) is a massive, multi-atomic anion.
- At the top of the group, $Be^{2+}$ is extremely small. There is a massive size mismatch. The lattice energy of $BeSO_4$ is relatively low. Furthermore, the tiny $Be^{2+}$ ion has an enormous hydration enthalpy. High $\Delta H_{hyd}$ easily overcomes the low $\Delta H_{lat}$, making it highly soluble.
- Moving down the group to $Ba^{2+}$, the cation becomes massive, perfectly matching the massive sulfate anion. The lattice packing becomes incredibly tight, keeping $\Delta H_{lat}$ very high. However, the large $Ba^{2+}$ has very low charge density, causing its $\Delta H_{hyd}$ to plummet. With plummeting hydration energy and strong lattice energy, $BaSO_4$ becomes highly insoluble.

Step 3: Analyze Hydroxides (Small Anion)
The hydroxide ion ($OH^-$) is a very small anion.
- $Be(OH)_2$ features a small cation and small anion (perfect match). The lattice energy is immense, making it insoluble.
- Moving down to $Ba^{2+}$, the massive cation creates a severe mismatch with the small $OH^-$ ion. The lattice energy drops drastically faster than the hydration energy drops. Because the lattice becomes so easy to break, $Ba(OH)_2$ is highly soluble.

Final Answer: For large anions ($SO_4^{2-}$), Lattice Energy remains strong down the group due to size matching, while Hydration Energy plummets, decreasing solubility. For small anions ($OH^-$), Lattice Energy drops faster than Hydration Energy due to increasing size mismatch, increasing solubility.
Problem 5: Ortho and Para Hydrogen (Spin Isomers)
Hydrogen gas exists as a mixture of two distinct nuclear spin isomers: Ortho-hydrogen and Para-hydrogen. At absolute zero ($0 \text{ K}$), pure hydrogen gas consists entirely of the para isomer. As temperature increases to room temperature, the ratio reaches an equilibrium of $3:1$ (ortho:para). Detail the quantum mechanical spin states of these isomers and explain the thermodynamic limits of their interconversion.
View Solution
Strategy: Evaluate the alignment of nuclear spins in the $H_2$ molecule. Remember that parallel spins (ortho) create a slightly higher energy state than antiparallel spins (para).

Step 1: Defining the Spin Isomers
In a molecule of $H_2$, the two protons (nuclei) have spin.
- Ortho-hydrogen: The nuclear spins are aligned parallel (same direction, $\uparrow \uparrow$).
- Para-hydrogen: The nuclear spins are aligned antiparallel (opposite directions, $\uparrow \downarrow$).

Step 2: Thermodynamic Stability
The antiparallel arrangement (para) has a lower internal magnetic energy. Therefore, para-hydrogen is the more thermodynamically stable isomer. This is why, at absolute zero ($0 \text{ K}$) where molecules settle into their lowest possible energy state, $100\%$ of the hydrogen exists as para-hydrogen.

Step 3: Temperature Effects and the 3:1 Limit
As thermal energy is added, some para molecules acquire enough energy to flip a nuclear spin and become the higher-energy ortho isomer. Statistically, there are 3 possible quantum states for parallel spins (ortho), and only 1 state for antiparallel spins (para).
As temperature increases, thermal energy overwhelms the slight energy gap between the two forms, and the population is dictated purely by statistical probability (number of microstates). Thus, at room temperature and above, the mixture maximizes at exactly $75\%$ ortho and $25\%$ para (a $3:1$ ratio). It is physically impossible to obtain a sample containing more than $75\%$ ortho-hydrogen.

Final Answer: Para (antiparallel spins) is the lower energy state, dominating at $0 \text{ K}$. Ortho (parallel spins) has three quantum microstates versus para's one, so increasing temperature drives the system to the statistical maximum ratio of $3:1$ (ortho:para).
Problem 6: The Solvay Process Limitation
The Solvay process is the primary industrial method for manufacturing Sodium Carbonate ($Na_2CO_3$). However, it completely fails if one attempts to use it to manufacture Potassium Carbonate ($K_2CO_3$). Write the key intermediate precipitation reaction in the Solvay process and explain the solubility dynamics that cause the process to fail for Potassium.
View Solution
Strategy: The Solvay process relies on the precipitation of a less soluble bicarbonate intermediate to drive the reaction forward. Compare the solubility of $NaHCO_3$ with $KHCO_3$.

Step 1: The Core Solvay Reaction
In the Solvay process, ammonia ($NH_3$) and carbon dioxide ($CO_2$) are passed through a cold, concentrated solution of sodium chloride (brine).
Reaction: $NaCl_{(aq)} + NH_3 + CO_2 + H_2O \rightarrow \mathbf{NaHCO_{3(s)} \downarrow} + NH_4Cl_{(aq)}$.

Step 2: The Driving Force
This reaction proceeds forward exclusively because Sodium Bicarbonate ($NaHCO_3$) has a relatively low solubility in cold water. It precipitates out as a solid, allowing it to be filtered off and subsequently heated to yield the final product: $2NaHCO_3 \xrightarrow{\Delta} Na_2CO_3 + H_2O + CO_2$.

Step 3: The Failure with Potassium
If we substitute $KCl$ for $NaCl$, the expected intermediate would be Potassium Bicarbonate ($KHCO_3$). However, $KHCO_3$ is highly soluble in water. It will not precipitate out of the solution under these conditions. Because no precipitate forms to pull the equilibrium to the right, the intermediate cannot be separated from the $NH_4Cl$ byproduct, causing the entire industrial process to fail.

Final Answer: The Solvay process relies on the precipitation of $NaHCO_3$. It fails for Potassium because the intermediate Potassium Bicarbonate ($KHCO_3$) is highly soluble in water and will not precipitate out of the reaction mixture.
Problem 7: Thermal Stability of Alkali Metal Carbonates
Arrange the alkali metal carbonates ($Li_2CO_3, Na_2CO_3, K_2CO_3, Rb_2CO_3, Cs_2CO_3$) in increasing order of their thermal stability. Lithium carbonate decomposes rapidly at gentle heat, while the others melt before decomposing. Explain this unique instability of Lithium utilizing Fajans' Rules.
View Solution
Strategy: Thermal decomposition of a carbonate involves the metal ion polarizing the carbonate oxygen to rip it away, forming a metal oxide and releasing $CO_2$. Assess polarizing power (charge density) of the cations.

Step 1: Apply Fajans' Rules (Polarizing Power)
Fajans' rules state that a small cation with high charge possesses immense polarizing power. It severely distorts the electron cloud of a large anion, introducing covalent character into the ionic bond.

Step 2: Analyze Lithium's Anomaly
The $Li^+$ ion is incredibly small compared to the other alkali metals. It has the highest charge density and greatest polarizing power in the group. When paired with the large, complex carbonate anion ($CO_3^{2-}$), the $Li^+$ ion violently polarizes the electron cloud of an adjacent oxygen atom.

Step 3: Mechanism of Decomposition
This intense polarization weakens the internal Carbon-Oxygen bonds of the carbonate ion. Under gentle heat, the $Li^+$ successfully rips the oxygen atom away entirely, decomposing the molecule into the highly stable lattice of Lithium Oxide ($Li_2O$) and releasing $CO_2$ gas.
$Li_2CO_3 \xrightarrow{\Delta} Li_2O + CO_2 \uparrow$

Step 4: Trend Down the Group
As we move down to $Na^+, K^+, Rb^+, Cs^+$, the ionic radius increases drastically. The charge density and polarizing power drop. They cannot distort the carbonate ion enough to break it. Hence, thermal stability heavily increases down the group.

Final Answer: Stability order: $Li_2CO_3 < Na_2CO_3 < K_2CO_3 < Rb_2CO_3 < Cs_2CO_3$. $Li^+$ has exceptionally high polarizing power (small size, high charge density), deeply polarizing the $CO_3^{2-}$ anion, weakening its bonds and causing rapid thermal decomposition to $Li_2O$.
Problem 8: Peroxides vs Superoxides (Lattice Matching)
When burned in an excess of air, Lithium forms primarily the normal oxide ($Li_2O$), Sodium forms the peroxide ($Na_2O_2$), and Potassium forms the superoxide ($KO_2$). Why do the heavier alkali metals prefer to form superoxides, which contain the seemingly unstable $O_2^-$ radical anion?
View Solution
Strategy: Evaluate the size match between the cation and the anion. A large cation stabilizes a large, complex anion in the crystal lattice.

Step 1: Size of the Anions
The normal oxide ion ($O^{2-}$) is relatively small and highly charged.
The peroxide ion ($O_2^{2-}$) is larger.
The superoxide ion ($O_2^-$) is massive and possesses a diffuse charge (a radical anion).

Step 2: The Lattice Energy Principle
A stable ionic crystal lattice requires the cation and anion to be of comparable size. A severe mismatch leads to poor packing and low lattice energy.

Step 3: Matching the Ions
- Lithium ($Li^+$) is a tiny cation. It pairs perfectly with the small $O^{2-}$ ion, creating a very strong lattice. It cannot stabilize the large superoxide ion.
- Sodium ($Na^+$) is larger and finds a better structural match with the medium-sized peroxide ion ($O_2^{2-}$).
- Potassium ($K^+$), Rubidium, and Cesium are massive cations. They create extremely strong, stable lattice networks when paired with the massive superoxide ion ($O_2^-$). The strong lattice energy provided by this perfect size match is the thermodynamic driving force that stabilizes the otherwise fragile superoxide radical.

Final Answer: Stability is dictated by Lattice Energy size-matching. Large cations ($K^+, Rb^+, Cs^+$) perfectly match the massive size of the superoxide ion ($O_2^-$), creating a highly stable crystal lattice that stabilizes the radical.
Problem 9: Beryllium Chloride Polymerization
Beryllium chloride ($BeCl_2$) exhibits complex structural shifts depending on its physical state. Detail its exact structure in (a) the solid phase, (b) the vapor phase below $1200 \text{ K}$, and (c) the vapor phase above $1200 \text{ K}$. What type of bonding holds the solid phase together?
View Solution
Strategy: Beryllium has only 4 valence electrons in $BeCl_2$ (highly electron-deficient). It will aggressively use empty p-orbitals to accept lone pairs from chlorine atoms to achieve an octet.

Step 1: Solid Phase (Polymer)
In the solid state, $BeCl_2$ exists as a long, continuous polymeric chain. The Beryllium atom is $sp^3$ hybridized. It satisfies its severe electron deficiency by accepting lone pairs from the Chlorine atoms of adjacent $BeCl_2$ molecules. This creates bridging $3c-4e$ coordinate (dative) bonds. Every Be atom is tetrahedrally coordinated to four Cl atoms.

Step 2: Vapor Phase below $1200 \text{ K}$ (Dimer)
When heated, the long polymer chains break apart, but it still seeks electron stability. In the vapor phase below $1200 \text{ K}$, it exists as a dimer ($Be_2Cl_4$). It features a single square-planar-like ring where two Chlorine atoms bridge two Beryllium atoms via coordinate bonds. Beryllium is $sp^2$ hybridized.

Step 3: Vapor Phase above $1200 \text{ K}$ (Monomer)
At extreme temperatures, the thermal energy shatters the remaining coordinate bonds. It exists as an isolated monomer ($BeCl_2$). To minimize electron repulsion, it adopts a perfectly linear geometry, with the central Beryllium atom being purely $sp$ hybridized (and heavily electron-deficient with only 4 valence electrons).

Final Answer: (a) Solid: $sp^3$ Polymeric chain with coordinate Cl bridges. (b) Vapor < 1200K: $sp^2$ Dimer. (c) Vapor > 1200K: $sp$ linear Monomer.
Problem 10: Anomalous Behavior of Lithium (Nitride Formation)
When exposed directly to atmospheric Nitrogen gas ($N_2$) at room temperature, Lithium slowly reacts to form a solid ruby-red compound, whereas Sodium and Potassium remain completely inert. Write the chemical equation for this reaction and explain the thermodynamic factor allowing Lithium to break the triple bond of $N_2$.
View Solution
Strategy: The $N \equiv N$ triple bond is one of the strongest bonds in nature. To break it, the resulting product must release an immense amount of energy (Lattice energy).

Step 1: The Reaction
Lithium reacts with nitrogen to form Lithium Nitride:
$6Li_{(s)} + N_{2(g)} \rightarrow \mathbf{2Li_3N_{(s)}}$

Step 2: The Energy Barrier
The $N \equiv N$ bond dissociation energy is massive ($\approx 941 \text{ kJ/mol}$). For the reaction to be spontaneous at room temperature, the formation of the product must be wildly exothermic to pay back this energy debt.

Step 3: The Lattice Energy Payoff
The Nitride ion ($N^{3-}$) is highly charged. The Lithium ion ($Li^+$) is exceptionally small and has the highest charge density of all alkali metals. When these two ions pack together in a crystal, the Lattice Energy released is phenomenal.
This massive release of lattice energy provides the necessary thermodynamic driving force to pull apart the $N \equiv N$ triple bond. Sodium and Potassium are too large; their lattice energies with $N^{3-}$ are far too low to compensate for breaking the $N_2$ bond.

Final Answer: Equation: $6Li + N_2 \rightarrow 2Li_3N$. Lithium succeeds because its exceptionally small size generates a massive Lattice Energy when pairing with $N^{3-}$, providing the thermodynamic energy required to break the strong $N \equiv N$ triple bond.
Problem 11: Structure of Ice and Density Anomaly
Water is one of the very few substances in the universe where its solid state (ice) is less dense than its liquid state. Detail the exact 3-dimensional molecular geometry and the specific intermolecular forces that force ice to expand. How many nearest neighbors does an oxygen atom have in the ice crystal?
View Solution
Strategy: Evaluate the maximization of hydrogen bonding in the solid state and the resulting physical voids it creates.

Step 1: The Hydrogen Bonding Network
In a single water molecule ($H_2O$), the oxygen atom is $sp^3$ hybridized. It has two hydrogen atoms and two lone pairs. This allows it to act as a donor for two hydrogen bonds and an acceptor for two hydrogen bonds.

Step 2: The Tetrahedral Crystal Lattice
When freezing into Ice (Ih phase), thermal motion stops, and the molecules arrange themselves to maximize hydrogen bonding. Every single Oxygen atom becomes tetrahedrally surrounded by four other Oxygen atoms at a distance of $276 \text{ pm}$.
- It is covalently bonded to 2 Hydrogens.
- It is hydrogen-bonded to 2 Hydrogens from neighboring molecules.
Thus, the coordination number of Oxygen is exactly 4.

Step 3: The Open Cage Structure
Because hydrogen bonds are highly directional and relatively long, forcing every molecule into this rigid, perfect 3D tetrahedral network prevents the molecules from packing closely together. This creates massive, open, hexagonal cage-like voids (empty spaces) throughout the crystal.
When ice melts, this rigid cage collapses, and water molecules slip into the voids, packing closer together and increasing the density.

Final Answer: Oxygen is tetrahedrally coordinated to 4 neighbors via H-bonds. This highly directional bonding forces the molecules apart, creating a rigid, open cage-like structure with massive empty voids, making the solid less dense than the collapsed liquid.
Problem 12: Kinetic Isotope Effect (Heavy Water)
Heavy water ($D_2O$) is used extensively in nuclear reactors as a moderator. Chemically, reaction rates are often significantly slower in $D_2O$ compared to standard water ($H_2O$). Explain the quantum mechanical origin of this "Primary Kinetic Isotope Effect."
View Solution
Strategy: Evaluate the mass difference between Protium and Deuterium and how it affects the Zero-Point Energy of the bonds they form.

Step 1: The Mass Difference
Deuterium ($^2H$ or $D$) has a nucleus containing one proton and one neutron, making it roughly twice as massive as a standard Hydrogen atom ($^1H$ or Protium, just one proton).

Step 2: Zero-Point Energy (ZPE)
In quantum mechanics, a bond behaves like a quantum harmonic oscillator. Even at absolute zero, bonds vibrate with a minimum energy called Zero-Point Energy. ZPE is inversely proportional to the reduced mass of the bonded atoms.
Because Deuterium is heavier, an $O-D$ bond (or $C-D$ bond) has a lower Zero-Point Energy than an $O-H$ bond. It sits deeper in the potential energy well.

Step 3: The Activation Energy Barrier
If a chemical reaction requires breaking that bond in its rate-determining step, the molecule must climb from its ZPE up to the transition state.
Because the $O-D$ bond starts from a deeper energy well, it requires significantly more activation energy to break than the $O-H$ bond. This higher activation energy drastically slows down the reaction rate in $D_2O$.

Final Answer: Deuterium is heavier, giving the $O-D$ bond a lower Zero-Point Energy. It sits deeper in the energy well, requiring higher activation energy to break, which significantly slows down reaction rates (Primary Kinetic Isotope Effect).
Problem 13: Industrial Manufacture of Sodium (Castner-Kellner Cell)
In the Castner-Kellner cell used for manufacturing Sodium Hydroxide, brine ($NaCl$) is electrolyzed. A specific metal is uniquely used as the cathode, which prevents the expected evolution of Hydrogen gas. Identify the cathode material and explain the electrochemical concept of "Overpotential" that dictates this.
View Solution
Strategy: Standard electrolysis of aqueous $NaCl$ yields $H_2$ at the cathode because water reduces easier than $Na^+$. To force $Na^+$ to reduce, we must use a cathode that creates a massive kinetic barrier for hydrogen evolution.

Step 1: The Cathode Material
The Castner-Kellner cell uniquely employs a flowing stream of Liquid Mercury ($Hg$) as the cathode.

Step 2: The Standard Expectation
Thermodynamically, the reduction potential of water ($2H_2O + 2e^- \rightarrow H_2 + 2OH^-, E^{\circ} \approx -0.83 \text{ V}$) is far less negative than the reduction of Sodium ($Na^+ + e^- \rightarrow Na, E^{\circ} = -2.71 \text{ V}$). We expect $H_2$ gas to evolve.

Step 3: The Overpotential Trap
Forming $H_2$ gas bubbles on a smooth, liquid Mercury surface is kinetically extremely difficult. It requires an immense Hydrogen Overpotential (extra activation voltage) to proceed. This overpotential pushes the required voltage for $H_2$ evolution far below $-2.71 \text{ V}$.

Step 4: The Amalgamation Payoff
Because $H_2$ evolution is kinetically blocked, the cell is forced to reduce $Na^+$ ions instead. As soon as $Na$ metal forms, it instantly dissolves into the liquid Mercury to form a highly stable Sodium Amalgam ($Na-Hg$). This alloy formation provides additional thermodynamic driving force, completely bypassing hydrogen evolution.

Final Answer: The cathode is Liquid Mercury ($Hg$). It possesses a massive Hydrogen Overpotential, blocking the reduction of water. This forces the reduction of $Na^+$ ions, which dissolve into the mercury to form stable Sodium Amalgam.
Problem 14: Crown Ethers and Selective Binding
Crown ethers are cyclic organic molecules that can selectively bind alkali metal cations, heavily boosting their solubility in non-polar solvents. Between 18-crown-6 and 15-crown-5, which one is specifically used to bind the Potassium ion ($K^+$) and which binds the Sodium ion ($Na^+$)? Explain the geometric logic.
View Solution
Strategy: Evaluate the internal cavity size of the crown ether ring versus the ionic radius of the target alkali metal.

Step 1: Analyze the Nomenclature
- 18-crown-6: An 18-membered ring containing 6 oxygen atoms pointing inward. It forms a relatively large central cavity (diameter $\approx 2.6 - 3.2 \text{ \AA}$).
- 15-crown-5: A 15-membered ring containing 5 oxygen atoms. It forms a smaller central cavity (diameter $\approx 1.7 - 2.2 \text{ \AA}$).

Step 2: Compare Ionic Radii
- The Potassium ion ($K^+$) is a larger Period 4 cation with an ionic diameter of $\approx 2.66 \text{ \AA}$.
- The Sodium ion ($Na^+$) is a smaller Period 3 cation with an ionic diameter of $\approx 1.90 \text{ \AA}$.

Step 3: The "Lock and Key" Fit
For a crown ether to effectively bind a cation, the ion must fit snugly inside the cavity. If it is too large, it can't enter. If it is too small, it rattles around and cannot simultaneously coordinate with all the oxygen lone pairs.
- The $K^+$ ion perfectly matches the large cavity of 18-crown-6.
- The $Na^+$ ion perfectly matches the smaller cavity of 15-crown-5.

Final Answer: 18-crown-6 specifically binds $K^+$. 15-crown-5 specifically binds $Na^+$. The selectivity is based on a perfect geometric size-match between the crown ether's internal cavity and the cation's ionic radius.
Problem 15: Amphoterism of Beryllium
Beryllium is the only alkaline earth metal that exhibits amphoteric behavior, reacting with both strong acids and strong bases. Write the balanced chemical equation for the reaction of Beryllium metal with boiling aqueous Sodium Hydroxide ($NaOH$), and identify the coordination complex formed.
View Solution
Strategy: Evaluate the diagonal relationship between Beryllium and Aluminum. Like Aluminum, Be dissolves in strong base to form a stable hydroxo-complex while liberating hydrogen gas.

Step 1: The Reactants
Beryllium metal ($Be_{(s)}$) is treated with aqueous $NaOH$ ($NaOH + H_2O$).

Step 2: Formation of the Complex
Because Beryllium has a very small size and high charge density, its hydroxide is amphoteric. In excess strong base, it acts as a Lewis acid, accepting hydroxide ligands to fulfill its octet. Beryllium, being in Period 2, can only accommodate a maximum coordination number of 4 (using one 2s and three 2p orbitals).

Step 3: The Chemical Equation
The metal reduces the hydrogen in water/hydroxide, liberating $H_2$ gas.
$Be_{(s)} + 2NaOH_{(aq)} + 2H_2O_{(l)} \rightarrow \mathbf{Na_2[Be(OH)_4]_{(aq)}} + H_{2(g)} \uparrow$

Step 4: Identification
The complex anion is $[Be(OH)_4]^{2-}$. This is the Tetrahydroxoberyllate(II) ion. (Older texts may simply write the salt as Sodium Beryllate, $Na_2BeO_2$, but the complex ion is the accurate aqueous representation).

Final Answer: $Be + 2NaOH + 2H_2O \rightarrow \mathbf{Na_2[Be(OH)_4]} + H_2 \uparrow$. The complex formed is Sodium Tetrahydroxoberyllate(II), resulting from Be's ability to act as a Lewis acid in strong base.
Problem 16: The Diagonal Relationship (Decomposition of Nitrates)
When standard alkali metal nitrates (like $NaNO_3$ or $KNO_3$) are heated, they decompose to yield metal nitrites and oxygen gas. However, when Lithium Nitrate ($LiNO_3$) is heated, it undergoes a far more severe decomposition. Write the balanced equation for the decomposition of $LiNO_3$ and explain the diagonal relationship causing this anomaly.
View Solution
Strategy: Evaluate the polarizing power of $Li^+$. Compare its behavior to its diagonal partner in Group 2, Magnesium.

Step 1: Standard Alkali Decomposition
Large alkali metals have low polarizing power. They cannot destabilize the nitrate ion fully:
$2KNO_3 \xrightarrow{\Delta} 2KNO_2 + O_2 \uparrow$

Step 2: Lithium's Anomaly
Lithium is exceptionally small. Due to its high polarizing power, it heavily distorts the electron cloud of the $NO_3^-$ ion, breaking the internal $N-O$ bonds completely under heat. This behavior perfectly mimics Magnesium (its diagonal partner), because their charge-to-size ratios (ionic potentials) are nearly identical.

Step 3: The Equation
Like alkaline earth metals, Lithium nitrate decomposes all the way down to the metal oxide, releasing toxic brown Nitrogen Dioxide gas ($NO_2$) and Oxygen.
$4LiNO_3 \xrightarrow{\Delta} \mathbf{2Li_2O} + 4NO_2 \uparrow + O_2 \uparrow$

Final Answer: $4LiNO_3 \rightarrow 2Li_2O + 4NO_2 + O_2$. Lithium mimics Magnesium (Diagonal Relationship). Its exceptionally high polarizing power deeply destabilizes the $NO_3^-$ anion, forcing decomposition completely down to the Oxide rather than the Nitrite.
Problem 17: Production of Syngas (Water-Gas Shift Reaction)
Synthesis gas (Syngas) is produced by passing steam over red-hot coke ($1270 \text{ K}$). To maximize the yield of pure Hydrogen gas from this mixture, the "Water-Gas Shift Reaction" is employed. Write the chemical equation for this shift reaction, specify the catalyst used, and explain how the carbon monoxide is subsequently removed.
View Solution
Strategy: Track the industrial purification of Hydrogen. Syngas is a mixture of $CO$ and $H_2$. We must convert the toxic $CO$ into something easily removable while generating more $H_2$.

Step 1: Initial Syngas Production
$C_{(s)} + H_2O_{(g)} \xrightarrow{1270 \text{ K}} CO_{(g)} + H_{2(g)}$ (This mixture is Syngas).

Step 2: The Water-Gas Shift Reaction
To get rid of the $CO$ and maximize hydrogen, more steam is added, and the mixture is passed over a catalyst at $\approx 673 \text{ K}$. The $CO$ is oxidized by the steam.
$CO_{(g)} + H_2O_{(g)} \xrightarrow{\mathbf{Fe_2O_3 / Cr_2O_3}} CO_{2(g)} + H_{2(g)}$
The catalyst is Iron(III) oxide promoted with Chromium(III) oxide.

Step 3: Removal of Carbon Dioxide
The mixture now contains $CO_2$ and a massive amount of $H_2$. To isolate the hydrogen, the gas mixture is scrubbed by passing it through a solution of Sodium Arsenite (or passed through water under high pressure), which preferentially dissolves the $CO_2$, leaving behind pure $H_2$ gas.

Final Answer: Eq: $CO + H_2O \xrightarrow{Fe_2O_3/Cr_2O_3} CO_2 + H_2$. Catalyst is Iron Chromate / $Fe_2O_3$. The $CO_2$ is subsequently removed by scrubbing the gas mixture with a Sodium Arsenite solution.
Problem 18: Setting of Plaster of Paris
Plaster of Paris (POP) has the formula $CaSO_4 \cdot \frac{1}{2}H_2O$. When mixed with water, it sets into a hard solid mass (Gypsum). Write the hydration equation. Furthermore, if POP is heated strictly above $393 \text{ K}$, what is formed and what are its physical properties?
View Solution
Strategy: Track the water of crystallization. POP is a hemihydrate. Gypsum is a dihydrate. Overheating strips all water.

Step 1: The Setting Reaction
When mixed with an adequate amount of water, POP absorbs water to re-form the interlocking crystalline structure of Gypsum, expanding slightly and setting into a hard solid within 10-15 minutes.
$CaSO_4 \cdot \frac{1}{2}H_2O + 1\frac{1}{2} H_2O \rightarrow \mathbf{CaSO_4 \cdot 2H_2O}$ (Gypsum)

Step 2: Overheating (Dead Burnt Plaster)
POP is prepared by carefully heating Gypsum to $393 \text{ K}$. If the temperature exceeds $393 \text{ K}$, the remaining half-molecule of water of crystallization is driven off.
$CaSO_4 \cdot \frac{1}{2}H_2O \xrightarrow{> 393 \text{ K}} \mathbf{CaSO_4} + \frac{1}{2}H_2O \uparrow$

Step 3: Properties
The resulting anhydrous Calcium Sulfate is called "Dead Burnt Plaster". It completely loses its ability to set with water, rendering it useless for casting or medical casts.

Final Answer: Setting Eq: $CaSO_4 \cdot \frac{1}{2}H_2O + \frac{3}{2}H_2O \rightarrow CaSO_4 \cdot 2H_2O$. Heating above $393 \text{ K}$ yields anhydrous $CaSO_4$ known as Dead Burnt Plaster, which permanently loses its ability to set with water.
Problem 19: Preparation of Hydrogen Peroxide (Auto-oxidation)
The modern industrial synthesis of Hydrogen Peroxide ($H_2O_2$) avoids electrolysis. Instead, it relies on the continuous cyclic auto-oxidation of an organic compound. Name the specific organic compound used, and outline the oxidation and reduction steps of the cycle.
View Solution
Strategy: Recall the anthraquinone process. It is a brilliant atom-economical cycle where only $H_2$ and $O_2$ are consumed to make $H_2O_2$.

Step 1: The Starting Material
The process utilizes 2-ethylanthraquinol (a derivative of anthraquinone).

Step 2: Auto-Oxidation Step
Air (Oxygen, $O_2$) is bubbled through a solution of 2-ethylanthraquinol. The oxygen abstracts the two hydroxyl hydrogens from the quinol. This yields a $1\%$ solution of Hydrogen Peroxide ($H_2O_2$) and converts the organic molecule into 2-ethylanthraquinone.
$2\text{-ethylanthraquinol} + O_2 \rightarrow H_2O_2 + 2\text{-ethylanthraquinone}$

Step 3: The Reduction (Recycling) Step
The $H_2O_2$ is extracted with water. The remaining 2-ethylanthraquinone is then passed over a Palladium catalyst and reacted with Hydrogen gas ($H_2$). This reduces the quinone back into the starting 2-ethylanthraquinol, completing the loop.
$2\text{-ethylanthraquinone} + H_2 \xrightarrow{Pd} 2\text{-ethylanthraquinol}$

Final Answer: The compound is 2-ethylanthraquinol. Auto-oxidation with $O_2$ yields $H_2O_2$ and 2-ethylanthraquinone. Catalytic reduction with $H_2/Pd$ converts the quinone back to the quinol, allowing a continuous, closed-loop industrial cycle.
Problem 20: Clark's Method for Temporary Hardness
Temporary hardness of water is caused by Magnesium and Calcium bicarbonates. While boiling easily removes this, large-scale municipal water treatment uses "Clark's Method." What specific chemical is added in Clark's method? Write the balanced chemical equations proving how it precipitates both Calcium and Magnesium.
View Solution
Strategy: Temporary hardness is due to soluble bicarbonates. We must add a calculated amount of a specific base to convert them into insoluble carbonates or hydroxides.

Step 1: The Reagent
Clark's method involves adding a calculated amount of Slaked Lime ($Ca(OH)_2$) to the hard water.

Step 2: Reaction with Calcium Bicarbonate
The $OH^-$ from the slaked lime neutralizes the acidic bicarbonate ion ($HCO_3^-$), converting it into the carbonate ion ($CO_3^{2-}$). This instantly reacts with the Calcium ions to form a highly insoluble precipitate.
$Ca(HCO_3)_2 + Ca(OH)_2 \rightarrow \mathbf{2CaCO_3 \downarrow} + 2H_2O$

Step 3: Reaction with Magnesium Bicarbonate
Magnesium reacts similarly, but Magnesium Carbonate is slightly soluble. With excess $OH^-$, it forms Magnesium Hydroxide, which is incredibly insoluble and drops out of solution alongside the Calcium Carbonate.
$Mg(HCO_3)_2 + 2Ca(OH)_2 \rightarrow \mathbf{2CaCO_3 \downarrow + Mg(OH)_2 \downarrow} + 2H_2O$

Final Answer: The reagent is calculated Slaked Lime ($Ca(OH)_2$). It neutralizes the soluble bicarbonates, precipitating them out as highly insoluble Calcium Carbonate ($CaCO_3$) and Magnesium Hydroxide ($Mg(OH)_2$), softening the water.
Problem 21: Dihedral Angles in Hydrogen Peroxide
Hydrogen peroxide ($H_2O_2$) famously adopts a non-planar "open book" structure. However, X-ray crystallography reveals that the dihedral angle (the angle between the two "pages" of the book) shrinks from $111.5^{\circ}$ in the gas phase down to $90.2^{\circ}$ in the solid phase. Explain the physical forces driving this structural compression in the solid state.
View Solution
Strategy: Evaluate the dominant forces in both phases. Gas phase is ruled by internal electron repulsion. Solid phase is ruled by external lattice packing and hydrogen bonding.

Step 1: Gas Phase (Internal Repulsion)
In the gas phase, the molecule is isolated. The primary force dictating the geometry is the severe lone-pair lone-pair repulsion between the two adjacent oxygen atoms. To minimize this repulsive interaction, the molecule twists along the $O-O$ bond, opening the dihedral angle wide to $111.5^{\circ}$.

Step 2: Solid Phase (External Hydrogen Bonding)
When $H_2O_2$ freezes into a solid crystal lattice, the molecules are forced closely together. $H_2O_2$ is an exceptional hydrogen-bonding molecule. To maximize the strength and number of intermolecular hydrogen bonds with its neighbors in the lattice, the molecule must distort its shape.

Step 3: The Compromise
The thermodynamic energy gained by forming a tight, highly ordered hydrogen-bonded crystal lattice vastly outcompetes the internal lone-pair repulsion penalty. The molecule is physically compressed, shrinking the dihedral angle down to $90.2^{\circ}$ to achieve optimal crystal packing.

Final Answer: In the gas phase, the angle is wide to minimize internal lone-pair repulsion. In the solid phase, the angle is compressed to $90.2^{\circ}$ to maximize external intermolecular hydrogen bonding and optimize crystal lattice packing.
Problem 22: Classification of Hydrides
Hydrogen forms three distinct classes of hydrides: Saline, Covalent (Molecular), and Interstitial (Metallic). Classify $NaH$, $PH_3$, and $LaH_2$, describing the nature of the hydrogen atom and electrical conductivity in each.
View Solution
Strategy: The nature of the hydride depends entirely on the electronegativity of the element Hydrogen is bonded to.

1. Sodium Hydride ($NaH$): Saline (Ionic) Hydride
Sodium is highly electropositive. It transfers an electron completely to Hydrogen, forming the discrete Hydride anion ($H^-$). It forms a solid ionic lattice. It is an insulator as a solid, but conducts electricity when molten (liberating $H_2$ gas at the anode).

2. Phosphine ($PH_3$): Covalent (Molecular) Hydride
Phosphorus is a p-block non-metal. Hydrogen shares electrons to form discrete covalent bonds. It exists as separate molecules held by weak van der Waals forces, making it a gas. It does not conduct electricity in any state. (Specifically, it is an electron-precise molecular hydride with a lone pair).

3. Lanthanum Hydride ($LaH_2$): Interstitial (Metallic) Hydride
Lanthanum is a d/f-block transition metal. The tiny hydrogen atoms occupy the interstitial voids in the metal lattice. They are often non-stoichiometric (e.g., $LaH_{2.87}$). Because the metallic lattice is largely intact and the "sea of electrons" remains, it conducts electricity strongly, though slightly less than the parent metal.

Final Answer: $NaH$ = Ionic (conducts only when molten, contains $H^-$). $PH_3$ = Molecular (insulator, covalent bonds). $LaH_2$ = Interstitial (metallic conductor, H atoms in lattice voids).
Problem 23: Reaction of Beryllium with Halogens
Beryllium chloride ($BeCl_2$) cannot be prepared by the direct combination of Beryllium and Chlorine gas, nor by reacting Beryllium oxide with $HCl$. Explain the specialized industrial process involving Carbon that is mandatory to synthesize pure $BeCl_2$.
View Solution
Strategy: Beryllium oxide ($BeO$) is exceptionally stable and unreactive (highly covalent lattice). Standard acids or halogens cannot break it. A powerful reducing agent must be coupled with the halogen.

Step 1: The Stability of BeO
Beryllium metal instantly forms a tough, impenetrable, passive oxide layer ($BeO$) upon exposure to air. This layer is so stable that it resists direct halogenation and acid attack.

Step 2: The Carbochlorination Process
To synthesize $BeCl_2$, the Beryllium oxide is intimately mixed with Carbon (coke) and heated to a very high temperature ($873-1073 \text{ K}$) while a stream of dry Chlorine gas ($Cl_2$) is passed over it.

Step 3: The Synergy of the Reaction
The Carbon acts as a powerful reducing agent, ripping the oxygen away from the Beryllium to form Carbon Monoxide ($CO$). Simultaneously, the highly reactive Chlorine atoms bond with the naked Beryllium atoms.
$BeO_{(s)} + C_{(s)} + Cl_{2(g)} \xrightarrow{\Delta} \mathbf{BeCl_{2(g)} + CO_{(g)} \uparrow}$

Final Answer: $BeO$ is too stable for direct reaction. It requires Carbochlorination, where Carbon is used simultaneously with $Cl_2$ at high heat to reduce the stable oxide to $CO$, allowing the Chlorine to capture the Beryllium.
Problem 24: Complexation of Alkaline Earth Metals
Chlorophyll is the green pigment in plants responsible for photosynthesis. It is a massive macrocyclic coordination complex. Which specific alkaline earth metal sits at the absolute center of the chlorophyll porphyrin ring, and why is this specific metal evolutionarily suited for this role?
View Solution
Strategy: Identify the biological role of s-block elements. Beryllium is toxic, Calcium is in bones, Magnesium is in chlorophyll.

Step 1: Identify the Metal
The central atom in the chlorin (porphyrin-like) ring of chlorophyll is Magnesium ($Mg^{2+}$).

Step 2: The Evolutionary Suitability
1. Coordination Chemistry: While most s-block metals form weak complexes, $Mg^{2+}$ has a relatively high charge density (small size, $+2$ charge). This allows it to strongly coordinate with the four Nitrogen atoms of the pyrrole rings, locking the complex together.

Step 3: Electronic Fine-Tuning
Unlike transition metals (like $Fe^{2+}$ in hemoglobin) which have d-electrons that actively participate in redox reactions, $Mg^{2+}$ has a stable noble gas core ($[Ne]$). It does not easily undergo oxidation or reduction. Its role is strictly to hold the massive ring rigid and fine-tune the electron cloud of the surrounding organic porphyrin ring, allowing the ring itself to efficiently capture specific wavelengths of visible light (red and blue) for photosynthesis without the metal interfering in the electron transfer chain.

Final Answer: The metal is Magnesium ($Mg^{2+}$). It is chosen because its high charge density secures the ring, but its lack of d-electrons ensures it does not undergo unwanted redox reactions, leaving the organic ring to handle light absorption perfectly.
Problem 25: Master Identification Cascade
A white solid A is strongly heated, yielding a solid B and a suffocating gas C. Solid B reacts violently with water to form a milky suspension D. Passing gas C through the milky suspension D turns it completely clear to form a soluble compound E. Boiling compound E precipitates solid A again. Deduce the exact formulas of A, B, C, D, and E.
View Solution
Strategy: This is the classic qualitative analysis cycle of Calcium Carbonate. Follow the thermal decomposition and aqueous chemistry step-by-step.

Step 1: Thermal Decomposition
Heating a white solid to yield a gas and a solid residue points to a carbonate. Calcium carbonate decomposes under intense heat.
$CaCO_3 \xrightarrow{\Delta} CaO + CO_2 \uparrow$
A = Calcium Carbonate ($CaCO_3$).
B = Quicklime ($CaO$).
C = Carbon Dioxide ($CO_2$).

Step 2: Reaction with Water
Quicklime reacts violently (highly exothermic) with water to form slaked lime, which is slightly soluble and forms a milky suspension (milk of lime).
$CaO + H_2O \rightarrow Ca(OH)_2$
D = Calcium Hydroxide suspension ($Ca(OH)_2$).

Step 3: Passing Gas C into D
Passing $CO_2$ through limewater initially turns it milky due to $CaCO_3$ precipitation. Passing excess $CO_2$ converts the insoluble carbonate into soluble calcium bicarbonate, turning the solution perfectly clear.
$CaCO_3 + H_2O + CO_2 \rightarrow Ca(HCO_3)_2$
E = Calcium Bicarbonate ($Ca(HCO_3)_2_{(aq)}$).

Step 4: Boiling E
Boiling the soluble bicarbonate destroys the temporary hardness, driving off $CO_2$ and precipitating $CaCO_3$ (Compound A) back out.
$Ca(HCO_3)_2 \xrightarrow{\Delta} CaCO_3 \downarrow + H_2O + CO_2 \uparrow$

Final Answer: A = $CaCO_3$. B = $CaO$. C = $CO_2$. D = $Ca(OH)_2$. E = $Ca(HCO_3)_2$.

Mastering the s-Block & Hydrogen

Congratulations on conquering these 25 ultra-challenging problems! While the s-block elements are often considered "simple" metals, their chemistry in JEE Advanced requires profound thermodynamic insight. You must constantly weigh the polarizing power of tiny cations like Lithium and Beryllium against the massive lattice energies required to stabilize complex anions like peroxides, superoxides, and nitrides. Keep practicing your anomaly deductions and diagonal relationships, and visit Chemca.in for more elite masterclasses!

Powered by

๐Ÿ“š Also Read

Lecture Notes

No comments:

Post a Comment

Featured Post

Most Important Name Reactions in Organic Chemistry | Chemca