Complete Detailed Solutions · 2018-19 (BS-CH-101)
(i) Which of the following is the expression of Schrödinger wave equation?
Answer: (b) ∇²Ψ + (8π²m/h²)(E - V)Ψ = 0
Explanation: This is the time-independent Schrödinger wave equation in 3D. ∇² is the Laplacian operator, m is mass of electron, h is Planck's constant, E is total energy, and V is potential energy.
(ii) All living body is the example of
Answer: (a) open system
Explanation: Living organisms exchange both energy (heat) and matter (food, waste, oxygen, carbon dioxide) with their surroundings.
(iii) The correct order of bond dissociation energy is
Answer: (b) O₂²⁻ < O₂⁻ < O₂ < O₂⁺
Explanation: Bond order (BO) determines bond dissociation energy. BO of O₂ = 2, O₂⁺ = 2.5, O₂⁻ = 1.5, O₂²⁻ = 1. Higher BO means stronger bond.
(iv) What is the hybridization of XeF₄?
Answer: (d) sp³d²
Explanation: Xe has 8 valence electrons. It forms 4 single bonds with F atoms and has 2 lone pairs. Total electron domains = 4 (bonding) + 2 (lone pairs) = 6. This corresponds to sp³d² hybridization (square planar geometry).
(v) (2R, 4S)-2, 4-dichloropentane and (2S, 4R)-2, 4-dichloropentane are
Answer: (c) identical
Explanation: This molecule has a plane of symmetry passing through C-3. The (2R, 4S) and (2S, 4R) isomers are superimposable mirror images; thus, it is a single meso compound.
(vi) In electrochemical corrosion
Answer: (a) oxidation occurs at the anode
Explanation: In any electrochemical cell, including corrosion cells, oxidation (loss of electrons) always occurs at the anode, leading to metal dissolution (corrosion).
(vii) Which of these exhibit fluorescence?
Answer: (c) CaF₂
Explanation: Fluorite (CaF₂) is known to exhibit fluorescence (the phenomenon was named after this mineral).
(viii) Unit of frequency is
Answer: (c) hertz
Explanation: Hertz (Hz) is the standard SI unit of frequency, representing one cycle per second.
(ix) Which of the following is not part of a polarimeter?
Answer: (b) Diffraction grading
Explanation: A polarimeter contains a Nicol prism (polarizer/analyzer) and a simple tube (sample tube). A diffraction grating is used in spectrometers, not polarimeters.
(x) The nucleus which will not show any peak in the NMR spectrum is
Answer: (c) ¹⁶O
Explanation: NMR requires a nucleus with a non-zero nuclear spin (I > 0). ¹⁶O has an even number of protons (8) and even number of neutrons (8), so its spin I = 0, making it NMR inactive.
(xi) Which of the following is true for the Galvanic cell?
Answer: (d) Chemical energy is converted to Electrical energy.
Explanation: A galvanic (voltaic) cell uses a spontaneous chemical redox reaction to generate electrical energy (current).
(xii) van der Waals type of bond is formed by
Answer: (d) weak electrostatic force of interaction among fluctuating dipoles.
Explanation: London dispersion forces (a type of van der Waals force) arise from temporary, fluctuating dipoles in molecules inducing dipoles in neighboring molecules.
(xiii) Silicon doped with gallium forms
Answer: (a) p-type semiconductor
Explanation: Silicon is a Group 14 element. Gallium is a Group 13 element. Doping Si with Ga creates electron deficiencies (holes), resulting in a p-type semiconductor.
(a) Chemical Potential (μ):
The chemical potential of a component in a mixture is defined as the partial molar free energy of that component. Mathematically, it is the change in the Gibbs free energy of the system when one mole of the substance is added to the system at constant temperature, pressure, and keeping the amounts of all other components constant.
Formula: μᵢ = (∂G / ∂nᵢ)_(T,P,n_j)
(b) Relation of EMF of cell with ΔG and ΔH:
In a reversible galvanic cell, the electrical work done is equal to the decrease in Gibbs free energy.
ΔG = -nFE --- (Equation 1)
where 'n' is the number of moles of electrons transferred, 'F' is the Faraday constant, and 'E' is the EMF of the cell.
From the Gibbs-Helmholtz equation:
ΔG = ΔH + T[∂(ΔG)/∂T]_P
Substitute ΔG = -nFE into the derivative:
[∂(-nFE)/∂T]_P = -nF(∂E/∂T)_P
where (∂E/∂T)_P is the temperature coefficient of the EMF.
Now, substituting back into the Gibbs-Helmholtz equation:
-nFE = ΔH + T[-nF(∂E/∂T)_P]
-nFE = ΔH - nFT(∂E/∂T)_P
Rearranging for ΔH:
ΔH = -nFE + nFT(∂E/∂T)_P
(a) Molecular Energy Level Diagram for O₂:
Oxygen (O) has 8 electrons, so O₂ has 16 electrons. The order of energy levels for molecules like O₂ and F₂ is:
σ1s < σ*1s < σ2s < σ*2s < σ2pz < (π2px = π2py) < (π*2px = π*2py) < σ*2pz
Filling the 16 electrons:
(σ1s)² (σ*1s)² (σ2s)² (σ*2s)² (σ2pz)² (π2px)² (π2py)² (π*2px)¹ (π*2py)¹
(b) Paramagnetic behaviour of O₂ as evidence of VBT failure:
According to Valence Bond Theory (VBT), the Lewis structure of O₂ features a double bond with all electrons paired (::O=O::). If all electrons are paired, the molecule should be diamagnetic.
However, experimentally, liquid oxygen is strongly paramagnetic (it is attracted to a magnetic field).
Molecular Orbital (MO) Theory successfully explains this. As seen in the electron configuration derived above, there are two unpaired electrons in the degenerate anti-bonding π* orbitals (π*2px¹ and π*2py¹). According to Hund's rule, these electrons occupy separate orbitals with parallel spins. The presence of these unpaired electrons gives O₂ its paramagnetic property, highlighting a major success of MO theory over VBT.
The total energy E of a quantum mechanical system is the sum of its Kinetic Energy (K) and Potential Energy (V):
E = K + V
In classical mechanics, Kinetic Energy (K) is given by p² / 2m, where p is momentum. Thus:
E = p²/2m + V
In quantum mechanics, observables are replaced by operators acting on a wave function Ψ. The momentum operator is:
p = -i(h/2π)∇
Squaring the momentum operator:
p² = (-i(h/2π)∇) * (-i(h/2π)∇) = - (h²/4π²)∇²
Now, substituting the p² operator into the kinetic energy term:
K = p²/2m = (-h²/4π²)∇² / 2m = -(h² / 8π²m)∇²
Now construct the Hamiltonian operator (H), which represents total energy (H = K + V):
H = -(h² / 8π²m)∇² + V
The time-independent Schrödinger equation states that applying the Hamiltonian operator to the wave function Ψ yields the total energy E multiplied by Ψ:
HΨ = EΨ
Substitute H into the equation:
(-(h² / 8π²m)∇² + V)Ψ = EΨ
Rearranging the terms on the left side gives the required proof:
(V - (h² / 8π²m)∇²)Ψ = EΨ
(a) Entropy of mixing of ideal gases ΔS_mix > 0:
When two or more ideal gases are mixed at constant temperature and pressure, they spontaneously expand into each other's volume. Since the process is spontaneous and increases the disorder (randomness) of the system, the entropy must increase.
Mathematically, for a mixture of ideal gases, the entropy of mixing is given by:
ΔS_mix = -R Σ (nᵢ ln xᵢ)
where nᵢ is the number of moles of gas i, and xᵢ is its mole fraction. Since the mole fraction xᵢ is always a fraction less than 1 (0 < xᵢ < 1), the natural logarithm ln(xᵢ) is always a negative value.
Therefore, -R multiplied by a negative summation yields a positive value. Hence, ΔS_mix > 0.
(b) Physical significance of free energy change (ΔG):
The change in Gibbs free energy (ΔG) represents the maximum amount of non-expansion (useful) work that can be extracted from a thermodynamically closed system at constant temperature and pressure.
- If ΔG < 0 (negative), the process is spontaneous (exergonic) and can do useful work.
- If ΔG > 0 (positive), the process is non-spontaneous (endergonic) and requires work to be driven.
- If ΔG = 0, the system is in a state of equilibrium.
(a) Specific Rotation:
Specific rotation [α] is a characteristic property of a chiral substance. It is defined as the angle of rotation (in degrees) of the plane of polarized light produced by a solution of concentration 1 g/mL and a path length of 1 decimeter (10 cm) at a specific temperature and wavelength (usually the sodium D-line).
Formula: [α] = α / (c × l)
(b) Necessary and sufficient condition for a molecule to be optically active:
The necessary and sufficient condition is that the molecule must be chiral. A chiral molecule is asymmetric or dissymmetric, meaning it lacks any alternating axis of symmetry (S_n), which includes lacking a plane of symmetry (σ) and a center of inversion (i). It must be non-superimposable on its mirror image.
(c) Optical activity of H₃C-CH=C=CH-CH₃ (2,3-pentadiene):
This molecule is an allene. In allenes (C=C=C), the central carbon is sp hybridized, and the two terminal carbons are sp² hybridized. The two π bonds are perpendicular to each other. As a result, the substituents on one terminal carbon lie in a plane perpendicular to the substituents on the other terminal carbon.
Because both terminal carbons have two different groups attached (an H and a CH₃), the entire molecule lacks a plane of symmetry and a center of symmetry. It exhibits axial chirality (it has a chiral axis rather than a chiral center) and exists as non-superimposable mirror images. Hence, it is optically active.
(a) Hund's Rule and Pauli Exclusion Principle:
- Hund's Rule of Maximum Multiplicity: In a set of degenerate orbitals (like the three p orbitals), electrons will fill them singly with parallel spins before pairing occurs. This maximizes total spin and minimizes electron-electron repulsion.
- Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers (n, l, ml, ms). Therefore, an orbital can hold a maximum of two electrons, and they must have opposite spins.
- Electronic configuration of Fe (Z=26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ (or [Ar] 3d⁶ 4s²).
(b) Effective nuclear charge (Z_eff) of 4s electrons of Fe (Z=26):
Using Slater's rules for an electron in the ns/np group (here, 4s):
Groupings: (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p)
For a 4s electron, the other electrons contribute to shielding (S) as follows:
- Electrons in the same group (4s): 1 electron × 0.35 = 0.35
- Electrons in (n-1) group (3s, 3p, 3d): (2 + 6 + 6) = 14 electrons × 0.85 = 11.90
- Electrons in (n-2) and lower groups (1s, 2s, 2p): (2 + 2 + 6) = 10 electrons × 1.00 = 10.00
Total Shielding Constant (S) = 0.35 + 11.90 + 10.00 = 22.25
Z_eff = Z - S = 26 - 22.25 = 3.75
(c) Pauling's Scale of Electronegativity:
Linus Pauling based his electronegativity scale on bond dissociation energies. He proposed that the difference in electronegativity between two atoms A and B is related to the extra bond energy caused by ionic resonance stabilization in the heteronuclear A-B bond compared to the average of A-A and B-B homonuclear bonds.
|χ_A - χ_B| = 0.102 × √(Δ_AB)
where Δ_AB = E_(A-B) - √(E_(A-A) × E_(B-B)) in kJ/mol. Fluorine is arbitrarily assigned a value of 4.0.
(d) Why Electron Affinity of Cl > F:
Fluorine is very small, leading to high electron density in its 2p subshell. When an incoming electron is added to F, it experiences strong inter-electronic repulsion. Chlorine is larger (3p subshell), so the added electron feels much less repulsion. Thus, Cl releases more energy (higher electron affinity) when gaining an electron than F does.
(e) Melting point of BeCl₂ vs BaCl₂:
BaCl₂ has a higher melting point than BeCl₂. According to Fajan's rules, Be²⁺ is very small and has a high charge density, giving it a high polarizing power. It severely distorts the electron cloud of Cl⁻, giving BeCl₂ significant covalent character (it is a covalent polymer in solid state). Ba²⁺ is much larger, with low polarizing power, so BaCl₂ is primarily ionic. Ionic compounds have strong lattice energies and much higher melting points than covalent compounds.
(f) Hybridization and CFSE of [Fe(H₂O)₆]²⁺ and [Fe(H₂O)₆]³⁺:
H₂O is a weak field ligand, so it forms high-spin (outer orbital) complexes in both cases, utilizing the outer 4d orbitals. The hybridization for both is sp³d² (octahedral).
- [Fe(H₂O)₆]²⁺: Fe²⁺ is a d⁶ system. In a weak octahedral field (high spin), electrons distribute as t₂g⁴ eg².
CFSE = [(-0.4 × 4) + (0.6 × 2)] Δo = -1.6 + 1.2 = -0.4 Δo.
- [Fe(H₂O)₆]³⁺: Fe³⁺ is a d⁵ system. In a weak octahedral field (high spin), electrons distribute as t₂g³ eg².
CFSE = [(-0.4 × 3) + (0.6 × 2)] Δo = -1.2 + 1.2 = 0 Δo.
(a) Corrosion and its Types:
- Definition: Corrosion is the gradual destruction or deterioration of a metal by chemical or electrochemical reaction with its environment.
- Types of Corrosion:
1. Dry/Chemical Corrosion: Direct reaction of atmospheric gases (O₂, halogens, H₂S) with metal surfaces without an aqueous phase.
2. Wet/Electrochemical Corrosion: Occurs in the presence of an electrolyte (moisture) where local anodic and cathodic areas are formed. Most common type (e.g., rusting of iron).
3. Galvanic Corrosion: When two dissimilar metals are in contact in an electrolyte, the more active metal (anode) corrodes rapidly.
4. Pitting Corrosion: Localized corrosion leading to the formation of deep holes or pits on the metal surface.
5. Crevice Corrosion: Intensive localized corrosion occurring within crevices or shielded areas where a stagnant solution accumulates.
(b) Hardness of Water:
- Meaning: Hardness of water is the property that prevents it from forming lather with soap, primarily caused by the presence of dissolved calcium (Ca²⁺) and magnesium (Mg²⁺) salts.
- Why it fails to form lather: Soap consists of sodium or potassium salts of higher fatty acids (like sodium stearate). When added to hard water, the Ca²⁺ and Mg²⁺ ions react with the soap to form insoluble precipitates (scum/curd) of calcium/magnesium stearate, rendering the soap ineffective until all hardness ions are precipitated.
2 C₁₇H₃₅COONa + Ca²⁺ → (C₁₇H₃₅COO)₂Ca↓ + 2 Na⁺
- Types of Hardness:
1. Temporary Hardness (Carbonate Hardness): Caused by dissolved bicarbonates of Ca and Mg. Can be removed by simple boiling.
2. Permanent Hardness (Non-Carbonate Hardness): Caused by chlorides and sulfates of Ca and Mg. Cannot be removed by boiling; requires chemical treatment (e.g., Zeolite process, lime-soda process).
(c) Potentiometric Titration (NaCl and AgNO₃):
Potentiometric titration is a volumetric method in which the potential between two electrodes (a reference electrode and an indicator electrode) is measured as a function of the added titrant volume.
For the precipitation titration of NaCl with AgNO₃:
Ag⁺(aq) + Cl⁻(aq) → AgCl(s)↓
- Electrodes: Indicator electrode = Silver wire (Ag); Reference electrode = Calomel electrode (isolated by a salt bridge to prevent Cl⁻ contamination).
- Principle: The potential of the Ag electrode depends on the concentration of Ag⁺ ions in the solution, governed by the Nernst equation: E = E° + (0.0591)log[Ag⁺].
- Before the equivalence point, [Ag⁺] is very low due to the common ion effect of excess Cl⁻. Potential changes slowly.
- At the equivalence point, a tiny drop of AgNO₃ causes a massive, sharp jump in [Ag⁺] concentration, resulting in a steep jump in the measured potential (E).
- Curve: A plot of EMF vs Volume of AgNO₃ yields an S-shaped curve. The inflection point (the steepest part of the curve) exactly indicates the equivalence point. Taking the first derivative (ΔE/ΔV) makes identifying the endpoint extremely precise.
(a) Stereoisomers of butane-2,3-diol:
Butane-2,3-diol has two chiral centers with identical substitution. It has 3 stereoisomers:
1. (2R, 3R)-butane-2,3-diol: Optically active.
2. (2S, 3S)-butane-2,3-diol: Optically active (enantiomer of the first).
3. meso-butane-2,3-diol (2R, 3S): Optically inactive. It contains a plane of symmetry that divides the molecule into two mirror-image halves, causing internal compensation of optical rotation.
(b) Fischer Projections:
- (2R, 3R)-2,3-dibromobutanedioic acid: Vertical chain with COOH at top and bottom. At C2, Br is on the right, H is on the left. At C3, Br is on the right, H is on the left.
- S-2-Hydroxy-2-phenylpropanoic acid: Vertical chain with COOH at top, CH₃ at bottom. At C2 (chiral center), OH is on the left, Phenyl (Ph) group is on the right (priorities: OH > COOH > Ph > CH₃, arranging for S configuration).
(c) Enantiomers vs Diastereomers:
- Enantiomers: Stereoisomers that are perfect, non-superimposable mirror images of each other. They have identical physical properties (BP, MP, solubility) except for the direction they rotate plane-polarized light.
- Diastereomers: Stereoisomers that are NOT mirror images of each other. They have different physical and chemical properties. They occur in molecules with multiple chiral centers where some, but not all, centers are inverted.
(d) SN1 Mechanism and Partial Racemization:
The SN1 mechanism proceeds via a planar carbocation intermediate. Theoretically, the nucleophile can attack this planar carbocation from either face with equal probability, leading to a 50:50 racemic mixture. However, in practice, the departing leaving group remains briefly associated with the carbocation as an "intimate ion pair." This leaving group partially blocks the front face, making back-side attack slightly more favorable. Thus, there is net inversion along with racemization, termed "partial racemization."
(e) Halogens are ortho-para orienting but deactivating:
Halogens attached to a benzene ring possess two opposing effects:
1. -I Effect (Inductive): Halogens are highly electronegative and withdraw electron density from the ring through the sigma bond, making the ring less reactive (deactivating) towards electrophilic attack than benzene.
2. +R Effect (Resonance): Halogens have lone pairs that can be delocalized into the ring via resonance. This +R effect specifically increases electron density at the ortho and para positions relative to the meta position.
Because the -I effect is stronger than the +R effect overall, halogens are net deactivating. However, because the +R effect directs the incoming electrophile to the ortho and para positions, they are ortho-para orienting.
(a) Elements of Symmetry:
1. Rotational axis of symmetry (Cn): An axis around which a rotation by 360°/n results in a molecule indistinguishable from the original. Example: H₂O has a C₂ axis.
2. Plane of symmetry (σ): A plane that divides the molecule into two halves that are mirror images of each other. Example: meso-tartaric acid.
3. Centre of symmetry (i): A point in the center of the molecule such that a line drawn from any atom through the center meets an identical atom at an equal distance on the opposite side. Example: trans-1,2-dichloroethene.
4. Alternating axis of symmetry (Sn): An axis around which rotation by 360°/n followed by reflection in a plane perpendicular to the axis yields the original molecule. Example: staggered ethane (S₆).
(b) Beer-Lambert Law:
The Beer-Lambert law states that the absorbance of a solution is directly proportional to the concentration of the absorbing species and the path length of the light through the solution.
A = εcl (where A is absorbance, ε is molar absorptivity, c is concentration, and l is path length).
Derivation: The rate of decrease of intensity of light (-dI) with thickness (dx) is proportional to the intensity (I) and concentration (c).
-dI/dx = k'Ic
-dI/I = k'c dx. Integrating from I₀ to I and 0 to l:
-ln(I/I₀) = k'cl => log(I₀/I) = (k'/2.303)cl
Since Absorbance A = log(I₀/I) and let ε = k'/2.303, we get A = εcl.
(c) Trans-Stilbene vs Cis-Stilbene Absorption:
Trans-stilbene is a highly planar molecule. This planarity allows for maximum overlap of the p-orbitals across the entire extended π-conjugated system (two phenyl rings and the central double bond). Extensive conjugation decreases the energy gap between the HOMO and LUMO (π to π* transition), resulting in absorption at a longer wavelength.
In cis-stilbene, the two bulky phenyl rings are on the same side, causing severe steric hindrance. To relieve this strain, the rings twist out of the plane, breaking the continuous π-conjugation. Reduced conjugation increases the HOMO-LUMO energy gap, causing it to absorb at a shorter wavelength.
(a) Postulates of Crystal Field Theory (CFT):
1. The interaction between the metal ion and the ligands is purely electrostatic (ionic).
2. Ligands are treated as point charges (if anions) or point dipoles (if neutral molecules).
3. The five d-orbitals of the isolated metal ion are degenerate. When ligands approach, this degeneracy is destroyed due to repulsion between ligand electrons and d-electrons, splitting the d-orbitals into different energy levels (e.g., t₂g and eg in an octahedral field).
(b) de Broglie Wavelength Calculation:
Formula: λ = h / mv (where h = 6.626 × 10⁻³⁴ J·s)
For Stone: m = 100g = 0.1 kg, v = 1 m/s
λ = (6.626 × 10⁻³⁴) / (0.1 × 1) = 6.626 × 10⁻³³ m
For Electron: m = 9.1 × 10⁻³¹ kg, v = 6 × 10⁵ m/s
λ = (6.626 × 10⁻³⁴) / (9.1 × 10⁻³¹ × 6 × 10⁵) = 1.21 × 10⁻⁹ m (or 1.21 nm)
Meaningfulness: The wavelength of the electron is meaningful because it is on the scale of atomic dimensions and can be experimentally observed (e.g., electron diffraction). The stone's wavelength is unimaginably small and has no macroscopic physical significance.
(c) Predicted Products:
1. Cyclohexanone + Methyl vinyl ketone + Base → Robinson Annulation product (a bicyclic α,β-unsaturated ketone).
2. Chiral secondary alcohol + SOCl₂ → Alkyl chloride (typically with inversion of configuration via SN2 if a base like pyridine is present, or retention via SNi if no base).
3. Acetophenone (Ph-CO-CH₃) + NaBH₄ → 1-Phenylethanol (Ph-CH(OH)-CH₃). NaBH₄ selectively reduces the ketone to a secondary alcohol.
(d) Measuring pH using Calomel Electrode:
A standard calomel electrode (SCE) is used as a reference electrode (known potential). It is coupled with an indicator electrode sensitive to H⁺ ions (like a glass electrode or hydrogen electrode) dipped in the unknown solution.
E_cell = E_cathode - E_anode
If a hydrogen electrode is the anode: E_cell = E_SCE - E_H₂
Since E_H₂ = -0.0591 × pH, we have E_cell = E_SCE + 0.0591 × pH. By measuring E_cell with a voltmeter, the pH can be calculated.
(e) Storage cell in a mobile phone:
Lithium-ion (Li-ion) battery.
(i) Fluorescence and its application:
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It occurs rapidly (10⁻⁸ seconds) after absorption as the excited electron drops back to the singlet ground state. Applications include fluorescent lamps, biological tagging/microscopy, and detecting forged currency.
(ii) Hard and Soft Acids and Bases (HSAB):
Pearson's HSAB principle classifies Lewis acids and bases as 'hard' or 'soft'. Hard species are small, highly charged, and non-polarizable (e.g., H⁺, F⁻). Soft species are large, have low charge, and are highly polarizable (e.g., Ag⁺, I⁻). The principle states that Hard acids prefer Hard bases, and Soft acids prefer Soft bases.
(iii) Gibbs-Helmholtz equation:
It relates the change in Gibbs free energy (ΔG) to the enthalpy change (ΔH) and the temperature dependence of ΔG.
ΔG = ΔH + T[∂(ΔG)/∂T]_P or [∂(ΔG/T) / ∂T]_P = -ΔH / T²
It is extremely useful for calculating ΔG at any temperature if ΔH and ΔG at one temperature are known.
(iv) Fajan's rule:
Fajan's rules predict whether a chemical bond will be covalent or ionic. Covalent character increases when:
1. The cation is small and highly charged (high polarizing power).
2. The anion is large and highly polarizable.
3. Cations with pseudo-noble gas configurations have greater polarizing power than noble gas configurations.
(v) n and p-type semiconductor:
- n-type: Formed by doping an intrinsic semiconductor (like Si) with a pentavalent impurity (like P or As). The extra electron acts as a charge carrier (n for negative).
- p-type: Formed by doping with a trivalent impurity (like B or Ga). This creates an electron deficiency or 'hole', which acts as a positive charge carrier (p for positive).
(vi) Ellingham diagram:
A graphical plot of ΔG° (standard Gibbs free energy of formation of oxides) versus Temperature (T). It is used in metallurgy to determine the feasibility of reducing metal oxides and to select the appropriate reducing agent (like Carbon or CO) at a given temperature. The metal whose oxide curve is lower on the graph can reduce the oxide of a metal whose curve is higher.