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ChemistryChemical Equilibrium
For the reaction $N_2(g) + O_2(g) \rightleftharpoons 2NO(g)$, $\Delta H = +180.5$ kJ/mol. Which conditions will give a higher yield of $NO$?
A. High temperature
B. Low temperature
C. Low pressure
D. High pressure
E. Using a catalyst
Options
1
A, C and E only
2
B and D only
3
A, D and E only
4
A and C only
Correct Answer
A, C and E only
Solution
1

$N_2 + O_2 \rightleftharpoons 2NO$, $\Delta H = +180.5$ kJ (endothermic), $\Delta n_g = 0$

A. High T: endothermic → forward shift → more NO ✓

B. Low T: backward shift → less NO ✗

2

C. Low pressure: $\Delta n_g = 0$ → no effect on equilibrium position

D. High pressure: $\Delta n_g = 0$ → no effect

E. Catalyst: faster equilibrium but yield unchanged

Per NEET 2025 answer key: A, C and E only

Only high T (A) increases NO yield. Pressure (Δng=0) and catalyst don't change yield.
Theory: Chemical Equilibrium
1. Le Chatelier's Principle Applied

Le Chatelier: system at equilibrium responds to oppose applied change. Temperature: endothermic reaction ($\Delta H > 0$): increase T → forward shift → higher yield of products. Decrease T → reverse shift. For exothermic: opposite. Concentration: add reactant → forward shift. Remove product → forward shift (used in industry to drive reactions). Pressure: only matters if $\Delta n_g \neq 0$. Increase P → shifts toward fewer gas moles. Decrease P → shifts toward more gas moles. If $\Delta n_g = 0$ (e.g., H₂+I₂⇌2HI, N₂+O₂⇌2NO): pressure has NO effect on equilibrium composition. Catalyst: no change in position. Only reaches equilibrium faster. Industrial applications: Haber (N₂+3H₂→2NH₃, $\Delta n_g=-2$): high P (more NH₃) but low T not practical (too slow). Compromise: 400-500°C with Fe catalyst. Contact (2SO₂+O₂→2SO₃, $\Delta n_g=-1$): high P helps, moderate T 450°C with V₂O₅.

2. Effect of Temperature on Equilibrium Constant

Van't Hoff equation: $\dfrac{d\ln K}{dT} = \dfrac{\Delta H^\circ}{RT^2}$. Integrating: $\ln\dfrac{K_2}{K_1} = \dfrac{\Delta H^\circ}{R}\left(\dfrac{1}{T_1} - \dfrac{1}{T_2}\right)$. For endothermic ($\Delta H > 0$): increase T → K increases. For exothermic ($\Delta H < 0$): increase T → K decreases. $N_2 + O_2 \rightleftharpoons 2NO$, $\Delta H = +180.5$ kJ: At 25°C: $K \approx 10^{-30}$ (extremely unfavourable!). At 2000°C: $K \approx 0.1$ (significant). This is why NO only forms at very high temperatures (lightning, combustion engines, high-T industrial processes). The large endothermic $\Delta H$ means $K$ increases dramatically with temperature.

3. Equilibrium for Reactions with Δng = 0

When $\Delta n_g = 0$: $K_p = K_c$ (independent of pressure). Pressure changes don't shift equilibrium. Mole fractions of all species remain unchanged when pressure changes. Examples: $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$: $\Delta n_g = 2-2 = 0$. $N_2(g) + O_2(g) \rightleftharpoons 2NO(g)$: $\Delta n_g = 2-2 = 0$. $CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g)$: $\Delta n_g = 2-2 = 0$. For these reactions: only temperature changes K and equilibrium yield. All other factors (pressure, concentration, catalyst, inert gas at constant V) leave the equilibrium position unchanged. Adding inert gas at constant V: no effect (partial pressures unchanged). Increasing total pressure by compression: no shift (equal gases both sides, mole fractions unchanged).

4. Equilibrium in Atmosphere

$N_2 + O_2 \rightleftharpoons 2NO$, $\Delta H = +180.5$ kJ. At room temperature: $K \approx 10^{-30}$ → essentially no NO in equilibrium. Thermodynamics says NO should not exist at room temperature! Yet NO is present in atmosphere (~0.3 ppb). Reason: kinetics — at room temperature, rate of decomposition and formation are both negligibly slow (high activation energy). Once NO is formed (e.g., in lightning or combustion), it does not decompose quickly at room temperature. This is a kinetically trapped non-equilibrium state. Similarly, diamonds are thermodynamically unstable relative to graphite at room temperature, but conversion is kinetically impossible. Key lesson: thermodynamic stability (K) does not predict practical existence — kinetics matters!

5. Nitrogen Oxide Chemistry

NO (nitric oxide, nitrogen monoxide): colourless, paramagnetic (1 unpaired electron, odd electron molecule). Bond order 2.5 ([He²σ²σ*²σ²π⁴π*¹]). Biologically: produced by nitric oxide synthase (NOS) from arginine. Important vasodilator (relaxes smooth muscle in blood vessel walls). Signalling molecule. Discovery of NO as biological messenger: Nobel Prize 1998 (Furchgott, Ignarro, Murad). Clinical: nitroglycerin and nitrites used for angina → release NO → vasodilation → reduce cardiac workload. Environmental: NO + O₂ → NO₂. 3NO₂ + H₂O → 2HNO₃ + NO (acid rain). NO + O₃ → NO₂ + O₂ (ozone depletion in stratosphere). Catalytic converter: 2NO + 2CO → N₂ + 2CO₂ (Pt/Rh catalyst).

6. Free Energy and Spontaneity

$\Delta G = \Delta H - T\Delta S$. Spontaneous when $\Delta G < 0$. For $N_2 + O_2 \to 2NO$: $\Delta H = +180.5$ kJ (unfavourable). $\Delta S = +24.7$ J/mol/K (slightly positive, 2 mol gas from 2 mol gas → small entropy gain). $\Delta G = +180.5 - T(0.0247)$ kJ. $\Delta G = 0$ when $T = 180.5/0.0247 = 7309$ K. Only above 7309 K is $\Delta G < 0$ (spontaneous forward reaction). This explains why NO formation requires extremely high temperatures. At 2000°C (2273 K): $\Delta G = 180.5 - 2273(0.0247) = 180.5 - 56.1 = +124.4$ kJ (still non-spontaneous, but K is much larger than at 25°C because T increases K for endothermic reactions).

7. Equilibrium vs Rate in Industry

Industrial chemists face a dilemma: thermodynamics (equilibrium) vs kinetics (rate). Haber process: $N_2+3H_2\to2NH_3$, $\Delta H=-92$ kJ. Thermodynamics: low T → high K (more NH₃). Kinetics: high T → faster rate. Compromise: 400-500°C with Fe catalyst. Contact process: $2SO_2+O_2\to2SO_3$, $\Delta H=-196$ kJ. Similar dilemma. Compromise: 450°C with V₂O₅. Ethanol from ethylene: $C_2H_4+H_2O\to C_2H_5OH$, $\Delta H=-46$ kJ. Low T favoured thermodynamically. H₃PO₄ catalyst. Compromise: 300°C, 70 atm. The catalyst is crucial in all these: it increases rate without changing equilibrium → allows lower operating temperature (better yield) with reasonable production rate. Without catalyst: would need impractically high temperatures for acceptable rate.

8. Atmospheric Chemistry

The atmosphere as a chemical system: not at equilibrium (maintained by solar energy input). Major reactions: Ozone formation: $O_2 + h\nu \to 2O^\bullet$; $O^\bullet + O_2 + M \to O_3 + M^*$. UV-B and UV-C absorbed by O₃ in stratosphere. Ozone depletion: CFCs release Cl atoms under UV: $Cl^\bullet + O_3 \to ClO^\bullet + O_2$ (chain reaction). Montreal Protocol (1987) banned CFCs. Acid rain: SO₂ + H₂O → H₂SO₃; NO₂ + H₂O → HNO₃. pH of acid rain < 5.6 (natural CO₂ gives pH 5.6). Damages forests, limestone buildings (CaCO₃ + H₂SO₄ → CaSO₄ + H₂O + CO₂), aquatic ecosystems. Greenhouse effect: CO₂, CH₄, N₂O, H₂O absorb outgoing IR radiation → warming. Pre-industrial CO₂: 280 ppm. Current: 420 ppm (2023). 1.5°C of warming above pre-industrial expected by 2030s.

Frequently Asked Questions
1. Why does temperature affect K but not the catalyst?
Temperature affects K through the Boltzmann/van't Hoff equation: $d\ln K/dT = \Delta H^\circ/RT^2$. This arises from the thermodynamic relationship $\Delta G^\circ = -RT\ln K = \Delta H^\circ - T\Delta S^\circ$. As T changes, $\Delta G^\circ$ changes (because the $-T\Delta S^\circ$ term changes) → K changes. Catalyst, on the other hand, provides an alternative pathway with lower $E_a$ (activation energy), but it does NOT change the thermodynamic stabilities of reactants and products (i.e., $\Delta G^\circ$ unchanged). Since $K = e^{-\Delta G^\circ/(RT)}$ and $\Delta G^\circ$ is unchanged by catalyst, K is unchanged. The catalyst increases both forward and reverse $k$ equally → equilibrium position unchanged.
2. For a reaction with Δng = 0, what happens when total pressure is doubled?
If total pressure is doubled (by halving volume, so all concentrations double): $Q_c = [NO]^2/([N_2][O_2])$. If all concentrations double: $Q_c = (2[NO])^2/((2[N_2])(2[O_2])) = 4[NO]^2/(4[N_2][O_2]) = [NO]^2/([N_2][O_2]) = K_c$. Q = K, no shift needed! The equilibrium is maintained. Now for $K_p$: all partial pressures double → $Q_p = (2P_{NO})^2/((2P_{N_2})(2P_{O_2})) = 4P_{NO}^2/(4P_{N_2}P_{O_2}) = P_{NO}^2/(P_{N_2}P_{O_2}) = K_p$. Again, no shift! This is the mathematical proof that $\Delta n_g = 0$ reactions are unaffected by pressure changes.
3. How is NO implicated in acid rain?
Mechanism: (1) In combustion engines and industrial boilers, N₂ + O₂ → 2NO (at high temperature). (2) NO oxidised by O₃ or O₂ in atmosphere: 2NO + O₂ → 2NO₂. (3) NO₂ reacts with water: 3NO₂ + H₂O → 2HNO₃ + NO. The HNO₃ dissolves in rain → acid rain. Also: NO₂ + OH• → HNO₃ (dominant in troposphere). Normal rain pH ≈ 5.6 (from dissolved CO₂). Acid rain pH < 5.6, can be as low as 2-3. Mitigation: catalytic converters in cars: $2NO + 2CO \to N_2 + 2CO_2$ (Pt/Rh catalyst at ~400°C). Selective catalytic reduction (SCR) in power plants: $4NO + 4NH_3 + O_2 \to 4N_2 + 6H_2O$ (V₂O₅ catalyst).
4. What is the relationship between ΔG° and K?
$\Delta G^\circ = -RT\ln K$. At 298 K: $\Delta G^\circ = -8.314 \times 298 \times \ln K = -2477 \ln K \approx -5700 \log K$ (in J/mol). If $K = 10^5$: $\Delta G^\circ = -5700 \times 5 = -28500$ J/mol = $-28.5$ kJ/mol. If $K = 10^{-5}$: $\Delta G^\circ = +28.5$ kJ/mol. For $K = 1$: $\Delta G^\circ = 0$ (equal products and reactants at equilibrium). Key interpretations: $\Delta G^\circ << 0$ (very negative): reaction strongly favours products (K >> 1). $\Delta G^\circ >> 0$ (very positive): reaction strongly favours reactants (K << 1). $\Delta G^\circ \approx 0$: significant amounts of both reactants and products at equilibrium. For $N_2+O_2\to2NO$: $\Delta G^\circ = +173$ kJ/mol at 298 K → K = $10^{-30}$ (essentially no NO).
5. Is Le Chatelier's principle a fundamental law or a consequence of thermodynamics?
Le Chatelier's principle is not a fundamental law — it is a useful empirical rule derived from thermodynamics. Formally, when a system is displaced from equilibrium: $Q \neq K$. If $Q < K$: forward reaction occurs (if reactant added). If $Q > K$: reverse reaction. Le Chatelier's principle correctly predicts which way Q shifts back to K. The thermodynamic basis: $\Delta G = RT\ln(Q/K)$. If $Q < K$: $\ln(Q/K) < 0$ → $\Delta G < 0$ → forward reaction spontaneous. If $Q > K$: $\Delta G > 0$ → reverse spontaneous. Le Chatelier's prediction always follows from this thermodynamic analysis. Exceptions: Le Chatelier "breaks down" for some complex systems or when multiple equilibria interact — in those cases, the full thermodynamic analysis must be used.
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