Spontaneity Of Chemical Reactions
NIOS · Class 12 · Chemistry
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For the reaction 2NO(g) + O₂(g) → 2NO₂(g), ΔH = –113 kJ mol⁻¹ and ΔS = –145 J K⁻¹ mol⁻¹. At what temperature (approximately) does this reaction change from spontaneous to non-spontaneous?
The standard Gibbs energy change for the reaction CO(g) + 2H₂(g) → CH₃OH(l) at 298 K is –24.8 kJ mol⁻¹. What is the equilibrium constant K at 298 K? (R = 8.314 J K⁻¹ mol⁻¹)
For the rusting of iron: 4Fe(s) + 3O₂(g) → 2Fe₂O₃(s), the standard molar entropies of Fe(s), O₂(g), and Fe₂O₃(s) are 27.3, 205.0, and 87.4 J K⁻¹ mol⁻¹ respectively. What is ΔrS° for this reaction?
The equilibrium constant for P(s) + 3/2 Cl₂(g) ⇌ PCl₃(g) is 2.00 × 10²⁴ at 500 K. What is the value of ΔrG°? (R = 8.314 J K⁻¹ mol⁻¹)
Sample Questions
Which of the following correctly explains why the spontaneous mixing of two ideal gases is NOT driven by an energy change?
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For ideal gases, ΔU = ΔH = 0 upon mixing at constant temperature because there are no intermolecular forces, so entropy increase is the only driving force.
Step 1: By definition, ideal gases have no intermolecular forces of attraction or repulsion. Step 2: Therefore, internal energy (U) and enthalpy (H) depend only on temperature for ideal gases, not on pressure or volume. Step 3: At constant temperature, mixing causes no change in U or H, so ΔU = ΔH = 0. Step 4: The driving force is purely the increase in entropy — the system moves to a state of greater disorder (maximum mixing). Step 5: This is a classic example showing that energy alone cannot explain all spontaneous processes; entropy is equally important.
Consider the reaction: CCl₄(l) + H₂(g) → HCl(g) + CHCl₃(l) at 298 K where ΔrH = 91.35 kJ mol⁻¹ and ΔrS = 41.5 J K⁻¹ mol⁻¹. Which statement is correct?
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ΔG = +79.0 kJ mol⁻¹, so the reaction is non-spontaneous at 298 K.
Step 1: ΔG = ΔH – TΔS. Step 2: TΔS = 298 × 41.5 × 10⁻³ = 298 × 0.0415 = 12.367 kJ mol⁻¹. Step 3: ΔG = 91.35 – 12.367 = +78.98 ≈ +79.0 kJ mol⁻¹. Step 4: Since ΔG > 0, the reaction is non-spontaneous at 298 K. Step 5: Here ΔH > 0 and ΔS > 0 (Case 3): at low temperatures, the positive ΔH dominates, making the reaction non-spontaneous. It could become spontaneous at very high temperatures where TΔS > ΔH.
Which thermodynamic statement correctly describes the relationship between ΔG of the system and ΔS of the universe at constant temperature and pressure?
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ΔG(system) = –T × ΔS(total), so a negative ΔG corresponds to positive ΔS(universe).
Step 1: For a non-isolated system at constant T and P, ΔS(surroundings) = –ΔH(system)/T. Step 2: ΔS(total) = ΔS(system) + ΔS(surroundings) = ΔS(system) – ΔH(system)/T. Step 3: Multiplying both sides by –T: –TΔS(total) = ΔH(system) – TΔS(system) = ΔG(system). Step 4: Therefore, ΔG = –TΔS(total). Step 5: Since T is always positive, ΔG < 0 ↔ ΔS(total) > 0, which is the second law criterion for spontaneity. Gibbs energy beautifully combines both system and surroundings into one property of the system alone.
For the combustion of methane: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), the standard Gibbs energies of formation of CH₄, CO₂, and H₂O are –50.8, –394.4, and –237.2 kJ mol⁻¹ respectively. What is ΔrG°?
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–818.0 kJ mol⁻¹
Step 1: ΔrG° = ΣΔfG°(products) – ΣΔfG°(reactants). Step 2: ΔfG°(O₂) = 0 (element in standard state). Step 3: ΔrG° = [ΔfG°(CO₂) + 2×ΔfG°(H₂O)] – [ΔfG°(CH₄) + 2×ΔfG°(O₂)]. Step 4: = [–394.4 + 2×(–237.2)] – [–50.8 + 2×0] = [–394.4 – 474.4] – [–50.8] = –868.8 + 50.8 = –818.0 kJ mol⁻¹. Step 5: The large negative ΔrG° confirms that methane combustion is highly spontaneous, which aligns with its use as a fuel in everyday life (LPG).
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