HSC Exam Practice

Sample response. Hess’s Law states that the total enthalpy change of a reaction is independent of the pathway taken — it depends only on the initial and final states of the system. This is possible because enthalpy is a state function: its value is determined only by the current state of the system, not by how that state was reached.

Marking notes. 1 mark for a correct statement of Hess’s Law (pathway independence / initial and final states only). 1 mark for identifying enthalpy as a state function.

Sample response. (a) Photosynthesis: 6CO₂(g) + 6H₂O(l) → C₆H₁₂O₆(s) + 6O₂(g)   ΔH = +2803 kJ mol⁻¹. (b) Cellular respiration: C₆H₁₂O₆(s) + 6O₂(g) → 6CO₂(g) + 6H₂O(l)   ΔH = −2803 kJ mol⁻¹.

Marking notes. 1 mark per equation for correct formula and balancing (accept minor state-symbol omissions if formulas correct). 1 mark per ΔH value (correct sign and magnitude). 4 marks total.

Sample response. Photosynthesis and cellular respiration involve identical reactants and products but in opposite roles — they are exact chemical reverses of each other. By Hess’s Law, reversing a thermochemical equation reverses the sign of ΔH while keeping the magnitude unchanged. Because enthalpy is a state function (value depends only on initial and final states), and both reactions start and end with the same set of substances, the magnitude of the enthalpy change must be equal. Therefore ΔH(respiration) = −ΔH(photosynthesis), giving equal magnitudes and opposite signs.

Marking notes. 1 mark for identifying the two reactions as exact chemical reverses. 1 mark for stating that reversing a thermochemical equation reverses the sign of ΔH (Hess’s Law). 1 mark for linking to enthalpy as a state function to explain why magnitudes must be equal.

Sample response. (a) 6CO₂(g) + 6H₂O(l) sit at the lower enthalpy level — these are the products of the exothermic respiration reaction, so they are at lower enthalpy than the reactants. (b) C₆H₁₂O₆(s) + 6O₂(g) sit at the higher enthalpy level — photosynthesis (endothermic, ΔH = +2803 kJ mol⁻¹) produces these from CO₂ + H₂O, so the products are 2803 kJ mol⁻¹ higher in enthalpy.

Marking notes. 1 mark per part (correct level with brief justification).

Sample response. A cell couples an endothermic biosynthesis reaction to one or more exothermic ATP hydrolysis reactions (ATP + H₂O → ADP + P_i; ΔH ≈ −30.5 kJ mol⁻¹ per mole). The cell applies Hess’s Law by adding the thermochemical equations: the positive ΔH of the biosynthesis and the negative ΔH(s) of ATP hydrolysis sum to give a combined ΔH that is negative. This makes the overall process enthalpy-favourable, allowing the cell to run the otherwise-endothermic reaction. The Hess’s Law operation performed is adding thermochemical equations.

Marking notes. 1 mark for identifying ATP hydrolysis as the exothermic source. 1 mark for describing the addition of thermochemical equations (Hess’s Law). 1 mark for stating that the result is a negative combined ΔH (enthalpy-favourable).

Sample response. Glucose is a solar energy storage molecule because the 2803 kJ mol⁻¹ of light energy captured by chlorophyll during photosynthesis is converted into chemical potential energy stored in the covalent bonds of glucose — energy is neither created nor destroyed, only converted (conservation of energy). Australian eucalypt forests sequester carbon by net photosynthesis exceeding respiration; the excess glucose accumulates as wood. This represents a flow of solar energy into long-term chemical storage, removing CO₂ from the atmosphere. On a global scale, forests act as energy sinks that store solar energy in biomass, modulating atmospheric CO₂ concentrations and the global carbon-energy budget.

Marking notes. 1 mark for explaining glucose as a converted (stored) form of solar energy with reference to the +2803 kJ mol⁻¹. 1 mark for describing net photosynthesis > respiration leading to biomass accumulation in Australian forests. 1 mark for linking forest carbon sequestration to atmospheric CO₂ and the global energy budget.

(a) From the graph, the combined ΔH first becomes negative at 3 ATP (value: −16.5 kJ mol⁻¹). Confirmation by calculation: ΔH(combined) = +75 + 3(−30.5) = +75 − 91.5 = −16.5 kJ mol⁻¹. Minimum = 3 ATP molecules. [1 mark for reading graph; 1 mark for correct calculation confirming the value.]

(b) The combined ΔH decreases linearly (becomes more negative) as the number of ATP molecules increases. The relationship is linear because each additional ATP contributes a constant −30.5 kJ mol⁻¹. The gradient of the line = −30.5 kJ mol⁻¹ per ATP molecule, which equals the ΔH of ATP hydrolysis. The line crosses zero between 2 and 3 ATP molecules. [1 mark for identifying linear/constant decrease; 1 mark for stating gradient = −30.5 kJ mol⁻¹ per ATP; 1 mark for identifying the zero-crossing between 2 and 3 ATP.]

(c) Coupling 10 moles of ATP releases 10 × 30.5 = 305 kJ mol⁻¹ of exothermic energy, but the reaction only requires 16.5 kJ mol⁻¹ to become favourable (at 3 ATP). The excess 288.5 kJ mol⁻¹ of ATP free energy is “spent” on nothing — ATP is wasted. By Hess’s Law, the combined ΔH must equal the sum of all the equations added, so adding more ATP than needed simply makes the combined ΔH far more negative without producing any additional useful product. Biologically, this wastes the glucose that was used to make those ATP molecules in the first place. [1 mark for identifying ATP wastage; 1 mark for Hess’s Law argument (excess exothermic contribution, no additional useful product).]

(a) 1.8 t CO₂ = 1 800 000 g. Moles CO₂ = 1 800 000 ÷ 44.01 = 40 899 mol (approx. 4.09 × 10⁴ mol). [1 mark for correct unit conversion; 1 mark for final moles value with correct working.]

(b) Moles glucose = 40 899 ÷ 6 = 6 817 mol. Energy stored = 6 817 × 2803 = 1.911 × 10⁷ kJ ha⁻¹ yr⁻¹ (approx. 19 100 GJ). [1 mark for dividing moles CO₂ by 6; 1 mark for correct multiplication by 2803 with appropriate units.]

(c) Sample assumption: all sequestered carbon is in the form of glucose (ΔH_f known). In reality, seagrass stores carbon as a range of organic molecules (cellulose, starch, lipids) with different enthalpies of formation, so the actual energy stored per tonne of CO₂ may differ from the value calculated using ΔH(photosynthesis of glucose) alone. This would make the calculated energy storage an approximation; the actual value could be higher or lower depending on the molecular composition of the biomass. [1 mark for identifying a valid assumption; 1 mark for assessing direction and nature of the resulting inaccuracy.]

Sample response. The claim is incorrect. The equal and opposite ΔH values for photosynthesis and cellular respiration are not a biological coincidence — they are a thermodynamic necessity that follows directly from Hess’s Law and the properties of enthalpy as a state function.

Hess’s Law states that the total enthalpy change of a reaction depends only on the initial and final states of the system, not on the pathway. Photosynthesis converts CO₂(g) + H₂O(l) into C₆H₁₂O₆(s) + O₂(g) with ΔH = +2803 kJ mol⁻¹. Cellular respiration converts those exact same reactants back to CO₂(g) + H₂O(l) — it is the exact chemical reverse. For any two reactions that are exact reverses of each other, enthalpy (being a state function) demands that ΔH(reverse) = −ΔH(forward). This is a mathematical requirement, not a coincidence arising from the molecules involved. If ΔH(respiration) were not −2803 kJ mol⁻¹, it would be possible to construct a cyclic process that produced net energy from nothing — a violation of the First Law of Thermodynamics.

The biological significance of this relationship is profound. The 2803 kJ mol⁻¹ absorbed from sunlight during photosynthesis is stored precisely in the bonds of glucose; no more, no less. When glucose is respired, that same 2803 kJ mol⁻¹ is released to drive cellular work. Australian eucalypt forests demonstrate this at scale: net photosynthesis exceeds respiration, storing 7.2 t CO₂-eq ha⁻¹ yr⁻¹ as biomass — locked solar energy. The carbon cycle depends on this Hess’s Law equality: every mole of CO₂ fixed by photosynthesis stores exactly the energy that respiration of the resulting glucose will release, maintaining the integrity of the global energy budget over geological time.

In summary, the relationship is a thermodynamic necessity arising from Hess’s Law and the state-function nature of enthalpy. The claim is rejected.

Marking notes. 1 mark — rejects the claim and identifies the relationship as a thermodynamic necessity. 1 mark — states Hess’s Law (pathway independence). 1 mark — correctly identifies photosynthesis and respiration as exact chemical reverses with identical initial and final states. 1 mark — applies state-function argument to explain why ΔH(reverse) = −ΔH(forward) is a mathematical necessity. 1 mark — links to the First Law (cyclic violation argument, or equivalent). 1 mark — names a real biological example (Australian eucalypt forest sequestration, ATP coupling, or carbon cycle) with specific data. 1 mark — explains the biological significance of the equal-and-opposite relationship (solar energy → glucose → ATP chain). 1 mark — reaches a clear, evidence-anchored evaluative conclusion.