Every cell in your body right now is breaking down glucose and releasing 2803 kJ mol⁻¹ of energy. Plants do the exact reverse — absorbing 2803 kJ mol⁻¹ of sunlight to build glucose. Hess's Law predicts this perfectly: reverse a reaction, reverse the sign of ΔH. But here is the puzzle — photosynthesis is endothermic, so how do plants actually run it continuously without violating the laws of thermodynamics?
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Every cell in your body right now is performing cellular respiration — breaking down glucose to release energy as ATP. Plants do the reverse — using sunlight to build glucose from CO₂ and water. Both processes involve the same molecules: glucose, CO₂, H₂O, and oxygen.
If respiration is exactly the reverse of photosynthesis, what does Hess's Law predict about their ΔH values?
Before this lesson: Write down: (1) What you predict ΔH(photosynthesis) and ΔH(respiration) look like relative to each other. (2) Photosynthesis is endothermic — yet plants do it continuously without any outside energy input except sunlight. Why is this not a violation of thermodynamics? Write your thinking before the lesson explains it.
Type your initial response below — you will revisit this at the end of the lesson.
Write your initial response in your book. You will revisit it at the end of the lesson.
📚 Core Content
A correctly drawn Hess's Law energy cycle for photosynthesis/respiration has two levels, two arrows, and a cycle that sums to zero — these features are non-negotiable in HSC answers.
How to draw the cycle:
Alternative Hess's Law cycle — via ΔH°f values:
You can also construct an energy cycle where the elements (C, H, O in their standard states) form the intermediate level. By Hess's Law:
This gives ΔH°f(glucose) = −4075.8 − (−2803) = −1272.8 kJ mol⁻¹ — the enthalpy of formation of glucose, consistent with published data.
Living organisms run many endothermic reactions — protein synthesis, ion pumping, muscle contraction — by coupling them to the highly exothermic hydrolysis of ATP. This is Hess's Law applied at the molecular level.
The ATP hydrolysis reaction:
ATP(aq) + H₂O(l) → ADP(aq) + Pᵢ(aq) ΔH ≈ −30.5 kJ mol⁻¹
How ATP coupling works (Hess's Law logic):
Suppose a biosynthesis reaction has ΔH = +45 kJ mol⁻¹ (endothermic — thermodynamically unfavourable from enthalpy alone). The cell couples this to the hydrolysis of 2 moles of ATP:
The combined reaction is exothermic overall — thermodynamically favourable from an enthalpy perspective. By adding the two thermochemical equations (exactly as in Hess's Law), the cell achieves a net negative ΔH.
🔬 Worked Examples
Given that ΔH for cellular respiration = −2803 kJ mol⁻¹, (a) calculate ΔH for photosynthesis using Hess's Law; (b) verify that the Hess's Law energy cycle closes (sums to zero); (c) explain the biological significance of the equal and opposite values.
A biochemical synthesis reaction has ΔH = +55 kJ mol⁻¹. The cell couples this to ATP hydrolysis (ΔH = −30.5 kJ mol⁻¹ per mole). How many moles of ATP must be hydrolysed for the coupled reaction to have a negative overall ΔH? Calculate the combined ΔH at that number of moles.
🔬 Activities
a In the Hess's Law energy cycle diagram for photosynthesis and respiration, which set of substances sits at the higher enthalpy level, and which sits at the lower level? Justify your answer using the ΔH value for photosynthesis.
b Describe how you would draw the two arrows in a Hess's Law energy cycle diagram for these reactions — direction, label, and ΔH value for each.
c Construct an alternative Hess's Law cycle that uses ΔH°f values to confirm ΔH(respiration) = −2803 kJ mol⁻¹. Use: ΔH°f[CO₂(g)] = −393.5; ΔH°f[H₂O(l)] = −285.8; ΔH°f[C₆H₁₂O₆(s)] = −1272.8; ΔH°f[O₂(g)] = 0 kJ mol⁻¹.
Type your responses below:
Answer in your workbook — draw the energy cycle diagram for part (b).
a The synthesis of alanine (an amino acid) from its precursors has ΔH = +42 kJ mol⁻¹. The cell couples this to the hydrolysis of 2 mol of ATP (ΔH = −30.5 kJ mol⁻¹ per mol). Using Hess's Law, write the combined thermochemical equation and calculate the overall ΔH.
b During cellular respiration, 1 mole of glucose releases 2803 kJ mol⁻¹. The cell captures approximately 38 moles of ATP from this process (ΔHf of each ATP = +30.5 kJ mol⁻¹ approximately).
(i) Calculate the energy stored in 38 mol of ATP.
(ii) Calculate the efficiency of energy capture (energy stored in ATP ÷ energy released by respiration × 100%).
(iii) Comment on where the remaining energy goes.
Type your responses below:
Answer in your workbook.
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
Wrong: Synthesis reactions always produce a single product from two elements.
Right: Synthesis reactions combine two or more reactants into a single product, but the reactants need not be elements. Compounds can also combine in synthesis reactions (e.g., SO₃ + H₂O → H₂SO₄). The defining feature is one product forming from multiple reactants.
5 random questions from a replayable lesson bank — feedback shown immediately
✍️ Short Answer
6. (a) Write balanced thermochemical equations for both photosynthesis and cellular respiration. Include state symbols and ΔH values. (2 marks)
(b) Explain, using Hess's Law, why the ΔH values for these two reactions are equal in magnitude and opposite in sign. (2 marks)
4 MARKS
Type your full answer below:
Answer in your workbook.
7. Photosynthesis is strongly endothermic (ΔH = +2803 kJ mol⁻¹), yet plants carry it out continuously.
(a) Explain why this does not violate the law of conservation of energy. (2 marks)
(b) Contrast this with an organism running an endothermic biochemical reaction using ATP coupling. In what way do both situations apply the same thermodynamic principle? (2 marks)
4 MARKS
Type your answer:
Answer in your workbook.
8. A student states: "Because photosynthesis and respiration have equal and opposite ΔH values, the energy released by respiration in animals exactly equals the energy absorbed during photosynthesis in plants — so global energy is perfectly balanced."
(a) Is the student's statement about ΔH values chemically correct? Justify using Hess's Law. (2 marks)
(b) Evaluate the student's broader claim about global energy balance. What additional factors would need to be considered for this claim to be valid? (3 marks)
5 MARKS
Type your answer below:
Answer in your workbook.
Go back to your Think First responses. Now you can evaluate precisely:
Type your reflection below:
Write your reflection in your book.
(a) Higher enthalpy level: C₆H₁₂O₆(s) + 6O₂(g). Lower enthalpy level: 6CO₂(g) + 6H₂O(l). Justification: ΔH(photosynthesis) = +2803 kJ mol⁻¹ — positive = endothermic = products (glucose + O₂) at higher enthalpy than reactants (CO₂ + H₂O).
(b) Photosynthesis arrow: upward from lower (CO₂ + H₂O) to upper (glucose + O₂) level; ΔH = +2803 kJ mol⁻¹. Respiration arrow: downward from upper to lower level; ΔH = −2803 kJ mol⁻¹. Cycle sum = 0 — Hess's Law verified.
(c) ΣΔH°f(products) = 6(−393.5) + 6(−285.8) = −4075.8 kJ mol⁻¹; ΣΔH°f(reactants) = 1(−1272.8) + 6(0) = −1272.8 kJ mol⁻¹; ΔH = −4075.8 − (−1272.8) = −2803.0 kJ mol⁻¹ ✓.
(a) Add: biosynthesis (ΔH = +42) + 2×ATP hydrolysis (ΔH = −61). Combined: ΔH = +42 + (−61) = −19 kJ mol⁻¹. Enthalpy-favourable — the cell has powered the endothermic synthesis via Hess's Law.
(b)(i) 38 × 30.5 = 1159 kJ mol⁻¹ stored in ATP. (ii) 1159 ÷ 2803 × 100 = 41.3% efficiency. (iii) The remaining 58.7% (~1644 kJ mol⁻¹) is released as heat — maintaining body temperature and supporting enzyme function. This is why your body is warmer than the environment.
1. B — Respiration is the reverse of photosynthesis. Hess's Law: reversing a reaction changes the sign of ΔH. Therefore ΔH(respiration) = −(+2803) = −2803 kJ mol⁻¹.
2. B — Photosynthesis is endothermic (+2803) — meaning glucose + O₂ sit at higher enthalpy than CO₂ + H₂O. Option A has the levels reversed.
3. C — 1 mol: +55 − 30.5 = +24.5 (still positive). 2 mol: +55 − 61 = −6 kJ mol⁻¹ (negative ✓). Minimum = 2 mol.
4. A — This is a direct consequence of Hess's Law and enthalpy being a state function. Mass conservation (option B) is always true but does not by itself explain the ΔH relationship.
5. D — ΣΔH°f(products) = 6(−393.5) + 6(−285.8) = −4075.8; ΣΔH°f(reactants) = 1(−1272.8) + 6(0) = −1272.8; ΔH = −4075.8 − (−1272.8) = −2803.0 kJ mol⁻¹. Option C is just the products sum, not the final answer.
Q6 (4 marks):
(a) Photosynthesis: 6CO₂(g) + 6H₂O(l) → C₆H₁₂O₆(s) + 6O₂(g) ΔH = +2803 kJ mol⁻¹ [1]; Respiration: C₆H₁₂O₆(s) + 6O₂(g) → 6CO₂(g) + 6H₂O(l) ΔH = −2803 kJ mol⁻¹ [1].
(b) Respiration is the exact chemical reverse of photosynthesis — the same reactants and products but in opposite roles [½]. By Hess's Law, reversing a thermochemical equation multiplies ΔH by −1 [½]. Therefore ΔH(respiration) = −ΔH(photosynthesis), making the values equal in magnitude and opposite in sign [1].
Q7 (4 marks):
(a) Plants are open systems that continuously absorb energy from sunlight [1]. The 2803 kJ mol⁻¹ required for photosynthesis is supplied by solar radiation absorbed by chlorophyll — energy is not created, it is converted from electromagnetic (light) energy to chemical energy stored in glucose bonds [1]. Conservation of energy is maintained.
(b) In both cases, an endothermic process is made thermodynamically feasible by coupling it to an exothermic energy source [1]. Plants couple photosynthesis to sunlight; animals couple biosynthesis to ATP hydrolysis. In both cases, the thermodynamic principle is identical: adding the endothermic and exothermic equations (Hess's Law) gives a combined ΔH that is negative (or at least more negative than the endothermic reaction alone) [1].
Q8 (5 marks):
(a) Yes — chemically correct per mole of glucose [½]. Respiration is the reverse of photosynthesis. By Hess's Law (reversing a reaction reverses ΔH), ΔH(respiration) = −ΔH(photosynthesis) = −(+2803) = −2803 kJ mol⁻¹ per mole of glucose [1]. The magnitudes are equal and the signs are opposite [½].
(b) The broader claim is oversimplified — at least three factors are missing: (i) Not all photosynthesised glucose is immediately respired — biomass accumulates (wood, fossil fuels), storing energy on geological timescales [1]; (ii) Combustion of fossil fuels releases carbon fixed by ancient photosynthesis that was not respired — adding CO₂ to the atmosphere that was previously sequestered [1]; (iii) The rates of photosynthesis and respiration globally are not equal, which is why atmospheric CO₂ levels have been changing — true global balance would require equal rates over all timescales and all organisms [1].
Hess's Law Applied — Photosynthesis & Respiration
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