Green plants utilize sunlight to convert CO2 and H2O to glucose (C6H12O6) and O2. — Thermodynamics Chemistry Question
Problem Context
Green plants utilize sunlight to convert CO2 and H2O to glucose (C6H12O6) and O2.
Write a balanced equation for this process.
Model Answer
6CO2+6H2O → C6H12O6+6O2
Use the information in the accompanying table to calculate
i. ∆H˚
Model Answer
∆H˚ = –1273.3+0–[6(–393.5)+6(–285.8)] = –1273.3–[–2361–1714.8] = –1273.3+4075.8 = 2802.5 kJ
ii. ∆S˚
Model Answer
ΔS˚ = 212.1+6(205.0)–[6(213.2)+6(69.9)] = 212.1+1230.0–[1279.2+419.4] = 1442.1–1698.6 = –256.5 J/mol K
iii. ∆G˚ at 298 K for this reaction.
Model Answer
ΔG˚ = ΔH˚–TΔS˚ = 2802.5 kJ–298(–.2565 kJ/mol) = 2802.5 kJ+76.44 = 2878.9 kJ/mol
Comment on the spontaneity of this reaction at 25˚C and other temperatures.
Model Answer
Reaction is not spontaneous at 25˚C because ΔG˚>0
Reaction is not spontaneous at other Ts because ∆H˚>0 and ΔS˚<0
Green plants use light with wavelengths near 600 nm for this process. Calculate
i. the energy of a 600 nm photon,
Model Answer
E = 3.31 × 10^-19 J
ii. ∆G˚ for the formation of one molecule of glucose by the reaction in 2a,
Model Answer
ΔG˚ = 4.78 × 10^-18 J/molecule
iii. the minimum number of 600 nm photons required to make one molecule of glucose by the reaction in 2a.
Model Answer
= 14.4 photons
All of the photosynthesis on earth in a year stores 3.4 × 10^18 kJ of solar energy.
i. Use the ∆G˚ for the photosynthetic reaction to calculate the number of moles of CO2 removed from the atmosphere by photosynthesis each year.
Model Answer
= 7.08 × 10^15 mol CO2
ii. Determine the mass of carbon that is fixed annually by photosynthesis.
Model Answer
= 8.50 × 10^16 g C