Question

Photosynthesis is the process by which plants effectively capture energy from the sun and store it for later use by organisms. It's the fundamental process that enables the entire food chain. Actual photosynthesis is a highly complex process involving many steps and many different chemicals, but we can get an idea of what's happening to thermodynamic quantities (enthalpy, Gibbs free energy, and entropy) using simpler reactions.

Let's consider a toy model in which an input of energy (for example from the sun) is be used to combine water and carbon dioxide to create an organic molecule (formaldehyde) and oxygen, effectively "storing" that energy for use later. The simplest possible such process is given by:

CO₂ + H₂O → O₂ + CH₂O

The table lists the enthalpy of formation, ΔH_f and the entropy S for 1 mol of each of the substances involved in this reaction at 298 K and 10⁵ Pa.

	ΔHf (kJ)	S (kJ/K)
CH2O	-115.9	0.2189
H2O	-241.82	0.1888
CO2	-393.51	0.2138
O2	0	0.2051

Answer the following questions assuming that 1 mol of formaldehyde molecules are formed.

1. What is the change in enthalpy of this reaction?
ΔH =  kJ

Does this change in enthalpy represent energy that must be added to the system, or energy that is released from the system?
---Select--- Energy must be added Energy is released

2. What is the change in entropy for this reaction?
ΔS =  kJ/K

Does the entropy increase or decrease?
---Select--- Entropy increases Entropy decreases

At 298 K, what is the heat transfer that corresponds to this change in entropy?
Q =  kJ
Does this heat transfer represent energy that is added to the system, or energy that is released from the system?
---Select--- Energy is added Energy is released

3. What is the change in Gibbs free energy for this reaction?
ΔG =  kJ

The Gibbs free energies of formation, ΔG_f, are: -228.57 kJ for water; -394.36 kJ for CO₂; and 0 kJ for O₂. What is the Gibbs free energy of formation for formaldehyde?
ΔG_f (formaldehyde) =  kJ

4. Using the formation of formaldehyde as a model, comment on photosynthesis and the formation of sugars using what we know about entropy and free energy.

Answer 1

1. given reaction
CO2 + H2O -> O2 + CH2O
let enthalapy of formation for the above reactants be x1, x2, x3, and x4
let entropy be y1, y2, y3, y4

then change in enthalapy of the reaction is dH
dH = (x4 + x3) - (X2 + x2) = (-115.9 - 0) - (-241.82 -393.51)
dH = 519.43 kJ

since this is +ve, this means enthalapy has to be added to the system
2. similiarly, dS = (y4 + y3) - (y2 + y1) = 0.0214 kJ/K
since this is +ve, the entropy increases

T = 298K
dS = dQ/T
dQ = 298*dS = 6.3772 kJ

3. Change in gibbs free energy for the reaction is dG
dG = dH - TdS
dG = 519.43 kJ - 6.3772 kJ = 513.0528kJ is the gibbs free energy change of the reaction

now, let gibbs energy of formation of the reactans and products be z1, z2, z3 and z4 respectively
then
dG = (z4 + z3) - (z2 + z1)
dG + (-228.57 kJ -394.36 kJ ) - 0 = z4
z4 = -109.8772 kJ

4. as we can see, gibbs free energy of formation of formaldehyde is -ve, change in entropy is +ve and enthalapy of reactio nis +ve
this means photosynthesis is a spontaneous reaction that can occur when energy is supplied to the reactants