   Chapter 24, Problem 29GQ

Chapter
Section
Textbook Problem

(a) Calculate the enthalpy change for the production of one mole of glucose by the process of photosynthesis at 25 °C.∆fH° [glucose(s)] = –1273.3 kJ/mol 6 CO2(g) + 6 H2O(ℓ) → C6H12O6(s) + 6 O2(g) (b) What is the enthalpy change involved in producing one molecule of glucose by this process? (c) Chlorophyll molecules absorb light of various wavelengths. One wavelength absorbed is 650 nm. Calculate the energy of a photon of light having this wavelength. (d) Assuming that all of this energy goes toward providing the energy required for the photo- synthetic reaction, can the absorption of one photon at 650 nm lead to the production of one molecule of glucose, or must multiple photons be absorbed?

(a)

Interpretation Introduction

Interpretation:

The value of enthalpy change ΔrH° for the production of one mole of glucose by the process of photosynthesis at 25°C has to be calculated.

6CO2(g)+6H2O(l)C6H12O6(s)+6O2(g)

Concept introduction:

The change in the enthalpy of a reaction when the reactant is converted into product under standard conditions is called standard enthalpy of reaction.

The expression for standard enthalpy of reaction is,

ΔrH°=nΔfH°(products)nΔfH°(reactants) (1)

Here, ΔfH° is the standard enthalpy of formation and n is the number of moles of reactant and product in the balanced chemical reaction.

Explanation

The value of ΔrH° for the production of one mole of glucose by the process of photosynthesis at 25°C is calculated below.

Given:

Refer to Appendix L for the values of standard enthalpy of formation.

The standard enthalpy of formation of C6H12O6(s) is 1273.3 kJ/mol.

The standard enthalpy of formation of O2(g) is 0 kJ/mol.

The standard enthalpy of formation of H2O(l) is 285.8 kJ/mol.

The standard enthalpy of formation of CO2(g) is 393.5 kJ/mol.

The reaction involved in photosynthesis is,

6CO2(g)+6H2O(l)C6H12O6(s)+6O2(g)

The ΔrH° can be calculated by the following expression,

ΔrH°=nΔfH°(products)nΔfH°(reactants)=[[(1 mol C6H12O6(s)/mol-rxn)ΔfH°[C6H12O6(s)]+(6 mol O2(g)/mol-rxn)ΔfH°[O2(g)]]</

(b)

Interpretation Introduction

Interpretation:

The enthalpy change involved in producing one molecule of glucose by the process of photosynthesis at 25°C has to be calculated.

Concept introduction:

The relationship between the number of moles and the number of molecules is,

Number of moles, n=number of molecules(N)Avagadro number(NA)

Also,

1 mole = 6.023×1023 molecules

(c)

Interpretation Introduction

Interpretation:

The energy of a photon of light having a wavelength 650 nm has to be calculated.

Concept introduction:

The energy of one photon (E) is given as,

E=hν=hcλ (2)

Here, c is the speed of light, λ is the wavelength of light, h is Planks constant.

Value of c=3.0×108 ms1 and h=6.626×1034 Js1.

(d)

Interpretation Introduction

Interpretation:

The absorption of one photon at 650 nm can lead to the production of one molecule of glucose or multiple photons must be absorbed has to be predicted.

Concept introduction: If the energy of one photon is greater than the energy required for the production of one mole of substance then single photon absorption is sufficient for the reaction to proceed else multiple photons must be absorbed.

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