Question

Photosynthetic efficiency. Use the following information to estimate the efficiency of photosynthesis. The \(\Delta G^{\circ}\) for the reduction of \(\mathrm{CO}_{2}\) to the level of hexose is \(+477 \mathrm{kJ} \mathrm{mol}^{-1}\left(+114 \mathrm{kcal} \mathrm{mol}^{-1}\right)\) A mole of 600 -nm photons has an energy content of \(199 \mathrm{kJ}\) \((47.6 \mathrm{kcal})\) Assume that the proton gradient generated in producing the required NADPH is sufficient to drive the synthesis of the required ATP.

Short answer

The photosynthetic efficiency is approximately 80%.

Step-by-step solution

Understanding the Energy Requirements

Photosynthesis involves the reduction of CO₂ to the level of hexose sugar, which requires energy. The change in Gibbs free energy (ΔG°) for this process is given as +477 kJ/mol. This means that 477 kJ of energy is needed to synthesize one mole of the hexose from carbon dioxide under standard conditions.

Calculate the Energy Available from Photons

Each photon at 600 nm has an energy of 199 kJ/mol. This is the energy available from one mole of these photons. Since photosynthesis utilizes light energy to drive the reaction, this value helps us understand the energy input we have at disposal for photosynthesis.

Determine Number of Photons Needed

To find out how many moles of 600 nm photons are required to meet the energy demand of 477 kJ/mol for reducing CO₂, divide the energy required by the energy per mole of photons: \[ \text{Number of photons} = \frac{477 \text{ kJ/mol}}{199 \text{ kJ/mol}} = 2.4 \] This indicates that at least 2.4 moles of photons are necessary for the process.

Interpret the Theoretical Efficiency

The theoretical efficiency of photosynthesis can be calculated based on the fraction of energy used versus the energy absorbed. Since 2.4 moles of photons are necessary, and photosynthesis must operate at whole numbers of molecules, it will typically require at least 3 moles of photons. Therefore, the theoretical efficiency is the ratio of required energy (ΔG°) to the energy provided by the photons used. The efficiency \( \eta \) can be estimated by: \[ \eta = \frac{477 \text{ kJ/mol}}{3 \times 199 \text{ kJ/mol}} \times 100 ext{%} = 80 ext{%} \]

Key concepts

Photosynthesis

Photosynthesis is a process used by plants, algae, and some bacteria to harness energy from sunlight to produce glucose from carbon dioxide and water. This glucose serves as a vital energy source for the plant and, indirectly, for other organisms through the food chain. To capture sunlight, plants use a green pigment called chlorophyll, located in chloroplasts. Chlorophyll absorbs specific light wavelengths, predominantly blue and red, facilitating the conversion of light energy into chemical energy.

During photosynthesis, light energy splits water molecules, releasing oxygen and transferring energy into ATP and NADPH molecules. The ATP and NADPH generated are used in the Calvin cycle, where carbon dioxide (CO₂) is fixed into glucose (a process known as carbon fixation).

Photosynthesis is crucial for life on Earth as it provides oxygen and acts as the foundation of food webs.

Gibbs Free Energy

Gibbs free energy, designated as \( \Delta G \), is a thermodynamic property that measures the energy available to do work in a system at constant temperature and pressure. It is especially crucial for understanding chemical reactions. In the context of photosynthesis, the \( \Delta G^{\circ} \) for the reduction of CO₂ to form glucose is +477 kJ/mol. This positive value indicates that the reaction requires an input of energy to proceed.

The value of Gibbs free energy determines how energy-intensive a reaction is, giving insight into how difficult a chemical transformation may be. During photosynthesis, this energy comes from sunlight absorbed by chlorophyll. Plants must capture and convert sufficient solar energy to match this required energy input to synthesize glucose effectively.

Photon Energy

Photon energy is the energy carried by a single photon, which is the basic unit of light. It depends on the wavelength or frequency of the light, following the equation E = h * c / λ, where 'E' is the energy, 'h' is Planck's constant, 'c' is the speed of light, and 'λ' is the wavelength.

In the exercise, photons with a wavelength of 600 nm carry an energy of 199 kJ/mol. This provides a quantifiable measure of how much solar energy is available for photosynthesis. Calculating the number of photons required to meet the energy demands of the photosynthetic process is essential for determining the efficiency of the system. By knowing the energy contribution from photon absorption, one can evaluate the entire photosynthetic process's potential efficiency.

NADPH and ATP Synthesis

NADPH and ATP are critical energy carriers in the photosynthetic process. Their synthesis is directly linked to the light-dependent reactions of photosynthesis that occur in the thylakoid membranes of chloroplasts.

1. **ATP Generation:** - ATP is produced through a process known as photophosphorylation. - Light energy creates a proton gradient across the thylakoid membrane, driving the synthesis of ATP from ADP and inorganic phosphate by the enzyme ATP synthase.

2. **NADPH Production:** - NADPH is formed when electrons, energized by light, are transferred through the electron transport chain. - Eventually, these electrons reduce NADP⁺ to NADPH, a critical reduction equivalent required for the Calvin cycle.

The energy stored in ATP and NADPH is then utilized in the Calvin cycle to fix carbon dioxide, producing glucose. Together, ATP and NADPH are indispensable for sustaining the energy-intensive processes channeled into forming carbohydrates during photosynthesis.