Question

Use the following information to estimate the efficiency of photosynthesis. The \(\Delta G^{\text {o\prime }}\) 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

Photosynthetic efficiency is approximately 41.7%.

Step-by-step solution

Understand the Objective

To estimate the efficiency of photosynthesis, we need to determine how effectively plants convert light energy, measured by the energy of the photons, into chemical energy, as represented by the reduction of CO2 to hexose.

Calculate Energy Required for Hexose

The exercise states that the \( \Delta G^{\text{o\prime }} \) (change in free energy) for converting CO2 to hexose is given as \(+477 \, \mathrm{kJ} \, \mathrm{mol}^{-1}(+114 \, \mathrm{kcal} \, \mathrm{mol}^{-1})\).

Determine the Energy of Photons Used

Each mole of 600-nm photons provides \(199 \, \mathrm{kJ} \, (47.6 \, \mathrm{kcal})\). This is the energy contribution per mole of photons.

Calculate Number of Photons Needed

To find out the number of photons needed to provide the required energy for one mole of hexose, divide the energy needed by the energy per mole of photons: \( \text{Number of photons needed} = \frac{477 \, \mathrm{kJ} }{199 \, \mathrm{kJ/mol}} \approx 2.40 \).

Compute Photosynthetic Efficiency

Efficiency is calculated as \( \text{Efficiency} = \frac{\text{Energy output (chemical energy)}}{\text{Energy input (photon energy)}} \. Using the calculated photon number, efficiency \approx \frac{1}{2.4} \approx 41.7\% \).

Interpret the Result

This efficiency shows that under the given conditions, approximately 41.7% of the photon's energy is converted into chemical energy during photosynthesis.

Key concepts

Photon Energy

Photon energy is a fundamental concept needed to understand photosynthesis efficiency. A photon is a basic unit of light, carrying energy that plants capture during photosynthesis.
In the context of our exercise, we refer to photons with a wavelength of 600 nm. This is within the visible spectrum, where most photosynthetic activity occurs due to optimal absorption by chlorophyll.
Each mole of these 600-nm photons carries an energy content of 199 kJ. This energy contributes directly to driving the photosynthetic reactions. The importance of photon energy cannot be understated as it represents the input energy needed for photosynthesis.
Understanding the energy provided by photons is crucial when you look at how efficiently this energy can be converted to chemical energy in plants, allowing them to grow and produce oxygen.

Hexose Formation

Hexose formation is the primary goal of photosynthesis. Hexose sugars, such as glucose, are key outputs of the photosynthetic process. These sugars serve as energy storage and structural components for the plant.
The chemical reaction involved in hexose formation is complex but efficient. It averts directly converting atmospheric CO2 into glucose, a six-carbon sugar, through a sequence of reactions known as the Calvin Cycle.
The process of forming one mole of hexose from CO2 requires a free energy change of +477 kJ/mol. This high energy requirement emphasizes the challenge plants face in converting light energy into chemical energy. Efficient hexose formation is crucial for plant growth and the continuation of the food chain.

Free Energy Change

Free energy change, represented by \( \Delta G^{\text{o\prime}} \), is a measure of energy conversion within a system. It tells us how much energy is either released or required during a chemical reaction.
In photosynthesis, the transformation of CO2 to hexose involves a positive free energy change of +477 kJ/mol. This indicates that the reaction is endergonic, requiring an input of energy to proceed.
Efficient photosynthesis hinges on the ability to supply this necessary energy through light absorption, converting photonic energy into chemical bonds.

• A positive \( \Delta G^{\text{o\prime}} \) means that energy absorption is pivotal for creating the sugars that plants rely on.
• Understanding free energy change also helps us account for environmental conditions and their effect on the efficiency of photosynthesis.

With these insights, we gain a deeper understanding of how plants efficiently harness energy from sunlight, bridging the gap from light energy to stored chemical energy.