Question

The sun supplies about \(1.0\) kilowatt of energy for each square meter of surface area \(\left(1.0 \mathrm{~kW} / \mathrm{m}^{2}\right.\), where a watt \(=1 \mathrm{~J} / \mathrm{s})\). Plants produce the equivalent of about \(0.20 \mathrm{~g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) per hour per square meter. Assuming that the sucrose is produced as follows, calculate the percentage of sunlight used to produce sucrose. $$ \begin{aligned} 12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+12 \mathrm{O}_{2}(g) \\ \Delta H &=5645 \mathrm{~kJ} \end{aligned} $$

Short answer

\(= 5.84 \times 10^{-4} \text{ mol}\)

Step-by-step solution

Convert sucrose mass to moles

In order to find the energy needed for the sucrose production, we will first convert the mass of sucrose to moles. We know that the molecular weight of sucrose is 342.30 g/mol (12*12 + 22*1 + 11*16). $$\text{Moles of sucrose} = \frac{\text{mass}}{\text{molecular weight}} = \frac{0.20 \text{ g}}{342.30 \text{ g/mol}}$$

Key concepts

Energy Conversion

Energy conversion in the context of photosynthesis is essentially the process of transforming solar energy into chemical energy. This transformation is what makes life on Earth sustainable, as plants capture light energy from the sun and use it to fuel their growth and the growth of organisms that depend on plants.
To calculate energy conversion efficiency, it’s essential to understand how much energy from the sunlight is being converted into chemical energy. Let's consider the energy provided by sunlight, which is about 1 kilowatt per square meter ( W/m^2). This is equivalent to 1000 joules per second per square meter.
When we think about energy conversion in photosynthesis:

• Plants capture the sunlight and convert it into chemical energy.
• This chemical energy is primarily stored in the form of glucose and other carbohydrates.
• By measuring how much of the incoming solar energy is transformed into chemical energy stored in molecules like sucrose, we can find out the efficiency of photosynthesis.

This gives us insight into how efficiently plants are using the solar energy they receive, a critical aspect in understanding the full potential of photosynthesis.

Sucrose Production

Sucrose production is an integral output of the photosynthesis process in plants. Sucrose, a type of sugar, is one of the primary compounds plants use to store the energy derived from sunlight.
To better grasp this, let's look at the role sucrose plays:

• Sucrose is synthesized in the plant leaves, where photosynthesis occurs, then transported to different parts of the plant for energy use or storage.
• This compound is essentially a disaccharide formulated from glucose and fructose.
• Plants produce around 0.20 g of sucrose per hour per square meter of leaf area under optimal sunlight.

The process is quite efficient and allows plants to manage their energy needs across different growth stages. Understanding how plants convert light energy into sucrose helps in realizing the importance of photosynthesis as a major energy conversion system in the natural world.

Photosynthesis Reaction

The photosynthesis reaction is a complex chemical process, crucial for the survival of many life forms. It involves converting light energy, water, and carbon dioxide into glucose and oxygen.
The general equation for the photosynthesis reaction highlighted in the problem is:\[ 12 ext{CO}_2 (g) + 11 ext{H}_2 ext{O} (l) \rightarrow ext{C}_{12} ext{H}_{22} ext{O}_{11} + 12 ext{O}_2 (g) \]This reaction specifically illustrates the formation of sucrose as a photosynthesis product.More on the reaction specifics:

• The reaction requires a significant amount of energy, \( ext{Δ}H = 5645 ext{kJ} \), for the formation of one mole of sucrose.
• By effectively performing this reaction, plants convert the absorbed light energy into a form that is chemically more stable - sucrose.
• The oxygen released as a byproduct is essential for the survival of aerobic organisms, including humans.

This chemical transformation not only produces essential sugars for the plants themselves but also supports the larger ecosystem by contributing to the atmospheric oxygen supply.