Question

The Sun supplies about 1.0 kilowatt of energy for each square meter of surface area \(\left(1.0 \mathrm{kW} / \mathrm{m}^{2},\) where a watt \(=1 \mathrm{J} / \mathrm{s}\right)\) 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. $$\begin{array}{c}{12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+12 \mathrm{O}_{2}(g)} \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad {\Delta H=5645 \mathrm{kJ}}\end{array}$$

Short answer

First, we need to convert the 0.20 g of sucrose produced per square meter per hour into moles, using the molar mass of sucrose, which is 342.29 g/mol: Number of moles = \(\frac{0.20\,\text{g}}{342.29\,\text{g/mol}}\) To calculate the energy used to produce sucrose, multiply the moles of sucrose by the given energy per mole (ΔH = 5645 kJ): Energy producing sucrose = moles of sucrose × ΔH Next, convert the energy provided by sunlight, 1.0 kW/m², into kJ per square meter per hour: Energy provided by sunlight = 3600 kJ/h Finally, calculate the percentage of sunlight energy used in sucrose production: Percentage efficiency = \(\frac{\text{Energy producing sucrose}}{\text{Energy provided by sunlight}} \times 100\%\)

Step-by-step solution

Convert Sucrose Produced to Moles

First, let's find out how many moles of sucrose are produced per square meter per hour. Use the molar mass of sucrose (C12H22O11) to convert the mass (0.20 g) into moles: Molar mass of sucrose = 12(12.01) + 22(1.01) + 11(16.00) = 342.29 g/mol Number of moles = \(\frac{0.20\,\text{g}}{342.29\,\text{g/mol}}\)

Calculate Energy Producing Sucrose

The energy required for the production of one mole of sucrose is given as 5645 kJ. Multiply the moles of sucrose obtained in Step 1 by this value to find out the energy used to produce sucrose. Energy producing sucrose = moles of sucrose × ΔH

Calculate Sunlight Energy per Hour

To find the energy provided by the sun per square meter per hour, convert the given value of 1.0 kW/m² in terms of kJ per square meter per hour. 1.0 kW = 1000 W = 1000 J/s Energy provided by sunlight = 1000 J/s × 3600 s/h = 3600,000 J/h = 3600 kJ/h

Calculate the Efficiency

Divide the energy used to produce sucrose (Step 2) by the energy provided by sunlight (Step 3) and multiply by 100 to find the percentage of sunlight energy used in sucrose production. Percentage efficiency = \(\frac{\text{Energy producing sucrose}}{\text{Energy provided by sunlight}} \times 100\%\) By following these steps, you'll be able to determine the energy conversion efficiency of sunlight to sucrose production in plants.

Key concepts

Sucrose Production in Plants

Plants have a remarkable ability to produce complex chemicals like sucrose through the process known as photosynthesis. Sucrose, a type of sugar, is created when plants convert carbon dioxide (CO2) and water (H2O) into glucose (C6H12O6), and then two glucose molecules combine to form sucrose (C12H22O11).

The process begins in the chloroplasts of cells, where CO2 and H2O enter the plant, and with the assistance of sunlight, they are transformed into glucose and oxygen (O2). This is a multi-step process that involves a series of reactions, both light-dependent and light-independent. In the light-dependent reactions, the energy from sunlight is captured and used to produce ATP and NADPH, which are energy carriers. The light-independent reactions, also known as the Calvin cycle, then use ATP and NADPH to convert CO2 into glucose. Once glucose is produced, two molecules combine through a series of enzymatic reactions to form sucrose.

Enzymes play a crucial role in this process, facilitating the chemical reactions needed for the synthesis of sucrose. These enzymes ensure that plants produce sucrose efficiently, which is crucial for their growth, as it serves as a primary energy source and metabolic intermediate. Additionally, plants store sucrose or convert it into other carbohydrates, such as starch, for long-term energy storage.

Energy Conversion in Photosynthesis

Photosynthesis is not only critical for producing essential molecules like sugars but also showcases the plant's talent in energy conversion. This phenomenon is where plants convert light energy from the sun into chemical energy stored in the bonds of sugars, like sucrose.

The whole process starts with light absorption by pigments in the chloroplast, most significantly chlorophyll, which captures specific wavelengths of light. This light energy is then converted into chemical energy through the previously mentioned stages of photosynthesis. The efficiency of this conversion is of paramount importance because it dictates how well a plant can sustain itself and grow.

To determine this efficiency, scientists look at the amount of light energy a plant receives versus the energy stored in the chemical bonds of the produced sugars. By calculating the energy used to produce a quantity of sucrose and comparing it with the total sunlight energy received by the plant over the same time period, we can express photosynthetic efficiency as a percentage. This tells us how effectively a plant transfers the energy from sunlight into the energy in sucrose.

Chemical Energy from Sunlight

Sunlight is the ultimate source of energy for nearly all life on Earth. Plants have adapted to harness this energy through photosynthesis, converting solar energy into chemical energy. The currency of this chemical energy is ATP and NADPH, which are then used to build organic compounds like sucrose.

The energy from sunlight is immense—about 1.0 kilowatt per square meter reaches the Earth's surface. Plants tap into a fraction of this energy, matching the extraordinary complexity of synthesizing sugar molecules from simple inorganic compounds. The conversion rate, or the percentage of sunlight energy that plants use for sucrose production, is typically not very high. However, it is sufficient to sustain the plant's needs and contribute to the energy requirements of other organisms that rely on plants for food.

By understanding the process and measuring the energy content of the resulting sucrose, we get an insight into the effectiveness of this energy conversion. The exercise provided illustrates this by estimating the percentage of sunlight used in the production of sucrose, which reflects the plant's photosynthetic efficiency in using solar energy to fuel its metabolic processes.