Question

It is estimated that the net amount of carbon dioxide fixed by photosynthesis on the landmass of Earth is \(5.5 \times\) \(10^{16} \mathrm{~g} / \mathrm{yr}\) of \(\mathrm{CO}_{2}\). Assume that all this carbon is converted into glucose. (a) Calculate the energy stored by photosynthesis on land per year in \(\mathrm{kJ}\). (b) Calculate the average rate of conversion of solar energy into plant energy in MW \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\). A large nuclear power plant produces about \(10^{3} \mathrm{MW}\). The energy of how many such nuclear power plants is equivalent to the solar energy conversion?

Short answer

(a) The energy stored by photosynthesis on land per year is approximately \(8.66 \times 10^{15}\, \mathrm{kJ}\). (b) The average rate of conversion of solar energy into plant energy is about \(2.75 \times 10^5\, \mathrm{MW}\). The solar energy conversion is equivalent to about 275 nuclear power plants, each producing \(10^{3} \mathrm{MW}\) of power.

Step-by-step solution

Calculate the moles of glucose produced from carbon dioxide

First, we need to find the moles of glucose (C_6H_{12}O_6) produced from the given amount of carbon dioxide (CO_2). Since the balanced equation for photosynthesis is: \[6 \,\text{CO}_2 + 6 \,\text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6 \,\text{O}_2\] From the equation, it's clear that 6 moles of CO_2 produce 1 mole of glucose. To determine the moles of glucose, we need to find the moles of CO_2 and divide it by 6: Moles of CO_2 = \(\frac{\text{mass of CO}_2}{\text{Molar mass of CO}_2}\) = \(\frac{5.5 \times 10^{16} \,\text{g}}{44.01 \,\text{g/mol}}\)

Calculate the amount of glucose produced

Now we can find the moles of glucose produced by dividing the moles of CO_2 by the moles of glucose: Moles of glucose = \(\frac{\text{moles of CO}_2}{6}\)

Calculate the mass of glucose produced

We can now find the mass of glucose produced by multiplying the moles of glucose with the molar mass of glucose (180.16 g/mol): Mass of glucose = moles of glucose × 180.16 g/mol

Calculate the energy stored in glucose per year

Using the energy content of glucose (4.18 kJ/g), we can find the energy stored in glucose per year: Energy stored in glucose per year = mass of glucose × 4.18 kJ/g

Calculate the average rate of solar energy conversion

We have the amount of energy stored in glucose per year. To calculate the average rate of solar energy into plant energy, first, convert the energy per year into energy per second: Energy per second = \(\frac{\text{Energy stored per year}}{\text{Seconds in a year}}\) Then, convert the energy per second into MegaWatt: Energy per second in MW = \(\frac{\text{Energy per second}}{10^6 \,\text{J/s}}\)

Calculate the equivalent number of nuclear power plants

We know that the large nuclear power plant produces about \(10^3 \,\text{MW}\). To find the equivalent number of such nuclear power plants to the solar energy conversion, we divide the average rate of solar energy conversion by the power plant energy production: Number of nuclear power plants = \(\frac{\text{Average rate of solar energy conversion}}{10^3\,\text{MW}}\) Following these steps will give us the energy stored by photosynthesis on land per year (a), and the average rate of conversion of solar energy into plant energy in MW (b), as well as the energy conversion equivalence to nuclear power plants.

Key concepts

Carbon Dioxide Fixation

Photosynthesis is a fascinating process where plants convert carbon dioxide (CO₂) and water (H₂O) into glucose (C₆H₁₂O₆) and oxygen (O₂) using sunlight energy. One of the critical steps in this process is carbon dioxide fixation. This refers to the transformation of inorganic carbon (CO₂) into organic molecules like glucose. During photosynthesis, plants capture CO₂ from the atmosphere and, through a molecule called RuBisCO, incorporate it into an organic molecule. This occurs in the Calvin Cycle, a series of reactions that take place in the chloroplasts of plant cells. - Carbon fixation reduces atmospheric CO₂ levels, playing an essential role in mitigating climate change. - The fixed carbon is stored as glucose, which can be used as energy or converted to other forms like starch for storage. Understanding carbon fixation helps us appreciate how plants contribute to both food chains and the global carbon cycle.

Energy Conversion

A significant aspect of photosynthesis is the conversion of solar energy into chemical energy. This energy conversion is crucial because it allows plants to store energy in a form that is usable both for themselves and other organisms. Through photosynthesis, light energy from the sun is absorbed by chlorophyll molecules in plant cells and converted into chemical energy. This happens via two stages: the light-dependent reactions and the Calvin Cycle.

• Light-dependent reactions: Solar energy is captured and used to generate ATP (adenosine triphosphate) and NADPH, which are energy carriers.
• Calvin Cycle: ATP and NADPH are used to fix carbon dioxide into glucose during the light-independent reactions.

This energy conversion is efficient enough to power a vast ecosystem, highlighting its importance in sustaining life on Earth.

Solar Energy

Sunlight is the primary source of energy for photosynthesis. Without solar energy, the entire process would not be possible. The energy from the sun provides the power needed for plants to transform carbon dioxide and water into glucose and oxygen. The efficiency of this conversion varies, but on average, plants use a small percentage of solar energy for photosynthesis. Despite the low efficiency, the immense amount of energy available from the sun compensates for this, allowing plants to produce significant amounts of glucose over time. - Solar energy powers the photosynthetic machinery of plants, enabling growth and development. - This energy drives ecosystems as it is transferred from plants to herbivores and up the food chain. By harnessing solar energy, photosynthesis forms the foundation of the planet's energy pyramid.

Glucose Production

The end product of photosynthesis that most people are familiar with is glucose. This molecule serves as an energy source for plants and, indirectly, for most life on Earth. Once produced, glucose can follow several pathways to fuel plant activities. - **Immediate use for energy:** Plants can break down glucose through respiration to release energy for cellular processes. - **Storage as starch:** Excess glucose can be converted into starch, a larger carbohydrate molecule that serves as an energy reserve. - **Building blocks for growth:** Glucose provides the raw materials for producing cellulose and other structural substances required for plant growth. Glucose is transported throughout the plant via the phloem, ensuring that energy reaches all cells. This versatile molecule not only sustains plant life but also supports animals and humans relying on plants for nutrition.