It is estimated that the net amount of carbon dioxide fixed by photosynthesis on the landmass of Earth is 5.5 * 10^16 g/yr of CO2. Assume that all this carbon is converted into glucose. (b) Calculate the average rate of conversion of solar energy into plant energy in megawatts, MW (1 W = 1 J/s). A large nuclear power plant produces about 10^3 MW. The energy of how many such nuclear power plants is equivalent to the solar energy conversion?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

검증된 단계별 안내

Step 1: Determine the moles of CO2 fixed per year. Use the molar mass of CO2 (44.01 g/mol) to convert the given mass of CO2 (5.5 * 10^16 g/yr) into moles.

Step 2: Use the balanced chemical equation for photosynthesis: 6 CO2 + 6 H2O -> C6H12O6 + 6 O2. From this equation, determine the moles of glucose (C6H12O6) produced from the moles of CO2 calculated in Step 1.

Step 3: Calculate the energy stored in glucose. The combustion of glucose releases approximately 2800 kJ/mol. Use this value to find the total energy stored in the glucose produced per year.

Step 4: Convert the total energy from kilojoules to joules (1 kJ = 1000 J) and then to watts (1 W = 1 J/s). Since the energy is per year, convert the time to seconds (1 year = 365 days * 24 hours/day * 3600 seconds/hour).

Step 5: Calculate the equivalent number of nuclear power plants. Divide the average rate of conversion of solar energy (in MW) by the power output of a large nuclear power plant (10^3 MW) to find the number of such plants needed to match the solar energy conversion.

주요 개념

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Photosynthesis and Carbon Fixation

Photosynthesis is the process by which green plants, algae, and some bacteria convert light energy into chemical energy, primarily in the form of glucose, using carbon dioxide and water. The net amount of carbon dioxide fixed during this process is a measure of how much CO2 is converted into organic compounds, which is essential for understanding the energy conversion efficiency of plants.

Energy Conversion and Units

Energy conversion refers to the process of changing energy from one form to another, such as converting solar energy into chemical energy during photosynthesis. In this context, energy is measured in joules (J), and power, which is the rate of energy conversion, is measured in watts (W), where 1 W equals 1 J/s. Understanding these units is crucial for calculating the average rate of energy conversion.

Comparative Energy Analysis

Comparative energy analysis involves evaluating different energy sources and their outputs. In this question, the energy produced by photosynthesis is compared to that of nuclear power plants, which produce energy in megawatts (MW). This comparison helps to contextualize the scale of energy conversion in plants relative to large-scale energy production facilities.

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교과서 질문

Sucrose (C12H22O11) is produced by plants as follows: 12 CO2(g) + 11 H2O(l) → C12H22O11 + 12 O2(g) H = 5645 kJ About 4.8 g of sucrose is produced per day per square meter of the earth's surface. The energy for this endothermic reaction is supplied by the sunlight. About 0.1 % of the sunlight that reaches the earth is used to produce sucrose. Calculate the total energy the sun supplies for each square meter of surface area. Give your answer in kilowatts per square meter 1kW/m2 where 1W = 1 J/s2.

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