a) Photosynthesis is estimated to produce 360.0 g (dry weight) of plant matter per square meter, 50% of which is carbon. Calculate the total number of grams of carbon "fixed" each year by 1000 square meters.
b) The photosynthetic reaction can be represented as:
6CO2 + 6H2O -> C6H12O6 + 6O2
Of the glucose produced, 20.0% is used by the plant to fuel respiration; the rest is converted to plant matter. Calculate the total moles of glucose produced annually in our reference 1000 square meter area.
c) Each mole of glucose produced represents the absorption of 2803 kJ of solar energy. If the average energy available from the sunlight over an eight-month period is 1.1 kJ/cm2 per day, what percentage of the incident solar energy is converted to chemical energy in our 1000 square meter area?
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a) To calculate the total number of grams of carbon fixed each year by 1000 square meters, we need to multiply the amount of plant matter produced per square meter by the percentage of carbon in that plant matter.
Given:
- Photosynthesis produces 360.0 g (dry weight) of plant matter per square meter.
- 50% of the plant matter is carbon.
So, the calculation would be:
Total grams of carbon fixed per square meter = 360.0 g (dry weight) / square meter * 0.50 (carbon percentage) = 180.0 g of carbon per square meter.
Now, to calculate the total number of grams of carbon fixed each year by 1000 square meters, we multiply the grams of carbon per square meter by the number of square meters:
Total grams of carbon fixed each year = 180.0 g of carbon per square meter * 1000 square meters = 180,000 g of carbon.
b) To calculate the total moles of glucose produced annually in our reference 1000 square meter area, we need to use the balanced equation for photosynthesis:
6CO2 + 6H2O -> C6H12O6 + 6O2
From the equation, we know that 1 mole of glucose (C6H12O6) is produced for every 6 moles of carbon dioxide (CO2) consumed.
Given:
- The total grams of carbon fixed each year is 180,000 g.
To convert grams of carbon to moles of glucose, we use the molar mass of carbon (12.01 g/mol) and the ratio from the balanced equation:
Total moles of glucose produced = (180,000 g / 12.01 g/mol) / 6 = 2500 moles of glucose.
c) To calculate the percentage of incident solar energy converted to chemical energy in our 1000 square meter area, we need to know the total energy absorbed in kJ and the total incident solar energy.
Given:
- Each mole of glucose produced represents the absorption of 2803 kJ of solar energy.
- The average energy available from sunlight over an eight-month period is 1.1 kJ/cm2 per day.
The first step is to calculate the total incident solar energy over the eight-month period in our 1000 square meter area:
Total incident solar energy = 1.1 kJ/cm2 per day * 1000 square meters * (8 months * 30 days/month)
Note: We assume each month has 30 days for simplicity.
Next, we calculate the total energy absorbed by the moles of glucose produced:
Total energy absorbed = 2500 moles of glucose * 2803 kJ/mol.
Finally, we calculate the percentage of incident solar energy converted to chemical energy:
Percentage of solar energy converted = (Total energy absorbed / Total incident solar energy) * 100.