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Chapter 5: Problem 111

It is estimated that the net amount of carbon dioxide fixed by photosynthesis on the landmass of Earth is \(5.5 \times 10^{16} \mathrm{~g} /\) 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 kJ. (b) Calculate the average rate of conversion of solar energy into plant energy in \(\mathrm{MW}(1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}) .\) 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

Expert verified
(a) The energy stored by photosynthesis on land per year is \(3.744 \times 10^{18} \mathrm{~kJ}\). (b) The average rate of solar energy conversion into plant energy is \(1.187 \times 10^{5} \mathrm{MW}\). The solar energy conversion by photosynthesis on land is equivalent to the energy produced by approximately 119 large nuclear power plants.

Step by step solution

01

Find the number of moles of glucose formed

First, we need to convert the given mass of carbon dioxide, \(5.5 \times 10^{16} \mathrm{~g}\), to moles. To do this, we will use the molar mass of carbon dioxide, \(44.01 \mathrm{~g/mol}\), and the stoichiometry of the reaction, which shows a 1:1 ratio between carbon dioxide and glucose. Number of moles of carbon dioxide = \(\frac{5.5 \times 10^{16} \mathrm{~g}}{44.01 \mathrm{~g/mol}} = 1.248 \times 10^{15} \mathrm{~moles}\) Since there is a 1:1 ratio between carbon dioxide and glucose in the photosynthesis reaction, the number of moles of glucose formed will also be \(1.248 \times 10^{15} \mathrm{~moles}\).
02

Calculate the energy stored per year in kJ

Now that we have the number of moles of glucose, we can find the energy stored per year by photosynthesis. During the respiration process, glucose releases energy, which is approximately \(3.0 \times 10^{3} \mathrm{~kJ/mol}\). Total energy stored per year = (Number of moles of glucose) × (Energy released per mole of glucose) Total energy stored per year = \(1.248 \times 10^{15} \mathrm{~moles} \times 3.0 \times 10^{3} \mathrm{~kJ/mol} = 3.744 \times 10^{18} \mathrm{~kJ}\)
03

Calculate the average rate of solar energy conversion

To find the average rate of solar energy conversion into plant energy, we can use the total energy stored per year and the number of seconds in a year. Total energy stored per year = \(3.744 \times 10^{18} \mathrm{~kJ}\) Number of seconds in a year = \(365 \times 24 \times 3600 = 3.1536 \times 10^{7} \mathrm{~s}\) Average rate of solar energy conversion = \(\frac{3.744 \times 10^{18} \mathrm{~kJ}}{3.1536 \times 10^{7} \mathrm{~s}} \times 10^{3} \mathrm{W/kJ} = 1.187 \times 10^{11} \mathrm{W} = 1.187 \times 10^{5} \mathrm{MW}\)
04

Find the equivalent number of nuclear power plants

A large nuclear power plant produces about \(10^3 \mathrm{MW}\) of energy. To find the equivalent number of such power plants, we can divide the energy conversion rate of photosynthesis by the energy produced by one nuclear power plant. Equivalent number of nuclear power plants = \(\frac{1.187 \times 10^{5} \mathrm{MW}}{10^3 \mathrm{MW}} = 118.7\) Therefore, the solar energy conversion by photosynthesis on land is equivalent to the energy produced by approximately 119 large nuclear power plants.

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Most popular questions from this chapter

Consider the decomposition of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) to gaseous acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g):\) $$ \mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \quad \Delta H=+630 \mathrm{~kJ} $$ (a) What is the enthalpy change for the reverse reaction? (b) What is \(\Delta H\) for the formation of 1 mol of acetylene? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) were consumed instead of \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

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