Suppose that the CO2 output from one of the plants in Example 7-4 is sequestered b reaction with MgO to form MgCO3, rather than injection into an aquifer. In order to sequester CO2 at a sufficient rate, the reactants must be heated to 680 K, consuming 34 kJ/mol CO2; the reaction itself releases 115

Question

Suppose that the CO[latex]_2[/latex] output from one of the plants in Example 7-4 is sequestered b reaction with MgO to form MgCO[latex]_3[/latex], rather than injection into an aquifer. In order to sequester CO[latex]_2[/latex] at a sufficient rate, the reactants must be heated to 680 K, consuming 34 kJ/mol CO[latex]_2[/latex]; the reaction itself releases 115 kJ/mol CO[latex]_2[/latex]. (a) What is the mass of MgO that is required each year to sequester the CO[latex]_2[/latex] stream? (b) What is the mass of MgCO[latex]_3[/latex] produced? (c) Ignoring any losses in the process, what is the net energy flux during MgCO[latex]_3[/latex] formation, in MW?

Accepted Answer

(a) The atomic masses, rounded to the nearest whole number, of magnesium, oxygen, and carbon are 24, 16, and 12, respectively.

Therefore, the mass of MgO is 40. Since the amount of CO[latex]_2[/latex] sequestered is
1.47 × 10[latex]^6[/latex] tonnes/year, the amount of MgO is (40/44)(1.47 × 10[latex]^6[/latex] tonnes/year) = 1.34 × 10[latex]^6[/latex] tonnes/year.

(b) The mass of MgCO[latex]_3[/latex] is 84, so the amount of MgCO[latex]_3[/latex] is (84/44)(1.47 × 10[latex]^6[/latex] tonnes/year) = 2.81 × 10[latex]^6[/latex] tonnes/year.

(c) The net energy released per mole is 115 – 34 = 81 kJ/mol. The number of moles of CO[latex]_2[/latex] per year is

[latex]\frac{1.47 imes 10^{6} ext { tonne }}{44 \mathrm{~g} / \mathrm{mol}}\left(\frac{10^{6} \mathrm{~g}}{ ext { tonne }} ight)=3.34 imes 10^{10}[/latex]

Therefore the net energy released per year is (3.34 × 10[latex]^{10}[/latex])(81) = 2.71 × 10[latex]^{12}[/latex] kJ. Dividing by the number of seconds per year, or 3.1536 × 10[latex]^{7}[/latex] s, gives 8.58 × 10[latex]^{4}[/latex] kW or 85.8 MW.

Question 7.5: Suppose that the CO2 output from one of the plants in Exampl...

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