One of the major concerns about a “positive feedback” loop in global warming cau
ID: 933024 • Letter: O
Question
One of the major concerns about a “positive feedback” loop in global warming caused by CO2 is that rising temperatures push more of the Earth’s CO2 into the atmosphere, which further causes warming. In this problem, we will explore, in a quantitative sense, this effect, in a simplified model. The following reactions are of interest. CO2 can exist in both a gaseous phase, or in an aqueous phase dissolved in water. However, dissolved CO2 can disassociate into carbonic acid: CO2 + H2O 2H+ + CO 3 Let us denote s = [CO2(g)], t = [CO2(aq)], x = [CO 3 ], a = [H+].
Henry’s law tells us that s = k(T)t with k 0 (T) > 0, and T the temperature. Similarly, we denote with the equilibrium coefficient for the CO2 dissolution reaction (absorb into the concentration of H2O).
(a) Using charge conservation, the equations of chemical equilibrium, and conservation of carbon (assume total concentration c), find the solution to the equations, and show that the solution is unique.
(b) Show that x, a and s increase when T increases, and that t decreases.1 Thus, this would cause a feedback loop with increases in CO2 increasing T
Explanation / Answer
(a): The equilibrium reaction for the dissolution of CO2 in water is
CO2(g) + H2O ---- > CO2(aq) or H2CO3
According to Henry's law,
[CO2(g)] = k * [CO2(aq)] * T
or s = k(T)t ---- (1)
The equilibrium reaction for the dissociation of CO2(aq) or H2CO3 is
CO2(aq) or H2CO3 < ---- > CO32-(aq) + 2 H+(aq)
K = ([CO32-(aq)]*[H+(aq)]2 ) / [CO2(aq)] = x*a2* / t ----- (2)
(b): From equation (1), when temperature, T is directly proportional to 's'.
Hene 's' increasees with T.
Now form equation (2), the value of equilibrium constant, 'K' increases with temperature.
As 'K' increases the value of 'x' and 'a' will also increase according to equation (2).
Hence x, a , and s increase when T increases (proved)
Hence
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