Chemistry 331 Homework 7: Atmospheric CO2 and Seawater Equilibria - Prof. Stefan Franzen, Assignments of Physical Chemistry

Download Chemistry 331 Homework 7: Atmospheric CO2 and Seawater Equilibria - Prof. Stefan Franzen and more Assignments Physical Chemistry in PDF only on Docsity! 1 Homework #7 Due: November 9 Name _________________________ Chemistry 331 1. The presence of carbon dioxide in the atmosphere is a concern because of the role it plays in absorbing blackbody emission by the earth. The atmosphere is 0.036% carbon dioxide. A. Calculate the mole fraction of CO2 and the total number of metric tons of CO2 in the atmosphere. For this calculation use 6400 km for the radius of the earth. B. If an average of 10 billion tons of CO2 is emitted into the atmosphere each year, calculate the partial pressure of CO2 that one can expect in 2105 (100 years from now) assuming that no CO2 is absorbed by the oceans. 2. CO2 sequestration has occurred on a geologic time scale by the formation of limestone (CaCO3) in the oceans. However the process is slow and there is a significant calcium carbonate and bicarbonate concentration in seawater and brackish water. The calcium content of seawater is about 410 mg/L. The solubility product of calcium carbonate is Ksp = [Ca2+][CO32-] = 5 x 10-9 at 298 K. CaCO3 (s) Ca2+(aq) + CO3-(aq) (I) Eqn. I is an example of a heterogeneous equilibrium. One does not consider the concentration of CaCO3 in the equilibrium constant. This expression can also apply to a particle of CaCO3 as it settles to the bottom of the ocean. The concentration of CO32- depends on pH because of the two acid equilibria. CO2 + H2O HCO3- + H+ (II) pKa(1) = 6.37 HCO3- CO32- + H+ (III) pKa(2) = 10.25) There are three different conditions possible: Q = [Ca2+][CO32-] > K supersaturated Q = [Ca2+][CO32-] = K saturated Q = [Ca2+][CO32-] < subsaturated A. Calculate the concentration of CO2 in seawater assuming 360 ppm CO2 in the atmosphere. The Henry’s law constant for CO2 is 29.76 atm/(mol/L). B. Calculate the concentration of bicarbonate and carbonate in seawater at pH = 8.1 using the equilibria above and assuming that there is not other source of carbonate or hydrogen carbonate other than from the atmosphere. 2 C. Based on this calculation find ∆G for formation of calcium carbonate in the ocean. Predict whether CaCO3 would precipitate or dissolve under the conditions that all of the carbon came from the atmosphere. In other words predict the degree of saturation. D. In reality there is much more carbonate in the ocean than one would predict based on Henry’s law and the above equilibria. The reason is that the ocean absorbes CO2. By Le Chatelier’s principle the CO2 gets converted to HCO3- and then to CO32- so that the ocean can absorb much more CO2 than Henry’s law would indicate. This is a complicated equilibrium and we will not attempt to calculate this from first principles. Current estimates are that the actual carbonate concentration is 200 µM. Calculate the degree of saturation when this concentration is present and the calcium ion concentration is 410 mg/L as above. Assume T = 298 K. E. Apparently the oceans are absorbing a lot of the CO2 that is emitted by human activity (by the equilibrium you calculated above using Henry’s law). As CO2 is absorbed it can react with the CO32- in the ocean according to the equilibrium: CO2 + CO32- + H2O 2 HCO3- Using the data above calculate the equilibrium constant for this reaction. Assuming that the concentration of [CO32-] is 200 µM and the concentration of CO2 is given by Henry’s law (calculated in part A. above) calculate the concentration of hydrogen carbonate in the ocean. F. If all of the carbonate were to sediment the ocean would keep absorbing CO2 (following the Henry’s law equilibrium). Calculate the change in pH according to the data you have calculated above, if all of the atmospheric CO2 were absorbed by the ocean. The volume of the oceans is 1.347 x 1018 m3. G. Calcium carbonate dissolves at high pressure. If one examines the bottom of the earth’s oceans, one finds that calcite and aragonite deposits (the two major forms of calcium carbonate) only occur in water that has depth less than about 5000 m. The depth of 5000 m is called the Carbonate Compensation Depth (CCD). It is also called the “snow line”. In water that is shallower than 5000 m calcium carbonate can precipitate (snow) and cover the ocean floor. In ocean water deeper than 5000 m there is no calcium carbonate and the ocean bottom is a clay flat known as the abyssal plain. It turns out the main driving force for the dissolution of calcium carbonate in deep water is the change in the density of water from its bulk density (1.0 g/ml.) to a high local density in the inner coordination sphere of calcium and carbonate ions. Calculate this local density assuming that the free energy for the dissolution of the crystal is 46.8 kJ/mol. In other words ∆G is 46.8 kJ/mol for the reaction CaCO3 Ca2+ + CO32-.