hw9_soln

hw9_soln - Homework#9 Name Due December 1 Chemistry 331 1...

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Homework #9 Due: December 1 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 CO 2 and the total number of metric tons of CO 2 in the atmosphere. For this calculation use 6400 km for the radius of the earth. Solution: Using Dalton’s law. P CO2 = y CO2 P total y CO2 = 3.6 x 10 -4 . P CO2 = 3.6 x 10 -4 atm The mass of the atmosphere is given by the definition of pressure. P = Force/Area = m atmosphere g/A earth m atmosphere = PA earth /g = P4 π R earth 2 /g = (1.01325 x 10 5 N/m 2 )(4)(3.141)(6400000 m) 2 /9.8 m/s 2 = 5.3 x 10 18 kg = 5.3 x 10 21 g Convert to moles since the molar mass of CO 2 is different from the other gases in the atmosphere. n atmosphere m atmosphere /M atmosphere = (5.3 x 10 21 g) /29 g/mol = 1.8 x 10 20 moles. n CO2 = n atmosphere y CO2 = (1.8 x 10 20 moles)(3.6 x 10 -4 ) = 6.5 x 10 16 moles m CO2 = n CO2 M CO2 = (6.5 x 10 16 moles)(44 g/mol) = 2.8 x 10 18 g m CO2 = 2.8 x 10 12 metric tons B. If an average of 20 billion tons of CO 2 is emitted into the atmosphere each year, calculate the partial pressure of CO 2 that one can expect in 2105 (100 years from now) assuming that no CO 2 is absorbed by the oceans. Solution: (2 x 10 10 tons)(100) = 2 x 10 12 tons m CO2 = 7.6 x 10 12 metric tons or 7.6/2.8(360 ppm) = 980 ppm 2. CO 2 sequestration has occurred on a geologic time scale by the formation of limestone (CaCO 3 ) 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 K sp = [Ca 2+ ][CO 3 2- ] = 5 x 10 -9 at 298 K. CaCO 3 (s) Ca 2+ (aq) + CO 3 - (aq) (I)

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Eqn. I is an example of a heterogeneous equilibrium. One does not consider the concentration of CaCO 3 in the equilibrium constant. This expression can also apply to a particle of CaCO 3 as it settles to the bottom of the ocean. The concentration of CO 3 2- depends on pH because of the two acid equilibria. CO 2 + H 2 O HCO 3 - + H + (II) pKa(1) = 6.37 HCO 3 - CO 3 2- + H + (III) pKa(2) = 10.25 There are three different conditions possible: Q = [Ca 2+ ][CO 3 2- ] > K supersaturated Q = [Ca 2+ ][CO 3 2- ] = K saturated Q = [Ca 2+ ][CO 3 2- ] < subsaturated A. Calculate the concentration of CO 2 in seawater assuming 360 ppm CO 2 in the atmosphere. The Henry’s law constant for CO 2 is 29.76 atm/(mol/L).
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