1. Acid rain refers to precipitation events in which the rainwater has a relatively low pH....

 

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1. Acid rain refers to precipitation events in which the rainwater has a relatively low pH. The acidic environment inside a rain droplet is produced when acid precursors present in the air (such as SO2) are absorbed into the droplet. In this problem, we will consider the absorption of SO into a spherical water droplet exposed to air with SO. A 2 mm-radius water droplet initially containing no SO is in a cloud that is suddenly exposed to air with an SO mole fraction of 0.01 at 15 and 1 atm. At 15 C, the diffusivity of SO2 in liquid water is 2.3 x 105 cm/s. Equilibrium between air and water is represented by Henry's law: P= 50 xa, where P is the partial pressure of SO in the air (atm), and xA is its mole fraction in the liquid. The molar density of liquid water is 0.0556 mol/cm. (a) Determine the time required for the center of the droplet to reach 95% of the steady-state concentration of SO2. (b) Calculate the total number of moles of SO in the water droplet at that time. You may assume that external convection produced by the relative motion between the air and the droplet is very fast, and that the SO2 will not undergo chemical reactions during its absorption. 1. Acid rain refers to precipitation events in which the rainwater has a relatively low pH. The acidic environment inside a rain droplet is produced when acid precursors present in the air (such as SO2) are absorbed into the droplet. In this problem, we will consider the absorption of SO into a spherical water droplet exposed to air with SO. A 2 mm-radius water droplet initially containing no SO is in a cloud that is suddenly exposed to air with an SO mole fraction of 0.01 at 15 and 1 atm. At 15 C, the diffusivity of SO2 in liquid water is 2.3 x 105 cm/s. Equilibrium between air and water is represented by Henry's law: P= 50 xa, where P is the partial pressure of SO in the air (atm), and xA is its mole fraction in the liquid. The molar density of liquid water is 0.0556 mol/cm. (a) Determine the time required for the center of the droplet to reach 95% of the steady-state concentration of SO2. (b) Calculate the total number of moles of SO in the water droplet at that time. You may assume that external convection produced by the relative motion between the air and the droplet is very fast, and that the SO2 will not undergo chemical reactions during its absorption.