19B.7 Time for a droplet to evaporate. A droplet of pure A of initial radius R is suspended in a large body of motionless gas B. The concentration of A in the gas phase is xAR at r = R and zero at an infinite distance from the droplet. (a) Assuming that R is constant, show that at steady state dx 1- XA AB (19B.7-1) dr where NAlER is the molar flux in the r direction at the droplet surface, c is the total molar concentration in the gas phase, and DAB temperature and pressure throughout. Show that integration of Eq. 19B.7-1 from the droplet surface to infinity gives is the diffusivity in the gas phase. Assume constant RNArlr=R = -cD AB In(1 – xAR) (19B.7-2) (b) We now let the droplet radius R be a function of time, and treat the problem as a quasi-steady one. Then the rate of decrease of moles of A within the drop can be equated to the instantaneous rate of loss of mass across the liquid-gas interface d - GTR°C) = 47R°N,rlr=R = -4rReDg In(1 – *AR) In(1 – XAR) (19B.7-3) %3D Ar r=R АВ dt where c is the molar density of pure liquid A. Show that when this equation is integrated from t = 0 to t = t, (the time for complete evaporation of the droplet), one gets to (19B.7-4) In[1/(1 – xAR)] 2cD AB

The normal boiling point of a 5-molal solution of sodium chloride in water is found to be 379.2 K. What will be the boiling point of the solution at 70kPa ? The vapour pressure of water is given by In P = 16.26205 3799.887 T - 46.854 where P is in kPa and T is in K. Assume that the relative vapour pressure is independent of temperature.

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You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved perfectly into the water. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round, with a 17.5 foot radius. It is 8 feet tall and has 8 feet of water in it.How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the Kool-Aid contaminated water is σ=64.1lbs/ft^3

A 0.103-m³ tank contains 8.6x1026 molecules of N₂ at 17 MPa. Compute the (a) specific volume. Also, determine the temperature in the tank using (b) the Van der Waals equation, (c) Beattie- Bridgeman equation and (d) Benedict-Webb-Rubin equation of state. Compare each temperature you obtained with the actual value (which is 182.8 K) by computing the % error.

Draw a Pxy diagram for an aqueous solution of NH3. The temperature is such that the vapor pressure of the pure water is 5 kPa and the vapor pressure of pure NH3 is 600 Pa. You need to include the bubble line and the dew 7. line. (a) What is the vapor pressure of the solution when rNH, = 0.6? (b) In which phase the solution will be at P = 4.8 kPa? (c) In which phase the solution will be at P =0.2 kPa? (d) Draw the path for a process that takes a liquid with INH, = 0.6 %3D and P= 4.8 kPa to P= 0.2 kPa.

Consider the following chemical equilibrium: HCOOH(aq) + H_2O(aq) \rightleftharpoons HCOO^-(aq) + H_3O^+(aq). Which of the following graphs represents the perturbation on the system and the change of pH when water is evaporated from the container?