Tetraethoxysilane, also called TEOS or Si(OC₂H₅)₄, is a liquid chemical used in the semiconductor industry to produce thin films of silicon dioxide by chemical vapor deposition (CVD). In order to deliver the TEOS vapor to the CVD reactor, liquid TEOS is fed to a wetted-wall column. The TEOS liquid uniformly coats the inner surface of the tube as a thin liquid film as it flows downward. The falling liquid film of TEOS evaporates into an inert helium carrier gas flowing upwards at a volumetric flow rate of 2000 cm³/s. The wetted-wall column has an inner diameter of 5.0 cm and a length of 2.0 m. The column temperature is maintained at 333 K, and the total system pressure is 1.0 atm. At 333 K, the kinematic viscosity of helium gas is 1.47 cm²/s, the diffusion coefficient of TEOS vapor in helium gas is 1.315 cm²/s, and the vapor pressure of liquid TEOS is P_A = 2133 Pa.
a. What is the gas mass-transfer coefficient, k_G?
b. What is the mole fraction of TEOS vapor exiting the column?
c. What is the required mass flow rate of liquid TEOS flowing into the column if all of the liquid TEOS evaporates by the time it reaches the bottom of the column?