Glass etching is an important industrial process that uses caustic solutions to dissolve the outer layer...

 

Transcribed Image Text:

Glass etching is an important industrial process that uses caustic solutions to dissolve the outer layer of glass to remove surface defects resulting from the tempering process. Consider a cylindrical rod of glass that is very long relative to its cross-sectional diameter such that L >> D and of density p. Here, the glass can be approximated as pure silica (SiO2), and the reaction occurs only at the solid-liquid interface with area rate constant k. For simplicity, assume the amount of hydroxide is in excess and the solution is well-stirred to maintain a constant concentration of [OH] at the surface. L>> D Initial Diameter (Do) = 2 SiO2 cm k = 4*102 gsi02 (m psio2 = 2 g (cm)-1 *S Note: The rate constant units imply that the surface reaction is first-order with respect to [OH] only. a) Set up a differential equation for the rate of change of the diameter of the glass rod. b) How long does it take for the glass rod to reach a diameter of 1.9 cm? Glass etching is an important industrial process that uses caustic solutions to dissolve the outer layer of glass to remove surface defects resulting from the tempering process. Consider a cylindrical rod of glass that is very long relative to its cross-sectional diameter such that L >> D and of density p. Here, the glass can be approximated as pure silica (SiO2), and the reaction occurs only at the solid-liquid interface with area rate constant k. For simplicity, assume the amount of hydroxide is in excess and the solution is well-stirred to maintain a constant concentration of [OH] at the surface. L>> D Initial Diameter (Do) = 2 SiO2 cm k = 4*102 gsi02 (m psio2 = 2 g (cm)-1 *S Note: The rate constant units imply that the surface reaction is first-order with respect to [OH] only. a) Set up a differential equation for the rate of change of the diameter of the glass rod. b) How long does it take for the glass rod to reach a diameter of 1.9 cm?

Answer rating: 100% (QA)

a To set up a differential equation for the rate of change of the diameter of the glass rod we can u... View the full answer