Theories of Mass Transfer

EXAMPLE $3\mathrm{.}5($Gas absorption in a laminar jet$)$ Gas absorption in a laminar liquid jet is model experimental technique for the determination of the liquid$-$phase diffusivity of a solubl gas and also for studying the kinetics of gas$-$liquid reactions. A sketch of a laminar jet apparatu is given in Figure $3\mathrm{.}9.$ A liquid jet is created by forcing the liquid through a narrow vertical tube fitted within an enclosure. If an appropriate flow rate is maintained, the liquid comes out as jet $($that very much looks like a liquid rod or cylinder$).$ The jet is collected in a tube of a diamete marginally greater than that of the jet and having a slightly flared opening. This liquid collectio tube is oriented vertically below the jet. The solute gas, diluted with a carrier if necessary, flow through the enclosure. The rate of absorption of the gas is determined either by measuring th inlet and the outlet gas flow rates or by analyzing the concentration of the dissolved gas in th exit liquid.

In an experiment for the determination of the diffusivity of hydrogen sulphide in water, pur $H_{2}S$ gas is passed through the enclosure of the jet. The following data were collected in particular experiment at steady state: temperature $=25C$; total pressure in the jet chamber $=1\mathrm{.}03$atm; length of the jet $=5cm$; rate of flow of water $=13\mathrm{.}2m\frac{l}{s}$; absorption rate of $H_2=4\mathrm{.}42{10}^{-4}\frac{g}{s}.$ The solubility of $H_{2}S$ in water at $1$atm pressure and $25C$ is $0\mathrm{.}1136$kmol $(m^3)(atm).$ Calculate the diffusivity of $H_{2}S$ in water from the above data.

Figure $3\mathrm{.}9$ A simplified sketch of the laminar jet apparatus.