The Mystery of Helium Diffusion Through Pyrex Glass
How can we explain the phenomenon of helium diffusion through pyrex glass?
What factors affect the rate at which helium will "leak" out of a pyrex tube?
Explanation:
Pyrex glass is known to be almost impermeable to all gases except Helium. The diffusivity of Helium through pyrex is significantly higher than that of other gases like Hydrogen. This unique property opens up the possibility of separating Helium from natural gas based on its relative diffusion through pyrex.
The expression for the rate at which Helium will leak out of a pyrex tube can be calculated using the diffusivity of Helium through pyrex, the interfacial concentrations of Helium in the pyrex, and the dimensions of the tube.
According to Fick's law, the rate of diffusion can be expressed as:
R = (-DHeA/L) * ((CHe,2 - CHe,1)/ln(R2/R1))
Here, DHe represents the diffusivity of Helium through pyrex, A is the cross-sectional area of the tube, L is the length of the tube, CHe,1 and CHe,2 are the interfacial concentrations of Helium at the inner and outer surfaces of the tube, and R1 and R2 are the inner and outer radii of the tube, respectively.
This equation illustrates the flux of Helium through the tube, where the negative sign indicates the direction of diffusion from high to low concentration. The natural logarithm term in the denominator takes into account the radial concentration gradient.
Factors such as diffusivity, concentration difference, and tube dimensions play a crucial role in determining the rate at which Helium will leak out. A higher diffusivity and concentration difference, coupled with smaller tube dimensions, will lead to a faster leakage of Helium.
Understanding this equation is fundamental in comprehending the separation process based on the relative diffusivities of Helium and other gases through pyrex glass, offering insights into the mysteries of gas diffusion phenomena.