The rate of diffusion is mathematically presented as:
\({\rm{\alpha }}{{\rm{u}}_{{\rm{rms}}}}\)
\(\begin{array}{l}{\rm{u}}_{{\rm{rms}}}^{\rm{2}}{\rm{ \alpha K}}{{\rm{E}}_{{\rm{avg}}}}{\rm{ \alpha }}\frac{{\rm{3}}}{{\rm{2}}}{\rm{RT \alpha T}}\\{\rm{u}}_{{\rm{rms}}}^{\rm{2}}{\rm{ \alpha T = u}}_{{\rm{rms}}}^{\rm{2}}{\rm{ \alpha }}\sqrt {\rm{T}} \end{array}\)
The rate of diffusion is \({\rm{(R) \alpha }}\sqrt {\rm{T}} \).
The \({\rm{c - }}\) proportional constant is \({\rm{R = cT}}\).
For the gas 1, the rate of diffusion is:
\({\rm{(}}{{\rm{R}}_{\rm{1}}}{\rm{) = }}{{\rm{c}}_{\rm{1}}}\sqrt {\rm{T}} \)
For gas 2, the rate of diffusion is:
\({\rm{(}}{{\rm{R}}_{\rm{2}}}{\rm{) = }}{{\rm{c}}_{\rm{2}}}\sqrt {\rm{T}} \)
Then the ratio is:
\(\begin{array}{c}\frac{{{{\rm{R}}_{\rm{1}}}}}{{{{\rm{R}}_{\rm{2}}}}}{\rm{ = }}\frac{{{{\rm{c}}_{\rm{1}}}\sqrt {\rm{T}} }}{{{{\rm{c}}_{\rm{2}}}\sqrt {\rm{T}} }}\\{\rm{ = }}\frac{{{{\rm{c}}_{\rm{1}}}}}{{{{\rm{c}}_{\rm{2}}}}}\end{array}\)
Therefore, the ratio is unaffected by temperature. As a result, the ratio of the rate of diffusion will remain the same at \({{\rm{0}}^{\rm{o}}}{\rm{ C}}\) and \({\rm{10}}{{\rm{0}}^{\rm{o}}}{\rm{ C}}\).
