If 30cm\(^3\) of oxygen diffuses through porous plug in 7s, how long will it take 60 cm\(^3\) of chlorine to diffuse through the same plug?
Given:
t\(_c\) = ? V\(_c\) = 60cm\(^3\) , M\(_c\) = 35.5 x 2 = 71
t\(_o\) = 7s; V\(_o\) = 30cm\(^3\) , M\(_o\) = 16 x 2 = 32
According to Graham's law of diffusion, R ∝ 1/√M
\(\frac{R_o}{R_c}\) = \(\sqrt{\frac{M_c}{M_o}}\)
Also, Rate of diffusion = \(\frac{Volume}{time}\)
\(\frac{R_o}{R_c}\) = \(\frac{V_o}{t_o}\) ÷ \(\frac{V_c}{t_c}\) = \(\frac{V_o}{t_o}\) X \(\frac{t_c}{V_c}\)
Therefore, \(\frac{V_o}{t_o}\) X \(\frac{t_c}{V_c}\) = \(\sqrt{\frac{M_c}{M_o}}\)
\(\frac{{30}\times{t_o}}{{7}{60}}\) = \(\sqrt{\frac{71}{32}}\)
\(\frac{t_c}{14}\) = 1.489
t\(_c\) = 14 x 1.489
t\(_c\) = 20.846
t\(_c\) = 21s
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