${C O}_{2}$ gas adsorbed on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of ${C O}_{2}$ adsorbed becomes 64 times when the pressure of ${C O}_{2}$ is doubled. The value of $n$ in the Freundlich isotherm equation is $. . . . \times 10^{- 2}$ (report to nearest integer value)

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answer is 17.

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Detailed Solution

According to Freundlich isotherm,

$\frac{x}{m} = k p^{\frac{1}{n}}$ ____(1)

When pressure is double then it can be written as,

$64 \frac{x}{m} = k (2 p)^{\frac{1}{n}}$ _____(2)

Divide equation (2) by (1).

$64 = \frac{(2 p)^{\frac{1}{n}}}{p^{\frac{1}{n}}} = 2^{\frac{1}{n}}$

$\frac{1}{n} = 6$

$n = \frac{1}{6} = 17 \times 10^{- 2}$

$n ≃ 17$

Hence the value $n$ is equal to $17$ .

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