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Calculate the diameter (d) of the cylindrical pores with length (C) present in a catalyst having internal surface area of $\mathrm{900 \mathrm{~m}^2}$ per $\mathrm{\mathrm{cm}^3}$ of a bulk material whose half of the bulk volume have pores and other half is made of solid substance considering that the measured surface area is the total area of the curved surfaces of the tubules.
Option: 1
$\mathrm{25 ~A^{\circ}}$

Option: 2
$\mathrm{32 \mathrm{~A}^{\circ}}$

Option: 3
$\mathrm{22 \mathrm{~A}^{\circ}}$

Option: 4
$\mathrm{15~ A^{\circ}}$

Answers (1)

best_answer

$\mathrm{\text { Basis }=1 \mathrm{~cm}^3 \text { of catalyst }}$

$\mathrm{\therefore \text { Total volume of pores }=0.5 \times 1}$

$\mathrm{=0.5 \mathrm{~cm}^3}$

Consider, n no. of total pores are present.

$\mathrm{\therefore \text { volume of each pore }=\frac{1}{4} \pi d^2 l}$

$\mathrm{=\frac{1}{4} \pi d^2 l \times n=0.5 \mathrm{~cm}^3}$

$\mathrm{\text { surface ara of total pores }=900 \mathrm{~m}^2}$

$\mathrm{9 \times 10^6 \mathrm{~cm}^2=n \times \pi \mathrm{dl}}$

$\mathrm{\therefore \frac{\frac{1}{4} \times \pi d^2 l \times n}{n \pi d l}=\frac{d}{4}=\frac{0.5 \mathrm{~cm}^3}{9 \times 10^6 \mathrm{~cm}^2}}$

$\mathrm{d=\frac{0.5 \times 4}{9 \times 10^6}}$

$\mathrm{=22 A^{\circ}}$

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