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The volume of nitrogen gas Vm (at STP) r...

The volume of nitrogen gas Vm (at STP) required to cover a sample of silica gel with a mono-molecular layer is `129 cm^2 g^(-1)` of gel. Calculate the surface area per gram of the gel if each nitrogen molecule occupies `16.23 xx 10^(-20) m^2`

A

562.6

B

461.8

C

831.6

D

941.8

Text Solution

Verified by Experts

The correct Answer is:
A
`22400 cm^3 of N_2 ` at STP contain ` = (6.02 xx 10^(23) xx 129)/(22400) = 3.4668 xx 10^(21)` molecules
Area occupied by a single molecule `= 16.23 xx 10^(-20) m^2`
Therefore, area occupied by `3.4668 xx 10^(21)` molecules of `N_2`
`= (16.23 xx 10^(-20)) xx (3.4668 xx 10^(21))m^2 = 562.6 m^2`
Therefore , surface area per gram of gel ` = 562.6 m^2`
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