# $10 \:\:mL$ of  $1\:\: mM$ surfactant solution forms a monolayer covering $0.24\:\:cm^{2}$ on a polar substrate . If the polar head is approximated as a cube , what is its edge length ? Option 1) $1.0\:pm$ Option 2) $2.0\:pm$ Option 3) $0.1\:nm$ Option 4) $2.0\:nm$

Mole Concept -

One mole is the amount of a substance that contains as many particles or entities as there are atoms in exactly 12 g (or 0.012 kg) of the 12C isotope.

- wherein

one mole = 6.0221367 X 1023

Number of Moles -

No of moles = given mass of substance/ molar mass of substance

-

given $1\:\:mM\:\:and\:\:10\:\:mL$

so

$No.\:\: of\:\: moles\:\: absorbed = 10^{-3}\times10^{-3}\times10=10^{-5}$

$No.\:\: of\:\: molecules\:\: absorbed = 10^{-5}\times N_{A}$

and

$total.\:\: area \:occupied\: = 10^{-5}\times N_{A}\times a^{2}$

given

$10^{-5}\times N_{A}\times a^{2}=0.24(adsorbed \:\:area)$

$a^{2}=\frac{0.24}{10^{-5}\times N_{A}}cm^{2}$

$a^{2}=\frac{0.24}{10^{-5}\times 6\times 10^{23}}=4\times10^{20}cm^{2}$

$a=2\times10^{-12}m=2\:\:pm$

Option 1)

$1.0\:pm$

Option 2)

$2.0\:pm$

Option 3)

$0.1\:nm$

Option 4)

$2.0\:nm$

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