KVPY Sample Paper KVPY Stream-SX Model Paper-30

10 mL of 1 mM surfactant solution forms a monolayer covering \[0.24\text{ }c{{m}^{2}}\] on a polar substrate. If the polar head is approximated as a cube, what is its edge length?

A) 2.0 nm

B) 0.1 nm

C) 2.0 pm

D) 1.0 pm

Correct Answer: C

Solution :

\[Moles=\frac{m{{v}_{ml}}}{1000}=\frac{{{10}^{-3}}\times 10}{1000}={{10}^{-5}}mole\]

\[{{10}^{-5}}{{N}_{A}}\]molecules covering area\[=0.24\text{ }c{{m}^{2}}\]

\[1{{N}_{A}}\]molecules covering area\[=\frac{0.24}{{{10}^{-5}}{{N}_{A}}}c{{m}^{2}}\]

\[\frac{0.24}{{{10}^{-5}}\times 6\times {{10}^{23}}}={{a}^{2}}\]

\[{{a}^{2}}=4\times {{10}^{-20}}c{{m}^{2}}\]

\[a=2\times {{10}^{-10}}cm\]

\[a=2\times {{10}^{-12}}m\]

\[a=2pm.\]