Chemistry - Mole Concept Question with Solution | TestHub

The reaction is $n({\mathrm{CH}}_3{)}_2{\mathrm{SiCl}}_2+2n{\mathrm{OH}}^{-}⟶2n{\mathrm{Cl}}^{-}+n{\mathrm{H}}_2\mathrm{O}+[({\mathrm{CH}}_3{)}_2\mathrm{SiO}{]}_n$.

The molar mass of $({\mathrm{CH}}_3{)}_2{\mathrm{SiCl}}_2$ is $2(12)+6(1)+28+2(35.5)=129g/mol$.

The molar mass of $({\mathrm{CH}}_3{)}_2\mathrm{SiO}$ is $2(12)+6(1)+28+16=74g/mol$.

Area of fabric = $1.00m\times 3.70m=3.70m^2=3.70\times 10^{4}c{m}^2$.

Total film thickness = $300layers\times 6.0\mathring{A}/layer=1800\mathring{A}=1800\times 10^{-8}cm=1.8\times 10^{-5}cm$.

Volume of film = Area $\times$ Thickness = $3.70\times 10^{4}c{m}^2\times 1.8\times 10^{-5}cm=0.666c{m}^3$.

Mass of film = Volume $\times$ Density = $0.666c{m}^3\times 1.0g/c{m}^3=0.666g$.

From the stoichiometry, 1 mole of $({\mathrm{CH}}_3{)}_2{\mathrm{SiCl}}_2$ produces 1 mole of $({\mathrm{CH}}_3{)}_2\mathrm{SiO}$ unit in the polymer.

Mass of $({\mathrm{CH}}_3{)}_2{\mathrm{SiCl}}_2$ needed = Mass of film $\times \frac{Molarmassof({\mathrm{CH}}_3{)}_2{\mathrm{SiCl}}_2}{Molarmassof({\mathrm{CH}}_3{)}_2\mathrm{SiO}}$

Mass of $({\mathrm{CH}}_3{)}_2{\mathrm{SiCl}}_2$ needed = $0.666g\times \frac{129g/mol}{74g/mol}=1.16g$.