In one process of waterproofing, a fabric is expsoed to `(CH_(3))_(2) SiCl` vapour. The vapour reacts with `(OH)` groups on the surface of the fabric or with traces of `H_(2) O` to form waterproofing film of by the reaction
Where `n` is large integer. The waterproofing film is deposited on the fabric layer upon layer. Each layer is `10 Å` thick [the thickness of the `(CH_(3))_(2) SiO` group]. How much `(CH_(3))_(2) SiCl_(2)` is required to waterproof one side of a piece of a fabric, `1.0 m` by `3.0 m`, with a film 1000 layers thick? The density of the film is `1.0 g cm^(-3)`. (Atomic weight of `Si = 28` and `Cl = 35.5`)

Answer

`0.9413` gram

Explanation

Volume `1xx3xx300xx6xx10^(-10)`
`=5.4xx10^(-7)m^(3)=0.54cm^(3)`
`p=1g//cm^(3)`
mass `=0.54g`
`n(CH_(3))_(2)SiCl_(2)+2nOH^(-)rarr2nCl^(-)+nH_(2)O+[(CH_(3))_(2)SiO]_(n)`
`(w)/(129)" "(w)/(129n)xx(74n)`
`(74w)/(129)=0.54implies w=0.9413 g`