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` thich [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`)

Explanation

Mass of film = (Volume of film) (Density of film)
= (Area of film) (Thickness of film) (density of film)
`= (100 cm xx 300 cm) (1000 xx 10 Å)(10^(-8) cm Å^(-1)) (1.0 g cm^(-3))`
`= 3.0 g`
The equation involves `n` moles each of `(CH_(3))_(2) SiCl` and `(CH_(3))_(2) SiO`. Therefore, 1 mol `(74 g)` of `(CH_(3))_(2) SiO` in the film requires 1 mol `(129 g)` of `(CH_(3))_(2) SiCl_(2)`.
Thus, `3.0 g (CH_(3))_(2) SiO` requires `= 3.0 xx (129)/(74) g`
`= 5.23 g (CH_(3))_(2) SiCl_(2)`