Question

In one process for waterproofing, a fabric is exposed to $(C{H}_3{)}_{2}SiC{l}_2$ vapour. The vapour reacts with hydroxyl groups on the surface of the fabric or with traces of water to form the waterproofing film $\left[\right(C{H}_3{)}_{2}SiO{]}_n$ by the reaction:
$n\left(C{H}_3\right)SiC{l}_2+2nOH\to 2nC{l}^{-}+n{H}_{2}O+\left[\right(C{H}_3{)}_{2}SiO{]}_n$
Here, $n$ stands for a large integer. The waterproofing film is deposited on the fabric layer upon layer. Each layer is $6.0$ $A^o$ thick [the thickness of the $(C{H}_3{)}_{2}SiO$ group].Then amount of $\left(C{H}_3\right)SiC{l}_2$ needed to waterproof one side of a piece of fabric, $1.00$ m by $3.00$ m with a film $300$ layers thick will be :
The density of the film is $1.0$ g/cc.

• A. $0.22$ g
• B. $0.552$ g
• C. $0.9413$ g
• D. $1.8826$ g

Answer 1

Answer: (C)

$0.9413$ g

We know, $1A^0={10}^{-10}m={10}^{-8}cm$
The volume of $1$ layer of the film is $1.00m\times \frac{100cm}{1m}\times 3.00m\times \frac{100cm}{1m}\times 6.0A^0\times \frac{{10}^{-8}cm}{1A^0}=0.0018c{m}^3$.
The volume of $300$ layers of the film is $300\times 0.0018c{m}^3=0.54c{m}^3$.
The density of the film is $1.0gc{m}^3$.
The mass of 300 layers of film is $M=d\times V=1.0g/c{m}^3\times 0.54c{m}^3=0.54g$.
The molar mass of $(C{H}_3{)}_{2}SiC{l}_2$ is $2\left(15\right)+28.1+2\left(35.5\right)=30+28.1+71=129.1g/mol$.
The molar mass of $(C{H}_3{)}_{2}SiO$ is $2\left(15\right)+28.1+16=30+28.1+16=74.1g/mol$.
Then amount of $(C{H}_3{)}_{2}SiC{l}_2$ needed to waterproof one side of a piece of fabric, $1.00$ m by $3.00$ m with a film $300$ layers thick will be $\frac{129.1}{74.1}\times 0.54=0.9413g$.