A plant makes a silicone from 1.00 kg of silicon (28.09 g/mol) by the steps Si + 2CH₃Cl →…

A plant makes a silicone from $1.00\ \text{kg}$ of silicon ($28.09\ \text{g/mol}$) by the steps $\text{Si} + 2\text{CH}_{3}\text{Cl} \to (\text{CH}_{3})_{2}\text{SiCl}_{2}$ and $(\text{CH}_{3})_{2}\text{SiCl}_{2} + \text{H}_{2}\text{O} \to (\text{CH}_{3})_{2}\text{SiO} + 2\text{HCl}$. All of the silicon reacts, and every step gives the full yield. The molar masses are $129.06\ \text{g/mol}$ for $(\text{CH}_{3})_{2}\text{SiCl}_{2}$, $74.15\ \text{g/mol}$ for the unit $(\text{CH}_{3})_{2}\text{SiO}$ and $36.46\ \text{g/mol}$ for HCl. Find the mass of the dichloride, the mass of the silicone, and the mass of hydrogen chloride that forms. Then find the number of $(\text{CH}_{3})_{2}\text{SiO}$ units in a chain of molar mass $37\,000\ \text{g/mol}$.