The stoichiometric reaction of 516 g of dimethyldichlorosilane with water results in a tetrameric cyclic product X in 75% yield. The weight (in g) of X obtained is:

The correct answer is 222.

Step 1: Understand the reaction mechanism
When dimethyldichlorosilane, ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{SiCl}}_2$, reacts with water ($H_{2}O$), it undergoes hydrolysis to form dimethylsilanediol, ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{Si(OH)}}_2$, releasing $\mathrm{HCl}$:

${\left({\mathrm{CH}}_3\right)}_2{\mathrm{SiCl}}_2+2H_{2}O\to {\left({\mathrm{CH}}_3\right)}_2{\mathrm{Si(OH)}}_2+2\mathrm{HCl}$

The hydrolysed product, ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{Si(OH)}}_2$, undergoes condensation. Four molecules of ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{Si(OH)}}_2$ condense with the elimination of water molecules to form a tetrameric cyclic siloxane, product X, which has the formula ${\left[{\left({\mathrm{CH}}_3\right)}_2\mathrm{SiO}\right]}_4$ (octamethylcyclotetrasiloxane):

$4{\left({\mathrm{CH}}_3\right)}_2{\mathrm{SiCl}}_2+4H_{2}O\to {\left[{\left({\mathrm{CH}}_3\right)}_2\mathrm{SiO}\right]}_4+8\mathrm{HCl}$

From the overall stoichiometric equation, 4 moles of ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{SiCl}}_2$ produce 1 mole of tetrameric product X, ${\left[{\left({\mathrm{CH}}_3\right)}_2\mathrm{SiO}\right]}_4$.

Step 2: Calculate the molar masses
Molar mass of dimethyldichlorosilane, ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{SiCl}}_2$:
• C: 2 × 12 = 24 g/mol
• H: 6 × 1 = 6 g/mol
• Si: 1 × 28 = 28 g/mol
• Cl: 2 × 35.5 = 71 g/mol
Molar Mass = 24 + 6 + 28 + 71 = 129 g/mol

Molar mass of repeating monomer unit ${\left({\mathrm{CH}}_3\right)}_2\mathrm{SiO}$:
• C: 2 × 12 = 24 g/mol
• H: 6 × 1 = 6 g/mol
• Si: 1 × 28 = 28 g/mol
• O: 1 × 16 = 16 g/mol
Molar mass of monomer unit = 74 g/mol

Molar mass of tetramer X, ${\left[{\left({\mathrm{CH}}_3\right)}_2\mathrm{SiO}\right]}_4$:
Molar Mass = 4 × 74 = 296 g/mol

Step 3: Calculate moles and theoretical yield
Given mass of ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{SiCl}}_2$ = 516 g

$\text{Moles of reactant}=\frac{516}{129}=4\text{moles}$

According to stoichiometry, 4 moles of reactant produce 1 mole of cyclic tetramer X.

$\text{Theoretical moles of X}=1\text{mole}$

$\text{Theoretical mass of X}=1\text{mole}\times 296\text{g/mol}=296\text{g}$

Step 4: Calculate actual weight obtained with 75% yield
Given reaction yield = 75%

$\text{Actual weight of X}=296\text{g}\times \frac{75}{100}=222\text{g}$

Thus, the weight of product X obtained is 222 g.