Chemistry · Some Basic Concepts of Chemistry (Mole Concept) + Stoichiometry

JEE Advanced 2023 — Paper 1 — Question 38

The stoichiometric reaction of $516\,\mathrm{g}$ of dimethyldichlorosilane with water results in a tetrameric cyclic product $X$ in $75\%$ yield. The weight (in $g$ ) of $X$ obtained is $\_\_\_\_$ . [Given: molar mass $\left(\mathrm{g} \mathrm{mol}^{-1}\right): \mathrm{H}=1, \mathrm{C}=12, \mathrm{O}=16, \mathrm{Si}=28, \mathrm{Cl}=35.5$ ]

Answer: 222

Numerical answer — enter this value.

Step-by-step solution

Molar mass of $\mathrm{(CH_3)_2SiCl_2}$ $= 2 \times 12 + 6 \times 1 + 28 + 2 \times 35.5 = 129\,\mathrm{g\,mol^{-1}}$

Moles of $\mathrm{(CH_3)_2SiCl_2}$ used $= \dfrac{516}{129} = 4\,\mathrm{mol}$

Hydrolysis: $\mathrm{(CH_3)_2SiCl_2 + 2H_2O \xrightarrow{} (CH_3)_2Si(OH)_2 + 2HCl}$

Tetramerization gives cyclic product $X$ : $\mathrm{4\,(CH_3)_2Si(OH)_2 \xrightarrow{} [(CH_3)_2SiO]_4 + 4H_2O}$

So, $4\,\mathrm{mol}$ monomer $\rightarrow 1\,\mathrm{mol}$ tetramer

Moles of $X$ (theoretical) = $1\,\mathrm{mol}$

Molar mass of $X = [(CH_3)_2SiO]_4$

Molar mass of one repeat unit $(CH_3)_2 SiO$ $= 2 \times 12 + 6 \times 1 + 16 + 28 = 74$

Molar mass of tetramer $= 4 \times 74 = 296\,\mathrm{g\,mol^{-1}}$

Actual yield at $75\%$ $= 0.75 \times 296 = 222\,\mathrm{g}$

Thus, the mass of $X$ obtained is $222\,\mathrm{g}$ .

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2023
Paper: Paper 1
Subject: Chemistry
Chapter: Some Basic Concepts of Chemistry (Mole Concept) + Stoichiometry
Topic: Chemical Equations, Stoichiometry and Limiting Reagent