Problem 76 - Chemistry and Chemical Reactivity

Question

A Cloth can be waterproofed by coating it with a silicone layer. This is done by exposing the cloth to \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}\) vapor. The silicon compound reacts with OH groups on the cloth to form a waterproofing film (density = \(\left.1.0 \mathrm{g} / \mathrm{cm}^{3}\right)\) of \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{n},\) where \(n\) is a large integer number. $$\begin{aligned}n\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}+2 n \mathrm{OH}^{-} & \longrightarrow \\\& 2 n \mathrm{Cl}^{-}+n \mathrm{H}_{2} \mathrm{O}+\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{n}\end{aligned}$$ The coating is added layer by layer, each layer of \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{n}\) being \(0.60 \mathrm{nm}\) thick. Suppose you want to waterproof a piece of cloth that is \(3.00 \mathrm{m}\) square, and you want 250 layers of waterproofing compound on the cloth. What mass of \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}\) do you need?

Step-by-Step Solution

Answer

1.35 g of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\) is needed.

Step 1: Calculate the Total Thickness

The cloth is to be coated with 250 layers, each 0.60 nm thick. First, convert the thickness of one layer from nanometers to meters: \[ 0.60 \text{ nm} = 0.60 \times 10^{-9} \text{ m} \]Then, calculate the total thickness for 250 layers by multiplying the thickness of one layer by the number of layers:\[ \text{Total thickness} = 250 \times 0.60 \times 10^{-9} \text{ m} = 150 \times 10^{-9} \text{ m} \].

Step 2: Calculate the Volume of the Coating

The area of the cloth is 3.00 m \( \times \) 3.00 m, which is \[ 3.00 \times 3.00 = 9.00 \text{ m}^2 \].Use the area and the total thickness to find the volume of the coating:\[ \text{Volume} = \text{Area} \times \text{Total thickness} = 9.00 \times 150 \times 10^{-9} = 1350 \times 10^{-9} \text{ m}^3 \].

Step 3: Convert the Volume to cm³

Since the density is given in \( \text{g/cm}^3 \), convert the volume from \( \text{m}^3 \) to \( \text{cm}^3 \) knowing that \( 1 \text{ m}^3 = 10^6 \text{ cm}^3 \):\[ 1350 \times 10^{-9} \text{ m}^3 = 1350 \times 10^{-9} \times 10^6 \text{ cm}^3 = 1.35 \text{ cm}^3 \].

Step 4: Calculate the Mass of the Coating

Use the density to find the mass. Given that density \( \rho = 1.0 \text{ g/cm}^3 \), use the formula:\[ \text{Mass} = \text{Density} \times \text{Volume} \]. Since the volume is \(1.35 \text{ cm}^3 \):\[ \text{Mass} = 1.0 \times 1.35 = 1.35 \text{ g} \].

Step 5: Relate Mass to \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\)

The chemical reaction and stoichiometry indicate equal moles of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\) are needed to form the units of \([ (\mathrm{CH}_3)_2\mathrm{SiO} ]_n\). Calculate molar mass of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\) to find necessary amount. Based on reaction, 1:1 mole ratio applies. Therefore, mass calculated is mass needed of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\).

Key Concepts

Silicone Waterproofing

Waterproofing cloth using silicone involves a fascinating chemical process that creates a durable coating. This technique uses a compound called dimethyldichlorosilane, represented by the formula \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\). When this chemical comes into contact with hydroxide ions (\(\mathrm{OH}^-\)), it forms a waterproof layer of polymer called polydimethylsiloxane \([ (\mathrm{CH}_3)_2 \mathrm{SiO} ]_n\). This layer resists water penetration, making the cloth highly waterproof.

Important aspects of silicone waterproofing include:

• Forming a continuous and even coating on the cloth to provide effective water resistance.
• Ensuring that the thickness and number of layers are consistent for reliable protection.

This process is routinely used not only in textile industries but also in various applications where water resistance is crucial, such as construction and automotive manufacturing.

Molecular Chemistry

Molecular chemistry revolves around understanding how different molecules interact and bind together to form new compounds. In the process of silicone waterproofing, the molecules undergo a transformation where chemical bonds break and new ones form. The key molecule, dimethyldichlorosilane, reacts with hydroxide ions to create a network of strong silicon-oxygen bonds, forming a durable polymer.

Molecular interactions and reactions:

• The interaction between \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\) and \(\mathrm{OH}^-\) initiates a sequence of reactions leading to water elimination and polymer formation.
• Understanding molecular weights and chemical formulas helps predict how much reactant is needed in a reaction.

Learning about these molecular changes helps in designing reactions for desired outcomes, which is a cornerstone of both chemistry and chemical engineering.

Stoichiometry

Stoichiometry involves calculating the quantitative relationships between reactants and products in a chemical reaction. It is a fundamental concept needed to precisely measure the components involved in silicone waterproofing. By understanding stoichiometry, one can calculate how many moles of the reactant are required to produce a certain amount of product.

Key Stoichiometry Principles:

• Balanced chemical equations show the proportional ratios needed for reactants and products.
• In the provided reaction, equal moles of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\) and the coating polymer are involved, highlighting a 1:1 molar relationship.

Mastering stoichiometry enables accurate predictions of material quantities needed for industrial applications, ensuring cost-effectiveness and minimal waste.

Chemical Engineering

Chemical engineering applies principles of chemistry, physics, math, and economics to efficiently utilize chemicals in processes. In silicone waterproofing, chemical engineering plays a significant role in scaling the laboratory reactions for commercial production. Engineers aim to optimize the reaction’s efficiency while considering aspects such as:

• Safety measures in handling volatile compounds like \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\)
• Cost-effective production methodologies that maximize resource use
• Environmental impact assessments to ensure sustainable practices

Being able to manage these factors helps chemical engineers develop processes that deliver consistent product quality and maintain environmental responsibility.

Reaction Stoichiometry

Reaction stoichiometry focuses on the detailed steps and mole relationships within a chemical reaction. For the waterproofing process, reaction stoichiometry is critical in determining the precise amounts of chemicals needed to achieve the desired coating thickness and number of layers.

Key Considerations:

• Understanding the balanced equation, which indicates the stoichiometric ratios: \(n\left((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\right) + 2n \mathrm{OH}^- \rightarrow 2n \mathrm{Cl}^- + n \mathrm{H}_2\mathrm{O} + \left[(\mathrm{CH}_3)_2 \mathrm{SiO}\right]_n\).
• The equation shows that every mole of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\) reacts with two hydroxide ions, yielding water, chloride ions, and the silicone polymer layer.

A thorough understanding of reaction stoichiometry allows for precise calculation of reactants, leading to efficiency and accuracy in chemical engineering applications.