Problem 100 - 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 \(=1.0 \mathrm{g} / \mathrm{cm}^{3}\) ) of \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{m},\) where \(n\) is a large integer number. \(n\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}+2 n \mathrm{OH}^{-} \rightarrow\) $$ 2 n \mathrm{Cl}^{-}+n \mathrm{H}_{2} \mathrm{O}+\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\right]_{n} $$ The coating is added layer by layer, with 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 square meters, 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

You need 0.783 grams of \(\left(\mathrm{CH}_3\right)_2 \mathrm{SiCl}_2\).

Step 1: Calculate the Total Thickness of Coating

Since each layer of \([\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}]_{n}\) is \(0.60 \mathrm{nm}\) thick and we want 250 layers, the total thickness is given by \(250 \times 0.60 \mathrm{nm} = 150 \mathrm{nm}\).

Step 2: Convert Thickness to Meters

Convert the total thickness from nanometers to meters: \(150 \mathrm{nm} = 150 \times 10^{-9} \mathrm{m} = 1.50 \times 10^{-7} \mathrm{m}\).

Step 3: Calculate Volume of the Coating

The area of the cloth is \(3.00 \mathrm{m}^2\), and the thickness of the coating is \(1.50 \times 10^{-7} \mathrm{m}\). Therefore, the volume of the coating is \(3.00 \times 1.50 \times 10^{-7} \mathrm{m}^3 = 4.50 \times 10^{-7} \mathrm{m}^3\).

Step 4: Convert Volume to Cubic Centimeters

Since 1 cubic meter is equivalent to \(10^6\) cubic centimeters, convert the volume: \(4.50 \times 10^{-7} \mathrm{m}^3 = 4.50 \times 10^{-7} \times 10^6 \mathrm{cm}^3 = 0.45 \mathrm{cm}^3\).

Step 5: Calculate Mass from Volume Using Density

The density of the coating is \(1.0 \mathrm{g/cm}^3\). Therefore, the mass of the coating is the same as its volume: \(0.45 \mathrm{cm}^3 \times 1.0 \mathrm{g/cm}^3 = 0.45 \mathrm{g}\).

Step 6: Relate It Back to Si Compound in Reaction

Given that \(n\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}\) reacts to give the coating material, assume \(n\) moles of \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}\) produce \(n\) moles of the coating. Use molar masses to find the mass needed.

Step 7: Determine Moles of Coating Produced

The molar mass of \((\mathrm{CH}_{3})_{2} \mathrm{SiO}\) is calculated by adding the atomic masses of two CH3 groups and one SiO: \(2(12.01 + 3(1.01)) + 28.09 + 16.00 = 74.15 \, \mathrm{g/mol}\). Thus, to produce 0.45 g, the moles of \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiO}\) are \(0.45 \, \mathrm{g} / 74.15 \, \mathrm{g/mol} = 0.006067 \, \mathrm{mol}\).

Step 8: Calculate Mass of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\)

Given the stoichiometry \(1:1\), \(0.006067 \, \mathrm{mol}\) of \((\mathrm{CH}_3)_2 \mathrm{SiCl}_2\) is needed. Its molar mass is \((2(12.01 + 3(1.01)) + 28.09 + 2(35.45)\) or \(129.06 \, \mathrm{g/mol}\). Therefore, the mass required is \(0.006067 \, \mathrm{mol} \times 129.06 \, \mathrm{g/mol} = 0.783 \, \mathrm{g}\).

Key Concepts

Silicone Coating

Silicone coating is a popular method used to waterproof materials like cloth. This process involves applying a silicone compound that forms a protective layer on the surface. In this context, the compound \(\text{(CH}_3\text{)}_2\text{SiCl}_2\) is employed. When it comes into contact with OH groups present on the cloth, a chemical reaction occurs, resulting in the formation of \left[\text{(CH}_3\text{)}_2\text{SiO}\right]_n\. This newly formed compound acts as the waterproof layer. It’s important to understand that each layer is extremely thin, just 0.60 nm thick, and multiple layers are applied for effectiveness. In practical applications, such as the given exercise, 250 layers might be used to ensure adequate waterproofing.

Chemical Stoichiometry

Chemical stoichiometry involves understanding and calculating the amounts of reactants and products in chemical reactions. In the reaction \(n\text{(CH}_3\text{)}_2\text{SiCl}_2 + 2n\text{OH}^- ightarrow 2n\text{Cl}^- + n\text{H}_2\text{O} + \left[\text{(CH}_3\text{)}_2\text{SiO}\right]_n\), stoichiometry helps determine how much of each compound is needed and produced. For instance, we assume that \(n\) moles of \(\text{(CH}_3\text{)}_2\text{SiCl}_2\) produce \(n\) moles of the waterproofing compound. By applying stoichiometry, we relate the mass of reactants to the mass of the products, as shown in the exercise, ensuring the necessary quantity of silicone compound is used to achieve the waterproofing goal.

Density Calculations

Density is a key concept in determining the mass of substances based on their volume. Given the density of the waterproofing film as \(1.0 \text{ g/cm}^3\), we can calculate the mass of the coating once we know the volume. In this exercise, the coating’s volume is found by multiplying the cloth's area by the total thickness of the 250 layers. By converting the volume from cubic meters to cubic centimeters, we use the density to find the mass: \(0.45 \text{ cm}^3 imes 1.0 \text{ g/cm}^3 = 0.45 \text{ g}\). Understanding density helps link the microscopic scale of molecules to the macroscopic properties we measure.

Chemical Reactions

Chemical reactions describe how substances interact to form new compounds. In waterproofing, \(\text{(CH}_3\text{)}_2\text{SiCl}_2\) reacts with hydroxyl groups (OH) on the cloth surface. Through the reaction, new substances like \(\text{H}_2\text{O}\) and \(\left[\text{(CH}_3\text{)}_2\text{SiO}\right]_n\) are formed. These reactions are not only about making new compounds but also about breaking and forming bonds, allowing the transformation of the cloth into a water-resistant material. By carefully selecting reactants and controlling reaction conditions, we can achieve the desired properties in the final product, like waterproofing.