Problem 89 - Chemistry and Chemical Reactivity

Question

One material needed to make silicones is dichlorodimethylsilane, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2} .\) It is made by treating silicon powder at about \(300^{\circ} \mathrm{C}\) with \(\mathrm{CH}_{3} \mathrm{Cl}\) in the presence of a copper-containing catalyst. (a) Write a balanced equation for the reaction. (b) Assume you carry out the reaction on a small scale with \(2.65 \mathrm{g}\) of silicon. To measure the \(\mathrm{CH}_{3} \mathrm{Cl}\) gas, you fill a \(5.60-\mathrm{L}\) flask at \(24.5^{\circ} \mathrm{C} .\) What pressure of \(\mathrm{CH}_{3} \mathrm{Cl}\) gas must you have in the flask to have the stoichiometrically correct amount of the compound? (c) What mass of \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SiCl}_{2}\) can be produced from \(2.65 \mathrm{g}\) of \(\mathrm{Si}\) and excess \(\mathrm{CH}_{3} \mathrm{Cl} ?\)

Step-by-Step Solution

Answer

(a) Si + 2 CH₃Cl → (CH₃)₂SiCl₂. (b) Pressure needed: 0.861 atm for CH₃Cl in 5.60 L at 24.5°C. (c) Mass of (CH₃)₂SiCl₂ produced: 12.24 g.

Step 1: Write the Balanced Equation

The reaction between silicon (Si) and chloromethane (CH\(_3\)Cl) to form dichlorodimethylsilane can be represented as follows: \[ \text{Si} + 2 \text{CH}_3\text{Cl} \rightarrow (\text{CH}_3)_2\text{SiCl}_2 \]. This equation is balanced because there is one Si, two Cl, four H, and two C atoms on both sides.

Step 2: Calculate the Molar Masses

Calculate the molar masses for silicon (Si) and dichlorodimethylsilane ((CH\(_3\))\(_2\)SiCl\(_2\)): - Si: Molar mass = 28.09 g/mol. - \((\text{CH}_3)_2\text{SiCl}_2\): Molar mass = \[2(12.01) + 6(1.01) + 28.09 + 2(35.45) = 129.63\, \text{g/mol}\].

Step 3: Calculate the Amount of Silicon in Moles

Determine moles of Si using its mass and molar mass: \[ \text{Moles of Si} = \frac{2.65}{28.09} = 0.0944\, \text{mol} \].

Step 4: Use Stoichiometry for CH\(_3\)Cl

For each Si, 2 moles of CH\(_3\)Cl are required. Therefore, moles of CH\(_3\)Cl needed = \(2 \times 0.0944 = 0.1888\, \text{mol}\).

Step 5: Calculate Pressure Using Ideal Gas Law

Use the Ideal Gas Law \( PV = nRT \) to calculate the pressure. Given info: - Volume \( V = 5.60\, \text{L} \)- Temperature \( T = 24.5^{\circ} \text{C} = 297.65\, \text{K} \)- R (ideal gas constant) = 0.0821 L·atm/mol·K- Moles calculated = 0.1888 molThus, the pressure is calculated as follows: \[ P = \frac{nRT}{V} = \frac{0.1888 \times 0.0821 \times 297.65}{5.60} \approx 0.861\, \text{atm} \].

Step 6: Calculate Mass of (CH\(_3\))\(_2\)SiCl\(_2\) Produced

Since 1 mole of Si produces 1 mole of \((\text{CH}_3)_2\text{SiCl}_2\), 0.0944 moles of Si will produce 0.0944 moles of \((\text{CH}_3)_2\text{SiCl}_2\).Therefore, mass = moles \( \times \) molar mass: \[ 0.0944 \times 129.63 = 12.24\, \text{g} \].

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental concept in chemistry that helps us understand the relationship between pressure, volume, temperature, and the amount of gas present. This is particularly useful for calculating the quantities involved in reactions where gases are used or produced.
In our exercise, we need to find the pressure of chloromethane (\( \text{CH}_3\text{Cl} \)) gas required to carry out a specific chemical reaction. By applying the Ideal Gas Law, which is expressed as:
\[PV = nRT\],
we can solve for the pressure \( (P) \) when we have:

• \( n = \) moles of gas
• \( R = \) the ideal gas constant \( 0.0821 \, \text{L} \cdot \text{atm}/\text{mol} \cdot \text{K} \)
• \( T = \) temperature in Kelvin
• \( V = \) volume

In this situation, you're given the number of moles of \( \text{CH}_3\text{Cl} \) needed (0.1888 mol), a volume of 5.60 L, and a temperature already converted to Kelvin (297.65 K). Plug these values into the equation to find \( P \), which will tell us the necessary pressure of \( \text{CH}_3\text{Cl} \) gas to successfully execute the reaction.

Molar Mass Calculation

Calculating the molar mass is crucial for understanding the stoichiometry of chemical reactions, as it allows you to convert between grams and moles of a substance. Molar mass is the mass of one mole of a substance and is usually expressed in grams per mole (g/mol).
For our exercise, we must determine the molar masses of several substances to proceed with our calculations. First, let's break down how you achieve this.

• Silicon (Si) is a single element, so its molar mass is just its atomic mass, 28.09 g/mol.
• For dichlorodimethylsilane, \((\text{CH}_3)_2\text{SiCl}_2\), consider the sum of the atomic masses:
  \[\text{Molar mass} = 2(12.01) + 6(1.01) + 28.09 + 2(35.45) = 129.63 \, \text{g/mol}\]

The molar mass helps us convert a given mass of silicon into moles, enabling us to apply stoichiometric principles and predict the amount of each reactant or product in a chemical reaction.

Balanced Chemical Equations

A balanced chemical equation ensures that the number of atoms of each element is the same on both sides of the reaction, thus obeying the Law of Conservation of Mass. Balancing chemical equations is foundational to correctly predicting the outcomes of reactions and calculations in chemical stoichiometry.
For the reaction in the exercise, you're given:\[\text{Si} + 2\text{CH}_3\text{Cl} \rightarrow (\text{CH}_3)_2\text{SiCl}_2\]This reaction indicates:

• One silicon atom reacts with two chloromethane molecules.
• The products will include one molecule of dichlorodimethylsilane.

Balancing ensures:

• Atoms of Si are balanced: 1 on each side.
• Atoms of Cl are balanced: 2 on each side.
• Atoms of H and C are also balanced: 4 and 2, respectively, on each side.

Balanced equations are essential for accurate stoichiometry calculations, allowing one to predict the quantities of reactants required and products formed. In our case, it lets us know precisely how much \( \text{CH}_3\text{Cl} \) and \( \text{Si} \) we need to form the compound \((\text{CH}_3)_2\text{SiCl}_2\).