Question

Silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) and trichlorosilane \(\left(\mathrm{SiHCl}_{3}\right)\) are both starting materials for the production of electronics-grade silicon. Calculate the densities of pure \(\mathrm{SiCl}_{4}\) and pure \(\mathrm{SiHCl}_{4}\) vapor at \(85^{\circ} \mathrm{C}\) and 635 torr.

Short answer

The densities of pure Silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) and pure trichlorosilane \(\left(\mathrm{SiHCl}_{3}\right)\) vapor at \(85^{\circ}\mathrm{C}\) and 635 torr are \(4.87\,\text{g/L}\) and \(3.90\,\text{g/L}\), respectively.

Step-by-step solution

Calculate the molar mass of both substances

First, we need to find the molar mass of Silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) and trichlorosilane \(\left(\mathrm{SiHCl}_{3}\right)\). Remember that to find the molar mass, simply add the atomic masses of the individual elements in the chemical formula (given in g/mol). Silicon tetrachloride: Molar mass of Si = 28.09 g/mol Molar mass of Cl = 35.45 g/mol So, molar mass of \(\mathrm{SiCl}_{4}= 28.09 + 4\times 35.45 = 169.39\,\text{g/mol}\) Trichlorosilane: Molar mass of Si = 28.09 g/mol Molar mass of H = 1.01 g/mol Molar mass of Cl = 35.45 g/mol So, molar mass of \(\mathrm{SiHCl}_{3}= 28.09 + 1.01 + 3\times 35.45 = 135.44\,\text{g/mol}\)

Convert the given pressure and temperature to appropriate units

We need to convert the given pressure and temperature to the SI units before using the Ideal Gas Law to calculate the density of vapor. Pressure = 635 torr, convert to atmospheres (atm) using the conversion factor: \(1\, \text{atm} = 760\, \text{torr}\) So, \(P = \frac{635\, \text{torr}}{760\, \text{torr/atm}} = 0.8368\,\text{atm}\) Temperature = \(85^{\circ}\mathrm{C}\), convert to Kelvin (K) using the conversion: \(T_{\text{K}} = T_{\text{C}} + 273.15\) So, \(T = 85 + 273.15 = 358.15\,\text{K}\)

Calculate the volume of one mole of gas using Ideal Gas Law

Using the Ideal Gas Law, \(PV = nRT\), we can find the volume of one mole of gas (i.e., n = 1 mol) by solving for V. For both \(\mathrm{SiCl}_{4}\) and \(\mathrm{SiHCl}_{3}\), we have: \(V = \frac{nRT}{P} = \frac{1\,mol\times 0.0821\, \mathrm{L\, atm/mol\, K} \times 358.15\, \mathrm{K}}{0.8368\, \mathrm{atm}}\) \$V_{\mathrm{SiCl}_{4}} = \frac{1\,mol\times 0.0821\, \mathrm{L\, atm/mol\, K} \times 358.15\, \mathrm{K}}{0.8368\, \mathrm{atm}} = 34.78\, \mathrm{L/mol}\$ \$V_{\mathrm{SiHCl}_{ださい

Key concepts

Density Calculations

Density is a measurement of how much mass is contained in a given volume. It is an essential concept when dealing with gases using the Ideal Gas Law. To determine the density of a gas, you can use the formula:

• Density = \( \frac{\text{mass}}{\text{volume}} \)

When using the Ideal Gas Law, we can rewrite this formula considering the molar mass and the conditions of temperature and pressure. Since the volume of a gas can be found using \( PV = nRT \), where \( n = 1 \) mole, we find:

• Volume \( V = \frac{RT}{P} \)

The mass in our density formula is essentially the molar mass of the molecule, hence:

• Density \( = \frac{\text{Molar Mass}}{V} = \frac{\text{Molar Mass}\times P}{RT} \)

This equation helps compute the density at a specific temperature and pressure.

Molar Mass Calculation

Molar mass is a critical aspect when calculating the properties of a gas. It helps in determining the amount of a substance on a molecular scale. The molar mass can be calculated by adding up the atomic masses of all atoms in a molecule.
For example, in the case of silicon tetrachloride \( \mathrm{SiCl}_{4} \), the individual atomic masses are:

• Silicon (Si) = 28.09 g/mol
• Chlorine (Cl) = 35.45 g/mol

The total molar mass of \( \mathrm{SiCl}_{4} \) is calculated as:

• Molar mass of \( \mathrm{SiCl}_{4} = 28.09 + 4 \times 35.45 \approx 169.39 \) g/mol

Knowing the molar masses of different compounds such as trichlorosilane \( \mathrm{SiHCl}_{3} \), where hydrogen is involved too, is essential:

• Hydrogen (H) = 1.01 g/mol

Therefore, tangibly calculating the total molar mass involves understanding and combining these atomic weights appropriately.

Silicon Compounds

Silicon tetrachloride and trichlorosilane are significant silicon compounds particularly used in electronics. These compounds are assessed for their various properties largely due to their application in sensitive technology environments.
Silicon tetrachloride \( \mathrm{SiCl}_{4} \) and trichlorosilane \( \mathrm{SiHCl}_{3} \) are important in manufacturing pure silicon due to their chemical stability and ability to transform into silicon dioxide, a critical component in semiconductors.

• Silicon tetrachloride is a clear liquid at room temperature, while trichlorosilane has flame-retardant properties.
• Both compounds' purposefulness stems from their consistency and interaction with other elements, which aids in producing high-purity silicon.

Understanding these elements is crucial not just in theoretical calculations but in practical implementations in electronics.

Pressure and Temperature Conversion

Converting units of pressure and temperature is vital when using the Ideal Gas Law, where standard units are necessary.

• Pressure is typically converted from torr to atmospheres since the Ideal Gas Law (PV = nRT) uses atmosphere (atm).
• To convert: \( 1 \text{atm} = 760 \text{torr} \); therefore, \( P = \frac{\text{torr value}}{760} \).

Temperature conversion from Celsius to Kelvin is also crucial, as computations in the Ideal Gas Law are standardized to Kelvin.

• To convert temperature: add 273.15 to the Celsius temperature (\( T_{\text{K}} = T_{\text{C}} + 273.15 \)).

By ensuring these conversions, equations remain consistent and accurate, allowing correct calculations related to gas properties.