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Chapter 5: Problem 86

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

Expert verified
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

01

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 \(\mathrm{SiHCl}_{3}= 28.09 + 1.01 + 3\times 35.45 = 135.44\,\text{g/mol}\)
02

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, \(T = 85 + 273.15 = 358.15\,\text{K}\)
03

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}_{銇犮仌銇�

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

An organic compound contains \(\mathrm{C}, \mathrm{H}, \mathrm{N},\) and \(\mathrm{O}\) . Combustion of 0.1023 \(\mathrm{g}\) of the compound in excess oxygen yielded 0.2766 \(\mathrm{g} \mathrm{CO}_{2}\) and 0.0991 \(\mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) A sample of 0.4831 \(\mathrm{g}\) of the compound was analyzed for nitrogen by the Dumas method (see Exercise 137\() .\) At STP, 27.6 \(\mathrm{mL}\) of dry \(\mathrm{N}_{2}\) was obtained. In a third experiment, the density of the compound as a gas was found to be 4.02 \(\mathrm{g} / \mathrm{L}\) at \(127^{\circ} \mathrm{C}\) and 256 torr. What are the empirical and molecular formulas of the compound?

Do all the molecules in a 1 -mole sample of \(\mathrm{CH}_{4}(g)\) have the same kinetic energy at 273 \(\mathrm{K}\)? Do all molecules in a 1 -mole sample of \(\mathrm{N}_{2}(g)\) have the same velocity at 546 \(\mathrm{K}\) ? Explain.

\(\mathrm{N}_{2} \mathrm{O}\) is a gas commonly used to help sedate patients in medicine and dentistry due to its mild anesthetic and analgesic properties; it is also nonflammable. If a cylinder of \(\mathrm{N}_{2} \mathrm{O}\) is at 10.5 atm and has a volume of 5.00 \(\mathrm{L}\) at \(298 \mathrm{K},\) how many moles of \(\mathrm{N}_{2} \mathrm{O}\) gas are present? The gas from the cylinder is emptied into a large balloon at 745 torr. What is the volume of the balloon at 298 \(\mathrm{K}\) ?

Silane, SiH, , is the silicon analogue of methane, \(\mathrm{CH}_{4}\) . It is prepared industrially according to the following equations: $$\begin{array}{c}{\mathrm{Si}(s)+3 \mathrm{HCl}(g) \longrightarrow \mathrm{HSiCl}_{3}(l)+\mathrm{H}_{2}(g)} \\ {4 \mathrm{HSiCl}_{3}(l) \longrightarrow \mathrm{SiH}_{4}(g)+3 \mathrm{SiCl}_{4}(l)}\end{array}$$ a. If \(156 \mathrm{mL}\) \(\mathrm{HSiCl}_{3} (d=1.34 \mathrm{g} / \mathrm{mL})\) is isolated when 15.0 \(\mathrm{L}\) \(\mathrm{HCl}\) at 10.0 \(\mathrm{atm}\) and \(35^{\circ} \mathrm{C}\) is used, what is the percent yield of \(\mathrm{HSiCl}_{3} ?\) b. When \(156 \mathrm{HSiCl}_{3}\) is heated, what volume of \(\mathrm{SiH}_{4}\) at 10.0 \(\mathrm{atm}\) and \(35^{\circ} \mathrm{C}\) will be obtained if the percent yield of the reaction is 93.1\(\% ?\)

Consider three identical flasks filled with different gases. Flask \(\mathrm{A} : \mathrm{CO}\) at 760 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{B} : \mathrm{N}_{2}\) at 250 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{C} : \mathrm{H}_{2}\) at 100 torr and \(0^{\circ} \mathrm{C}\) a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity?
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