Problem 84 - Chemistry The Science in Context

Question

Silane \(\left(\mathrm{SiH}_{4}\right)\) is used in the electronics industry to manufacture thin films of silicon. What is the percent Si by mass in \(\mathrm{SiH}_{4} ?\) Does silane have the same percent Si by mass as disilane, \(\mathrm{Si}_{2} \mathrm{H}_{6} ?\)

Step-by-Step Solution

Answer

Answer: No, silane (SiH4) has a percent Si by mass of 87.4%, while disilane (Si2H6) has a percent Si by mass of 90.3%.

Step 1: Find the molar mass of SiH4

To find the molar mass of SiH4, we add the molar mass of Si and four times the molar mass of H: Molar mass of Si = 28.09 g/mol Molar mass of H = 1.01 g/mol So, molar mass of SiH4 = 28.09 + 4 * 1.01 = 28.09 + 4.04 = 32.13 g/mol

Step 2: Calculate the percent Si by mass in SiH4

To calculate the percent Si by mass in SiH4, we divide the molar mass of Si by the molar mass of SiH4 and multiply it by 100: Percent Si = (28.09 g/mol) / (32.13 g/mol) * 100 = 87.4%

Step 3: Find the molar mass of Si2H6

To find the molar mass of Si2H6, we add two times the molar mass of Si and six times the molar mass of H: Molar mass of Si2H6 = 2 * 28.09 + 6 * 1.01 = 56.18 + 6.06 = 62.24 g/mol

Step 4: Calculate the percent Si by mass in Si2H6

To calculate the percent Si by mass in Si2H6, we divide the combined molar mass of the two Si atoms by the molar mass of Si2H6 and multiply it by 100: Percent Si = (56.18 g/mol) / (62.24 g/mol) * 100 = 90.3%

Step 5: Compare the percentages of Si in SiH4 and Si2H6

Now we compare the percentages of Si in SiH4 (87.4%) and Si2H6 (90.3%). From the comparison, we can see that silane (SiH4) does not have the same percent Si by mass as disilane (Si2H6).

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. It's crucial for converting between mass and number of moles, which allows chemists to accurately determine the proportions of elements in compounds.

The molar mass of a molecule is calculated by summing the molar masses of its individual atoms. For example, the molar mass of silane (\( ext{SiH}_4\)) is derived by adding the molar mass of one silicon atom and four hydrogen atoms as shown:

• Molar mass of silicon (Si): 28.09 g/mol
• Molar mass of hydrogen (H): 1.01 g/mol

Thus, the molar mass of silane is calculated as:\( 28.09 ext{ g/mol} + 4 imes 1.01 ext{ g/mol} = 32.13 ext{ g/mol} \). Understanding molar mass is essential not just for calculating percent composition, but also for various other chemical calculations.

Silane

Silane, represented by the chemical formula \( ext{SiH}_4 \), is a compound in the silicon hydride family. It's especially significant in the electronics industry for creating thin silicon films.

In terms of percent composition, silane is analyzed to determine what fraction of its molar mass comes from silicon. This is calculated using the formula: \[ ext{Percent Si} = \left( \frac{28.09 \text{ g/mol}}{32.13 \text{ g/mol}} \right) \times 100 \] which results in a silicon composition of approximately 87.4%. This indicates that most of the mass of silane is due to silicon, with a smaller portion due to hydrogen atoms. Learning about silane and its properties is crucial for anyone looking to understand silicon-based technologies.

Disilane

Disilane, \( ext{Si}_2 ext{H}_6 \), is another molecule from the silicon hydride group, but it contains two silicon atoms. The construction of disilane involves more silicon, which influences its percent composition.

The molar mass of disilane is computed by totalling the mass of two silicon atoms and six hydrogen atoms:

• Molar mass of disilane: 62.24 g/mol

Using this, the percent composition of silicon in disilane is calculated as: \[ ext{Percent Si} = \left( \frac{56.18 \text{ g/mol}}{62.24 \text{ g/mol}} \right) \times 100 \] The result, about 90.3%, reflects a higher silicon content compared to silane. This underscores the difference in the composition of silicon across different silicon hydrides.

Silicon

Silicon, a key element represented by the symbol \( ext{Si}\), is central in many technological applications, particularly in electronics. It forms compounds like silane and disilane, which are used to manipulate silicon in various industrial processes.

As a basic building block of these compounds, silicon’s molar mass (28.09 g/mol) is foundational for calculating the percent composition in chemical formulas.

Understanding the role and distribution of silicon within such compounds aids in discerning their chemical behavior and efficiency in their specific industrial applications. For instance, recognizing the differences in silicon content can influence decisions in materials science or electronics manufacturing, where precise compositional knowledge is paramount.