Problem 100 - Chemistry The Molecular Science

Question

Silicon and hydrogen form a series of interesting compounds, \(\mathrm{Si}_{x} \mathrm{H}_{y}\). To find the formula of one of them, a \(6.22-\mathrm{g}\) sample of the compound is burned in oxygen. All of the \(\mathrm{Si}\) is converted to \(11.64 \mathrm{~g} \mathrm{SiO}_{2}\) and all of the \(\mathrm{H}\) to \(6.980 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} .\) Determine the empirical formula of the silicon compound.

Step-by-Step Solution

Answer

The empirical formula is \( \mathrm{SiH}_4 \).

Step 1: Calculate moles of Si from Silicon Dioxide

The molar mass of SiO₂ is 60.08 g/mol. Number of moles of Si in 11.64 g of SiO₂ can be found by using the formula: \( \text{moles of Si} = \frac{\text{mass of SiO}_2}{\text{molar mass of SiO}_2} \). Thus, \( \text{moles of Si} = \frac{11.64 \text{ g}}{60.08 \text{ g/mol}} \approx 0.194 \text{ moles}. \)

Step 2: Calculate moles of H from Water

The molar mass of H₂O is 18.02 g/mol. Number of moles of H in 6.980 g of H₂O can be found by using the formula: \( \text{moles of H} = 2 \times \frac{\text{mass of H}_2\text{O}}{\text{molar mass of H}_2\text{O}} \). Thus, \( \text{moles of H} = 2 \times \frac{6.980 \text{ g}}{18.02 \text{ g/mol}} \approx 0.775 \text{ moles}. \)

Step 3: Calculate the Empirical Formula

Divide the moles of each element by the smallest number of moles calculated to find their ratio: 1. For Si: \( \frac{0.194}{0.194} = 1 \).2. For H: \( \frac{0.775}{0.194} \approx 4 \).Thus, the empirical formula of the compound is \( \mathrm{SiH}_4 \).

Key Concepts

Moles Calculation

The concept of moles is fundamental in chemistry, serving as the bridge between the mass of a substance and the number of atoms or molecules it contains. This calculation allows us to measure quantities in chemistry in a practical way.
1 mole is equivalent to Avogadro's number (aught{6.022 \times 10^{23}}) of particles, whether they are atoms, molecules, ions, etc.
Let's consider how we calculate moles from a given mass:

• First, determine the molar mass of the compound. This is the mass of one mole of the compound and is measured in g/mol.
• Divide the mass of the sample by its molar mass to find the number of moles.
  This formula can be expressed as: \[ \text{moles} = \frac{\text{mass (in g)}}{\text{molar mass (in g/mol)}} \]

For example, in the given exercise, we calculated the moles of silicon (Si) from silicon dioxide (SiO_2). We used the molar mass of SiO_2, which is 60.08 g/mol, and found that 11.64 g of SiO_2 contains approximately 0.194 moles of silicon. This method helps us translate mass into a usable chemical quantity.

Silicon Compounds

Silicon compounds are intriguing due to their vast applications in industries ranging from electronics to chemistry. These compounds form as a result of silicon's ability to bond with other elements, one of the most common being hydrogen.
Silicon compounds such as SiH_4 (silane) are examined to understand the bond structures, properties, and the behavior of silicon when it interacts with other elements.
Here are a few key points about silicon compounds:

• Silicon shares properties with carbon due to its position on the periodic table, allowing it to form multiple bonds.
• In compounds like silanes, silicon forms single bonds with hydrogen.
• The formulation of a silicon compound's empirical formula helps identify the simple ratio of its constituent elements, which aids in understanding its molecular structure.

Understanding silicon compounds is essential in fields such as materials science and electrical engineering because they form the backbone of semiconductor technology.

Empirical Formula Calculation

The empirical formula of a compound is the simplest whole-number ratio of elements within it. Determining this involves a few direct, logical steps that convert complex experimental data into simple, tangible insights.
To calculate an empirical formula:

• Begin by determining the moles of each element present in the compound, as described in the previous sections.
• Then, identify the smallest number of moles among the elements. This value acts as the divisor for the mole quantities of each element to find their simplest ratio.
• Express these ratios as whole numbers.
  For the given silicon compound, with 0.194 moles of Si and 0.775 moles of H, dividing by the smallest number of moles (0.194) yields a ratio of 1:4. Hence, the empirical formula is SiH_4.

The process of calculating an empirical formula is invaluable for chemists because it gives a clearer understanding of a compound's composition, which is critical for applications in chemical reactions and material formulation.