Problem 89 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

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

Step 1: Calculate Moles of SiO2

The molecular weight of SiO2 is calculated as follows: \( \text{Si: } 28.0855 \, \text{g/mol, O: } 16.00 \, \text{g/mol} \times 2 = 32.00 \, \text{g/mol} \). Thus, the molar mass of SiO2 is \( 28.0855 + 32.00 = 60.0855 \, \text{g/mol} \). To find the moles of SiO2 formed, divide the mass of SiO2 by its molar mass: \( \frac{11.64 \, \text{g}}{60.0855 \, \text{g/mol}} \approx 0.1937 \, \text{mol} \).

Step 2: Find Moles of Si in SiO2

In one mole of SiO2, there is one mole of Si. Therefore, the moles of Si are the same as moles of SiO2, which is approximately \(0.1937 \, \text{mol} \).

Step 3: Calculate Moles of H2O

The molecular weight of H2O is \( \text{H: } 1.008 \, \text{g/mol} \times 2 = 2.016 \, \text{g/mol + O: } 16.00 \, \text{g/mol} = 18.016 \, \text{g/mol} \). To find the moles of H2O, use: \( \frac{6.980 \, \text{g}}{18.016 \, \text{g/mol}} \approx 0.3875 \, \text{mol} \).

Step 4: Determine Moles of H in H2O

Each mole of H2O contains 2 moles of H. Therefore, the moles of H are \(0.3875 \, \text{mol} \times 2 = 0.775 \, \text{mol} \).

Step 5: Ratio of Moles of Si to H

The ratio of moles of Si to moles of H can be expressed as \( \frac{0.1937}{0.1937} : \frac{0.775}{0.1937} \), which simplifies to 1:4. This indicates the compound is composed of one silicon atom for every four hydrogen atoms.

Step 6: Empirical Formula

The empirical formula of the compound is determined by using the simplest ratio of Si to H. From Step 5, the empirical formula is \(\text{SiH}_4\).

Key Concepts

Chemical Reactions

Chemical reactions are processes where chemical substances transform into new substances through the breaking and forming of bonds. In the given exercise, the chemical reaction involves burning a compound of silicon and hydrogen in oxygen.
This reaction converts all silicon to silicon dioxide ( SiO_{2} ) and all hydrogen to water ( H_{2}O ).
These transformations are typical examples of chemical reactions where substances combine or rearrange to form new products.
Some key aspects of chemical reactions include:

• Reactants and Products: Reactants are the starting materials that undergo change, while products are the substances formed by the reaction.
• Conservation of Mass: In a chemical reaction, the total mass of reactants is equal to the total mass of the products. This principle is crucial for understanding the stoichiometry of a reaction.
• Energy Changes: Chemical reactions often involve energy changes, with energy absorbed to break bonds and released when new bonds form.

Understanding the basic nature of such reactions helps in determining the empirical formula, as seen in extracting information from the mass of reactants and products.

Molecular Weight

Molecular weight, also known as molecular mass, is the sum of the atomic weights of all atoms in a molecule.
It is expressed in atomic mass units (amu) or grams per mole (g/mol). Calculating molecular weight is a foundational concept for determining the number of moles of substances involved in chemical reactions.
In the problem presented, molecular weights played a crucial role. The molecular weights of SiO_{2} and H_{2}O were calculated as follows:

• For SiO₂: Molecular weight is the sum of one Si (28.0855 g/mol) and two O atoms (16.00 g/mol each), totaling 60.0855 g/mol.
• For H₂O: The molecular weight combines two H atoms (1.008 g/mol each) and one O atom (16.00 g/mol), resulting in 18.016 g/mol.

These weights were used to convert masses into moles, a pivotal step in the determination of the empirical formula, allowing for the calculation of moles based on provided product masses.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the balanced equations representing chemical reactions.
Stoichiometry calculations rely on the concept of moles, providing a means to predict the amounts of products formed or reactants required.
Key Steps in Stoichiometric Calculations:

• Identifying the Data: Determine the masses or quantities of reactants and products.
• Convert Masses to Moles: Use molecular weights to change grams to moles as shown in the exercise: 11.64 g of SiO₂ corresponds to approximately 0.1937 moles, and 6.980 g of H₂O corresponds to approximately 0.3875 moles.
• Relate Substances by Mole Ratios: The exercise reveals a ratio of moles of Si to H of 1:4, indicating the composition of the compound as SiH₄.

The simplest ratio derived from stoichiometric calculations is often the empirical formula.
It provides insight into the basic composition of a compound, as demonstrated by the task of computing the empirical formula of silicon hydride.