Problem 133 - Introductory Chemistry Atoms First

Question

For the reaction \(\mathrm{SiCl}_{4}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{SiO}_{2}+\mathrm{HCl}\), (a) Balance the equation. (b) If you want to make \(120.0 \mathrm{~g}\) of \(\mathrm{HCl}\), how many grams of \(\mathrm{SiCl}_{4}\) and \(\mathrm{H}_{2} \mathrm{O}\) do you need? (c) How many grams of \(\mathrm{SiO}_{2}\) are produced from the quantities calculated in (b)?

Step-by-Step Solution

Answer

(a) The balanced equation is \(SiCl_4 + 2H_2O \rightarrow SiO_2 + 4HCl\). (b) To produce 120.0 g of HCl, you would need 139.5 g of SiCl4 and 29.58 g of H2O. (c) 49.36 g of SiO2 are produced from the calculated amounts of SiCl4 and H2O.

Step 1: (Step 1: Balance the chemical equation)

First, let's balance the given chemical equation: \(SiCl_4 + H_2O \rightarrow SiO_2 + HCl\) \(SiCl_4 + 2H_2O \rightarrow SiO_2 + 4HCl\) Now the chemical equation is balanced.

Step 2: (Step 2: Calculate moles of HCl)

To find the moles of HCl needed to produce 120.0 g of HCl, use the molar mass of HCl (M(HCl) = 1 + 35.5 = 36.5 g/mol): Moles of HCl = (mass of HCl) / M(HCl) = (120.0 g) / (36.5 g/mol) = 3.287 moles

Step 3: (Step 3: Determine moles of SiCl4 and H2O required)

Using the balanced chemical equation and the stoichiometry of the reaction, calculate the moles of SiCl4 and H2O needed to produce 3.287 moles of HCl: Moles of SiCl4 = (3.287 moles HCl) * (1 mol SiCl4 / 4 mol HCl) = 0.8218 moles SiCl4 Moles of H2O = (3.287 moles HCl) * (2 mol H2O / 4 mol HCl) = 1.6435 moles H2O

Step 4: (Step 4: Calculate grams of SiCl4 and H2O required)

Now, find the mass of SiCl4 and H2O needed by multiplying their moles by their respective molar masses (M(SiCl4) = 169.9 g/mol and M(H2O) = 18.0 g/mol): Mass of SiCl4 = (0.8218 moles SiCl4) * (169.9 g/mol) = 139.5 g Mass of H2O = (1.6435 moles H2O) * (18.0 g/mol) = 29.58 g So, 139.5 g of SiCl4 and 29.58 g of H2O are needed to produce 120.0 g of HCl.

Step 5: (Step 5: Calculate grams of SiO2 produced)

Using the balanced chemical equation, calculate the mass of SiO2 produced from 0.8218 moles of SiCl4. We already know M(SiO2) = 60.1 g/mol: Mass of SiO2 = (0.8218 moles SiCl4) * (1 mol SiO2 / 1 mol SiCl4) * (60.1 g/mol) = 49.36 g Thus, 49.36 g of SiO2 are produced from the calculated amounts of SiCl4 and H2O.

Key Concepts

Chemical Balancing

Balancing chemical equations is an essential foundation in chemistry. It ensures that the number of atoms for each element is the same on both sides of the equation, adhering to the law of conservation of mass. In the reaction given, unbalanced equations can lead to incorrect stoichiometric calculations. The original reaction is:

• \(\mathrm{SiCl}_{4} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{SiO}_{2} + \mathrm{HCl}\)

To balance this, we count the number of each type of atom on both sides and adjust coefficients accordingly:

• One \(\mathrm{SiCl}_{4}\) molecule has 1 silicon, 4 chlorine atoms, while \(\mathrm{H}_2\mathrm{O}\) contributes 2 hydrogen and 1 oxygen.
• On the products side, \(\mathrm{SiO}_{2}\) and \(\mathrm{HCl}\) need proportional coefficients for a balance.

The balanced equation becomes:

• \(\mathrm{SiCl}_{4} + 2\mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{SiO}_{2} + 4\mathrm{HCl}\)

Now, each element's atoms match on both sides, a crucial step for accurate calculations.

Moles Calculation

Moles play a critical role in chemistry, functioning as a bridge between atoms or molecules and grams, which are more measurable. To determine moles from a mass, use the molar mass of a compound. For example, finding moles of \(\mathrm{HCl}\) from a given mass requires:

• Molar mass of \(\mathrm{HCl}\) is calculated as \(1 + 35.5 = 36.5\) g/mol.
• The moles of \(\mathrm{HCl}\) from \(120.0\) g is \((120.0\,\text{g}) / (36.5\,\text{g/mol})\approx 3.287\) moles.

This calculation provides the amount of substance in terms of measurable quantity, enabling further stoichiometric computations for other reactants and products.

Molar Mass

Molar mass is the weight of one mole of a substance and is expressed in g/mol. Calculating molar mass involves adding the atomic masses of the elements that makeup one mole of a molecule. Let's examine the molar masses of key compounds in the reaction.

• \(\mathrm{SiCl}_{4}:\mathrm{Si} (28.1) + 4\times\mathrm{Cl} (35.5) = 169.9\) g/mol.
• \(\mathrm{H}_2\mathrm{O}: 2\times\mathrm{H} (1) + \mathrm{O} (16) = 18.0\) g/mol.
• \(\mathrm{SiO}_{2}:\mathrm{Si} (28.1) + 2\times\mathrm{O} (16) = 60.1\) g/mol.

Knowing these values allows conversion from moles to grams, an essential step in quantifying reactants and products.

Chemical Reaction

A chemical reaction involves the transformation of reactants into products. Understanding the reaction mechanism is crucial to comprehend material changes. In the given reaction:

• \(\mathrm{SiCl}_{4}\) reacts with \(\mathrm{H}_2\mathrm{O}\) to produce \(\mathrm{SiO}_{2}\) and \(\mathrm{HCl}\).

The balanced equation \(\mathrm{SiCl}_{4} + 2\mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{SiO}_{2} + 4\mathrm{HCl}\) reveals the stoichiometric relationships between reactants and products. For every mole of \(\mathrm{SiCl}_{4}\) that reacts, one mole of \(\mathrm{SiO}_{2}\) and four moles of \(\mathrm{HCl}\) are produced, along with consuming two moles of \(\mathrm{H}_2\mathrm{O}\). This stoichiometry is foundational in predicting and calculating the amounts of substances involved.