Question

Hydrogen fluoride is one of the few substances that react with glass (which is made of silicon dioxide, \(\mathrm{SiO}_{2}\) ). \(4 \mathrm{HF}(g)+\mathrm{SiO}_{2}(s) \longrightarrow \mathrm{SiF}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (a) How many moles of HF will react completely with \(9.90 \mathrm{~mol}\) of \(\mathrm{SiO}_{2}\) ? (b) What mass of water (in grams) is produced by the reaction of \(23.0 \mathrm{~g}\) of \(\mathrm{SiO}_{2}\) ?

Short answer

(a) 39.6 moles of HF. (b) 13.80 grams of water.

Step-by-step solution

Understanding the Reaction Equation

The balanced chemical equation is: \[4 \mathrm{HF}(g) + \mathrm{SiO}_{2}(s) \rightarrow \mathrm{SiF}_{4}(g) + 2 \mathrm{H}_{2} \mathrm{O}(l)\] This equation shows that 4 moles of HF react with 1 mole of SiO₂ to produce 1 mole of SiF₄ and 2 moles of H₂O.

Calculate Moles of HF Required (Part a)

Using the mole ratio from the equation, 4 moles of HF are needed for every 1 mole of SiO₂. Therefore, to find the moles of HF required for 9.90 moles of SiO₂: \[ \text{Moles of HF} = 9.90 \text{ mol } \mathrm{SiO}_{2} \times \frac{4 \text{ mol HF}}{1 \text{ mol } \mathrm{SiO}_{2}} = 39.6 \text{ mol HF} \]

Convert Mass of SiO₂ to Moles (Part b)

To find the mass of water produced, first convert grams of SiO₂ to moles using its molar mass. The molar mass of SiO₂ is approximately 60.08 g/mol. \[ \text{Moles of SiO}_{2} = \frac{23.0 \text{ g SiO}_{2}}{60.08 \text{ g/mol}} \approx 0.383 \text{ mol } \mathrm{SiO}_{2} \]

Calculate Moles of Water Produced

According to the balanced equation, 2 moles of water are produced per mole of SiO₂. Therefore, \[ \text{Moles of } \mathrm{H}_{2} \mathrm{O} = 0.383 \text{ mol SiO}_{2} \times \frac{2 \text{ mol } \mathrm{H}_{2} \mathrm{O}}{1 \text{ mol } \mathrm{SiO}_{2}} = 0.766 \text{ mol } \mathrm{H}_{2} \mathrm{O} \]

Convert Moles of Water to Grams

Convert the moles of H₂O to grams using the molar mass of water, which is approximately 18.02 g/mol. \[ \text{Mass of } \mathrm{H}_{2} \mathrm{O} = 0.766 \text{ mol H}_{2}\mathrm{O} \times 18.02 \text{ g/mol} = 13.80 \text{ g H}_{2}\mathrm{O} \]

Key concepts

Chemical Reactions

A chemical reaction involves the transformation of one or more substances, known as reactants, into different substances, referred to as products. These transformations occur through the breaking and forming of chemical bonds. In the reaction between hydrogen fluoride (HF) and silicon dioxide (SiO₂), HF reacts with the SiO₂ to form silicon tetrafluoride (SiF₄) and water (H₂O), which are the products.

Key characteristics of chemical reactions include:

• The conservation of mass: the total mass of reactants equals the total mass of products.
• Energy changes: reactions can be exothermic (releasing energy) or endothermic (absorbing energy).
• New substance formation: different chemical identities from the original reactants.

In this scenario, the chemical reaction illustrates the reactive nature of hydrogen fluoride with glass, a property that makes HF useful in glass etching applications.

Mole Concept

The mole concept is a fundamental component of chemistry that helps quantify chemical reactions. A mole is a unit that measures the amount of substance, and it's based on Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities (atoms, molecules, ions, etc.).

For the given reaction, it's important to understand the stoichiometric relationships:

• 4 moles of HF are needed to react with 1 mole of SiO₂.
• One mole of a substance is equivalent to its molar mass in grams.
• Stoichiometry allows us to convert between moles of reactants and moles of products.

In part (a) of the exercise, we used the mole ratio from the balanced equation to determine that 39.6 moles of HF are required to react completely with 9.90 moles of SiO₂. This is a clear application of the mole concept, using it as a counting tool for precise chemical measurements.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They describe how reactants transform into products and provide quantitative information about the reaction.

A balanced chemical equation, like the one given, ensures that the number of atoms for each element is the same on both sides of the equation. This reflects the law of conservation of mass.

The balanced equation \[4 \mathrm{HF}(g) + \mathrm{SiO}_{2}(s) \rightarrow \mathrm{SiF}_{4}(g) + 2 \mathrm{H}_{2} \mathrm{O}(l)\] indicates that:

• Four molecules of HF combine with one molecule of SiO₂.
• One molecule of SiF₄ and two molecules of H₂O are produced.

In problems like part (b), the coefficients play a crucial role. They help us determine the mole-to-mole relationships needed to find out how much product is formed from a given amount of reactant. Understanding the role of coefficients is essential for accurately predicting the outcomes of chemical reactions.