Question

Hydrofluoric acid, HF \((a q)\), cannot be stored in glass bottles because compounds called silicates in the glass are attacked by the \(\mathrm{HF}(a q)\). Sodium silicate \(\left(\mathrm{Na}_{2} \mathrm{SiO}_{3}\right)\), for example, reacts as follows: $$ \mathrm{Na}_{2} \mathrm{SiO}_{3}(s)+8 \mathrm{HF}(a q) \longrightarrow(a q)+2 \mathrm{NaF}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) How many moles of HF are needed to react with \(0.300 \mathrm{~mol}\) of \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) ? (b) How many grams of NaF form when \(0.500 \mathrm{~mol}\) of HF reacts with excess \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) ? (c) How many grams of \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) can react with \(0.800 \mathrm{~g}\) of \(\mathrm{HF}\) ?

Short answer

(a) 2.4 moles of HF are needed to react with 0.300 mol of Na2SiO3. (b) 5.25 grams of NaF will form when 0.500 mol of HF reacts with excess Na2SiO3. (c) 0.610 grams of Na2SiO3 can react with 0.800 g of HF.

Step-by-step solution

Problem (a)

We are given 0.300 mol of Na2SiO3 and asked to find how many moles of HF are needed to react with it. We will use the stoichiometry ratios given by the balanced equation: 1 mol Na2SiO3 : 8 mol HF Step 1: Calculate the moles of HF Using the stoichiometry ratio, we can calculate the moles of HF needed by multiplying the given moles of Na2SiO3 by the ratio of moles of HF to moles of Na2SiO3. Moles of HF = (0.300 mol Na2SiO3) x (8 mol HF / 1 mol Na2SiO3) Step 2: Solve for moles of HF Moles of HF = (0.300 mol) x (8) = 2.4 mol So, 2.4 moles of HF are needed to react with 0.300 mol of Na2SiO3.

Problem (b)

We are given 0.500 mol of HF and asked to find how many grams of NaF form when HF reacts with excess Na2SiO3. We will use the stoichiometry ratios given by the balanced equation: 8 mol HF : 2 mol NaF Step 1: Calculate the moles of NaF Using the stoichiometry ratio, we can calculate the moles of NaF formed by multiplying the given moles of HF by the ratio of moles of NaF to moles of HF. Moles of NaF = (0.500 mol HF) x (2 mol NaF / 8 mol HF) Step 2: Solve for moles of NaF Moles of NaF = (0.500 mol) x (2 / 8) = 0.125 mol Step 3: Convert moles of NaF to grams To convert moles of NaF to grams, we need to know the molar mass of NaF. From the periodic table, we find that the molecular weight of Na = 22.99 g/mol and F = 19.00 g/mol. Therefore, the molar mass of NaF = (22.99 + 19.00) g/mol = 41.99 g/mol. Grams of NaF = (0.125 mol) x (41.99 g/mol) Step 4: Solve for grams of NaF Grams of NaF = (0.125 mol) x (41.99 g/mol) = 5.25 g So, 5.25 grams of NaF will form when 0.500 mol of HF reacts with excess Na2SiO3.

Problem (c)

We are given 0.800 g of HF and asked to find how many grams of Na2SiO3 can react with it. We will use the stoichiometry ratios given by the balanced equation and convert between moles and grams. Step 1: Find the moles of HF From the periodic table, the molecular weight of H = 1.01 g/mol and of F = 19.00 g/mol. So, the molar mass of HF = (1.01 + 19.00) g/mol = 20.01 g/mol. To find the moles of HF given, we will divide the given mass of HF by its molar mass. Moles of HF = (0.800 g HF) / (20.01 g/mol) Step 2: Solve for moles of HF Moles of HF = (0.800 g) / (20.01 g/mol) = 0.0400 mol Step 3: Calculate the moles of Na2SiO3 that can react with the given moles of HF Using the stoichiometry ratio, we calculate the moles of Na2SiO3 that can react with the given moles of HF. Moles of Na2SiO3 = (0.0400 mol HF) x (1 mol Na2SiO3 / 8 mol HF) Step 4: Solve for moles of Na2SiO3 Moles of Na2SiO3 = (0.0400 mol) x (1 / 8) = 0.00500 mol Step 5: Convert moles of Na2SiO3 to grams From the periodic table, the molecular weight of Na = 22.99 g/mol, Si = 28.09 g/mol, O = 16.00 g/mol. The molar mass of Na2SiO3 = 2(22.99) + 28.09 + 3(16.00) = 122.08 g/mol. Grams of Na2SiO3 = (0.00500 mol) x (122.08 g/mol) Step 6: Solve for grams of Na2SiO3 Grams of Na2SiO3 = (0.00500 mol) x (122.08 g/mol) = 0.610 g So, 0.610 grams of Na2SiO3 can react with 0.800 g of HF.

Key concepts

Hydrofluoric Acid Reaction

Hydrofluoric acid (HF) is a unique compound due to its ability to react with silicates, which are commonly found in glass. This property makes it impossible to store HF in glass containers as it would etch or dissolve them over time. The reaction of interest typically involves HF attacking the silicon-oxygen bonds within silicates, such as sodium silicate (Na₂SiO₃).

In the example provided, the chemical equation representing this reaction is:
\[ \mathrm{Na}_{2} \mathrm{SiO}_{3}(s) + 8 \mathrm{HF}(aq) \longrightarrow 3 \mathrm{H}_{2}\mathrm{O}(l) + 2 \mathrm{NaF}(aq) \] This reaction demonstrates that hydrofluoric acid not only dissociates silicate structures but also forms other compounds, such as sodium fluoride (NaF) and water (H₂O), in the process.

Stoichiometric Calculations

Stoichiometric calculations are a cornerstone of chemical problem-solving. They enable chemists to predict the amounts of reactants and products involved in a chemical reaction based on the balanced chemical equation. A balanced chemical equation provides the mole ratios necessary to perform these calculations - for example, in the provided reaction, one mole of sodium silicate reacts with eight moles of hydrofluoric acid to produce two moles of sodium fluoride and three moles of water.

To solve stoichiometric problems, such as determining how many moles of one substance are required to react with a given amount of another, you would use the ratios from the balanced equation. For instance, if you needed to find out how many moles of HF are required to react with 0.300 moles of Na₂SiO₃, the stoichiometry ratio tells us it is an 8:1 relationship. Therefore, multiplying 0.300 by 8 gives the necessary moles of HF for the reaction.

The Mole Concept

The mole concept is fundamental to understanding chemical reactions and stoichiometry. It is a unit that represents a specific number of particles, typically atoms or molecules, similar to how a dozen represents twelve items. Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole, quantifies this amount.

In stoichiometric calculations, the mole allows chemists to convert between the mass of a substance and the amount of substance in terms of particles. To translate mass into moles, the formula is simple: divide the mass of the substance by its molar mass. Conversely, to find the mass from the amount in moles, multiply the number of moles by the substance's molar mass. Utilizing the mole concept enables precise reaction predictions and is crucial for tasks such as determining the grams of NaF produced from moles of HF.