Question

Hydrofluoric acid, HF(aq), cannot be stored in glass bottles because compounds called silicates in the glass are attacked by the HF(aq). Sodium silicate (Na \(_{2} \mathrm{SiO}_{3} ),\) for example, reacts as follows: $$ \mathrm{Na}_{2} \mathrm{SiO}_{3}(s)+8 \mathrm{HF}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{SiF}_{6}(a q)+2 \operatorname{NaF}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) How many moles of HF are needed to react with 0.300 mol of \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (b) How many grams of NaF form when 0.500 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 g of HF?

Short answer

(a) 2.4 mol of HF are needed to react with 0.300 mol of Na2SiO3. (b) 5.25 g of NaF form when 0.500 mol of HF reacts with excess Na2SiO3. (c) 0.61 g of Na2SiO3 can react with 0.800 g of HF.

Step-by-step solution

(a) Moles of HF required

Using the stoichiometry of the balanced equation, we can find the moles of HF required. We have that 8 moles of HF react with 1 mole of Na2SiO3. So, for 0.300 mol of Na2SiO3: Moles of HF = (0.300 mol Na2SiO3) × (8 mol HF / 1 mol Na2SiO3) = 2.4 mol HF

(b) Mass of NaF formed

We are given that 0.500 mol of HF reacts with excess Na2SiO3. We need to find the moles of NaF formed first. From the balanced equation, we have the mole ratio 2 mol NaF are produced for every 8 mol HF reacted. Moles of NaF = (0.500 mol HF) × (2 mol NaF / 8 mol HF) = 0.125 mol NaF Now, we need to find the mass of NaF formed. The molar mass of NaF is 22.99 (Na) + 18.998 (F) = 41.988 g/mol. So, the mass of NaF produced is: Mass of NaF = (0.125 mol NaF) × (41.988 g/mol) = 5.25 g NaF

(c) Mass of Na2SiO3 that reacts with 0.800 g HF

First, we need to find the moles of HF given its mass as 0.800 g. The molar mass of HF is 1.008 (H) + 18.998 (F) = 20.006 g/mol. So, the moles of HF are: Moles of HF = (0.800 g HF) / (20.006 g/mol) = 0.040 mol HF Now, we need to find the moles of Na2SiO3 that reacts with these moles of HF using the mole ratio from the balanced equation: 1 mol Na2SiO3 reacts with 8 mol HF. Moles of Na2SiO3 = (0.040 mol HF) × (1 mol Na2SiO3 / 8 mol HF) = 0.005 mol Na2SiO3 Finally, we need to find the mass of Na2SiO3 that reacts. The molar mass of Na2SiO3 is 2 × 22.99 (Na) + 28.085 (Si) + 3 × 15.999 (O) = 122.067 g/mol. So, the mass of Na2SiO3 reacting is: Mass of Na2SiO3 = (0.005 mol Na2SiO3) × (122.067 g/mol) = 0.61 g Na2SiO3

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that involves using balanced chemical equations to calculate the quantities of reactants and products involved in a chemical reaction. In essence, it enables us to quantitatively relate the amounts of substances that participate in a chemical transformation.

For instance, in the reaction of hydrofluoric acid with sodium silicate, the balance of atoms dictates how many moles of HF are needed to react with sodium silicate to form sodium fluoride, silicon hexafluoride, and water. The balanced equation tells us the specific ratios, which in this case, indicate that eight moles of HF react with one mole of Na₂SiO₃.

The problem given demonstrates practical applications of stoichiometry, such as determining the mass of NaF produced when a certain amount of HF reacts, by using the mole ratios from the balanced equation. Understanding stoichiometry is essential for many scientific endeavours including chemical manufacturing, pharmacology, and environmental science where precise chemical composition is crucial.

Mole Concept

The mole concept is foundational to stoichiometry and involves understanding that a mole is a standard unit of measurement in chemistry. One mole represents Avogadro's number (\(6.022 \times 10^{23}\) particles) of particles, which could be atoms, molecules, ions, or electrons. It's like a bridge that connects the atomic, microscopic world with the macroscopic world we can measure and observe.

In chemical reactions, the mole concept allows chemists to count entities in bulk by weighing them. For our exercise, we transition from moles of HF needed to react with sodium silicate to the mass of NaF produced, by knowing their molar masses and the mole ratios from the balanced chemical equation.

For example, to determine the mass of sodium fluoride (NaF) produced from the reaction, we must first find the amount in moles (using the mole ratios given by the balanced equation), and then convert these moles to grams with the molecular mass of NaF. Such calculations require a firm grasp of the mole concept, as this abstraction helps us to handle vast numbers of molecules in a practical, measurable way.

Molecular Mass

Molecular mass, or molar mass, represents the mass of one mole of a substance (typically expressed in grams per mole). It is equal to the sum of the atomic masses of all the atoms that make up the molecule, as listed on the periodic table of elements. Knowing the molecular mass is essential to convert between moles of a substance and its mass in grams.

In our exercise, working out how many grams of NaF form from a reaction requires us to use the molecular mass of NaF (Na's mass plus F's mass). Similarly, when calculating how many grams of Na₂SiO₃ can react with HF, we must determine the molecular mass of Na₂SiO₃ to make the conversion.

Molecular mass calculations could sometimes be more complex with larger molecules, as they consist of many atoms; however, the underlying principle remains the same. The ability to manipulate molecular mass is vital for chemists and students alike, as it enables the quantitative analysis of reactants and products in a chemical reaction, further reinforcing the practical power of the mole concept and stoichiometry in chemistry.