Question

Hydrofluoric acid, \(\mathrm{HF}(a q)\), 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: \(\mathrm{Na}_{2} \mathrm{SiO}_{3}(\mathrm{~s})+8 \mathrm{HF}(a q) \longrightarrow\) $$ \mathrm{H}_{2} \mathrm{SiF}_{6}(a q)+2 \mathrm{NaF}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) How many moles of \(\mathrm{HF}\) 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 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 are formed when 0.500 mol of HF reacts with excess Na2SiO3. (c) 0.61 grams of Na2SiO3 can react with 0.800 g of HF.

Step-by-step solution

Write the balanced chemical equation

The balanced chemical equation is given: Na2SiO3(s) + 8 HF(aq) → H2SiF6(aq) + 2 NaF(aq) + 3 H2O(l)

Use stoichiometry to find moles of HF needed

From the balanced chemical equation, we see that 1 mole of Na2SiO3 reacts with 8 moles of HF. Given that we have 0.300 mol of Na2SiO3, we can find the moles of HF needed: moles of HF = moles of Na2SiO3 * (8 moles of HF / 1 mole of Na2SiO3) = 0.300 * 8 = 2.4 moles Answer: 2.4 moles of HF are needed to react with 0.300 mol of Na2SiO3. #b) Calculate grams of NaF formed when 0.500 mol of HF reacts with excess Na2SiO3#

Use stoichiometry to find moles of NaF formed

From the balanced chemical equation, 8 moles of HF react to form 2 moles of NaF. Given that we have 0.500 mol of HF, we can find the moles of NaF formed: moles of NaF = moles of HF * (2 moles of NaF / 8 moles of HF) = 0.500 * (2 / 8) = 0.125 mol

Convert moles of NaF to grams

We can find the molecular weight (M) of NaF: M(NaF) = M(Na) + M(F) = 22.99 + 19 = 41.99 g/mol Convert moles of NaF to grams: grams of NaF = moles of NaF * M(NaF) = 0.125 * 41.99 = 5.25 g Answer: 5.25 grams of NaF are formed when 0.500 mol of HF reacts with excess Na2SiO3. #c) Calculate grams of Na2SiO3 that can react with 0.800 g of HF#

Convert grams of HF to moles

To find out how many grams of Na2SiO3 can react with HF, we need to first convert grams of HF to moles. The molecular weight (M) of HF: M(HF) = M(H) + M(F) = 1 + 19 = 20 g/mol moles of HF = grams of HF / M(HF) = 0.800 / 20 = 0.040 mol

Use stoichiometry to find moles of Na2SiO3

From the balanced chemical equation, 1 mole of Na2SiO3 reacts with 8 moles of HF. moles of Na2SiO3 = moles of HF * (1 mole of Na2SiO3 / 8 moles of HF) = 0.040 * (1 / 8) = 0.005 mol

Convert moles of Na2SiO3 to grams

Find the molecular weight (M) of Na2SiO3: M(Na2SiO3) = 2 * M(Na) + M(Si) + 3 * M(O) = 2* 22.99 + 28.09 + 3* 16 = 122.08 g/mol grams of Na2SiO3 = moles of Na2SiO3 * M(Na2SiO3) = 0.005 * 122.08 = 0.61 g Answer: 0.61 grams of Na2SiO3 can react with 0.800 g of HF.

Key concepts

Balanced Chemical Equation

In any chemical reaction, reacting substances need to follow a balanced chemical equation. This equation represents the application of the law of conservation of mass, meaning the number of atoms of each element must equal on both sides of the equation.
It ensures that the moles of reactants directly convert into moles of products without leaving excess leftover unless specified otherwise.
For the reaction between sodium silicate (\(\mathrm{Na}_2\mathrm{SiO}_3\)) and hydrofluoric acid (\(\mathrm{HF}\)), the equation given is balanced:

• \(\mathrm{Na}_2\mathrm{SiO}_3(\mathrm{s}) + 8\ \mathrm{HF}(\mathrm{aq}) \rightarrow \mathrm{H}_2\mathrm{SiF}_6(\mathrm{aq}) + 2\ \mathrm{NaF}(\mathrm{aq}) + 3\ \mathrm{H}_2\mathrm{O}(l)\)

This equation tells us that 1 mole of sodium silicate reacts with 8 moles of hydrofluoric acid to produce products in a fixed ratio. Understanding and verifying such a balanced equation is foundational to solving problems around stoichiometry.

Moles Calculation

In stoichiometry, moles calculation is vital to determine the quantity of reactants and products needed or formed in a chemical reaction. Moles provide a convenient means of converting between molecules and grams.
Let's focus on the specific reaction involving \(\mathrm{Na}_2\mathrm{SiO}_3\) and \(\mathrm{HF}\). According to the balanced equation, 1 mole of \(\mathrm{Na}_2\mathrm{SiO}_3\) reacts with 8 moles of \(\mathrm{HF}\).
To find out how many moles of \(\mathrm{HF}\) are required to react with 0.300 moles of \(\mathrm{Na}_2\mathrm{SiO}_3\):

• \(\text{moles of HF} = 0.300 \times 8 = 2.4 \text{ moles}\)

This calculation shows how the coefficients in the chemical equation directly correlate to the moles needed and produced, transforming mole ratios from theoretical descriptions to practical quantities in reactions.

Mass Conversion

Mass conversion from moles involves using the molecular weight of substances to transition between the mass and the amount of substance expressed in moles. This is an essential skill in stoichiometry for practical lab work.
When discussing the reaction between \(\mathrm{HF}\) and \(\mathrm{Na}_2\mathrm{SiO}_3\), if you convert moles of a substance to grams: 1. Find the molecular weight of the compound.2. Multiply the moles by the molecular weight.For instance, if converting \(\mathrm{NaF}\) formed from the reaction of 0.500 mol of \(\mathrm{HF}\):

• First calculate moles of \(\mathrm{NaF}\): \(0.500\ \times \frac{2}{8} = 0.125 \text{ mol NaF}\)
• Grass Conversion: \(\text{Molecular Weight of NaF} = 22.99 + 19 = 41.99 \text{ g/mol}\)
• Convert to mass: \(0.125 \times 41.99 = 5.25\ \text{ grams of NaF}\)

Understanding this conversion process allows you to predict the physical amount of products or reagents involved in reactions, thereby facilitating real-world applications of chemical experiments.