Question

Write a balanced equation for the reaction of hydrofluoric acid with \(\mathrm{SiO}_{2}\). What volume of \(2.0 \mathrm{M}\) HF is required to react with one gram of silicon dioxide?

Short answer

Answer: The volume of 2.0 M hydrofluoric acid required to react with one gram of silicon dioxide is approximately 33.2 mL.

Step-by-step solution

Write the balanced chemical equation for HF and SiO2

The reaction between hydrofluoric acid (HF) and silicon dioxide (SiO2) can be written as: $$\mathrm{SiO}_{2}(s) + 4\mathrm{HF}(aq) \rightarrow \mathrm{SiF}_{4}(g) + 2\mathrm{H}_{2}\mathrm{O}(l)$$

Calculate the molar mass of SiO2

In order to find the moles of SiO2, we first need to find the molar mass of SiO2. The atomic mass of Silicon (Si) is 28.09 g/mol, and the atomic mass of Oxygen (O) is 16.00 g/mol. Therefore, the molar mass of SiO2 is: $$\mathrm{Molar\:mass\:of\:SiO}_{2} = \mathrm{1 \times (28.09\:g/mol)} + \mathrm{2 \times (16.00\:g/mol)} = 60.09\:\mathrm{g/mol}$$

Calculate the moles of SiO2

We are given that 1 gram of SiO2 reacts with HF. To find the moles of SiO2, we use the formula: $$\mathrm{Moles\:of\:SiO}_{2} = \frac{\mathrm{Mass\:of\:SiO}_{2}}{\mathrm{Molar\:mass\:of\:SiO}_{2}}$$ $$\mathrm{Moles\:of\:SiO}_{2} = \frac{1\:\mathrm{g}}{60.09\:\mathrm{g/mol}} \approx 0.0166\:\mathrm{mol}$$

Use stoichiometry to find moles of HF

From the balanced chemical equation, we can see that 4 moles of HF react with 1 mole of SiO2. So, we can find the moles of HF required to react with 0.0166 moles of SiO2. $$\mathrm{Moles\:of\:HF} = \mathrm{4\:moles\:HF\: \times\:0.0166\:moles\:of\:SiO}_{2} \approx 0.0664\:\mathrm{mol}$$

Calculate the volume of 2.0 M HF

The formula for calculating the volume of a solution given its molarity and moles of the solute is: $$\mathrm{Volume\:of\:solution (L)} = \frac{\mathrm{Moles\:of\:solute}}{\mathrm{Molarity\:of\:solution}}$$ We are given that the molarity of HF is 2.0 M. Using this information, we can find the volume of HF required to react with 0.0166 moles of SiO2: $$\mathrm{Volume\:of\:HF\:solution (L)} = \frac{0.0664\:\mathrm{mol}}{2.0\:\mathrm{M}} = 0.0332\:\mathrm{L}$$ $$\mathrm{Volume\:of\:HF\:solution (mL)} = 0.0332\:\mathrm{L} \times \frac{1000\:\mathrm{mL}}{1\:\mathrm{L}} = 33.2\:\mathrm{mL}$$ Therefore, the volume of 2.0 M hydrofluoric acid required to react with one gram of silicon dioxide is approximately 33.2 mL.

Key concepts

Understanding Stoichiometry

Stoichiometry is a division of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's akin to a recipe for a chemical reaction, laying out the precise amounts of each substance required to react fully without any leftover ingredients.

For instance, take the balanced equation we have for the reaction of hydrofluoric acid with silicon dioxide (\r\(\mathrm{SiO}_2 + 4\mathrm{HF} \rightarrow \mathrm{SiF}_4 + 2\mathrm{H}_2\mathrm{O}\)). This equation tells us that one mole of silicon dioxide reacts with four moles of hydrofluoric acid to produce one mole of silicon tetrafluoride and two moles of water. Stoichiometry allows us to use this ratio to calculate quantities, like how much reactant is needed to produce a certain amount of product.

Calculating Molar Mass

Molar mass calculation is crucial for converting between grams and moles, and vice versa. The molar mass of a substance is the weight of one mole (6.022 x 10²³ particles) of that substance. It is expressed in grams per mole (g/mol).

To calculate the molar mass of silicon dioxide (\r\(\mathrm{SiO}_2\)), we add up the masses of the individual atoms in the compound based on values found on the periodic table: Silicon (\r\(28.09\) g/mol) and Oxygen (\r\(16.00\) g/mol). As silicon dioxide consists of one silicon and two oxygen atoms, its molar mass would be \r\(1\times 28.09 \)g/mol + \r\(2\times 16.00\) g/mol = \r\(60.09\)g/mol. Knowing the molar mass is vital for subsequent calculations, such as determining the amount of substance needed for a reaction.

Working with Molarity and Volume

Molarity and volume calculations are integral when working with solutions. Molarity (\r\(M\)) measures the concentration of a solution, represented as moles of solute per liter of solution (\r\(mol/L\)). When you have a solution of known molarity, you can calculate the volume of solution needed to provide a certain number of moles of solute.

For example, if you need \r\(0.0664\) moles of hydrofluoric acid (HF) and it's supplied as a 2.0 M solution, calculate the required volume using the formula: Volume of solution (L) = Moles of solute / Molarity of solution. Here, it translates to \r\(0.0332\) L or \r\(33.2\) mL, indicating the specific amount of hydrofluoric acid solution needed for our chemical reaction.