HF Required To React Completely With 182 Grams Of SiO2

In the world of chemistry, understanding stoichiometry is paramount to predict the amount of reactants needed or products formed in a chemical reaction. Stoichiometry, derived from the Greek words stoicheion (element) and metron (measure), allows us to quantify these relationships. This article delves into a specific chemical reaction, the reaction between silicon dioxide ($SiO_2$) and hydrofluoric acid ($HF$), to illustrate how stoichiometric principles can be applied to determine the mass of reactants required for a complete reaction. Specifically, we will calculate the mass of $HF$ needed to react completely with 182 grams of $SiO_2$, a problem that highlights the practical applications of stoichiometry in chemistry.

The given chemical reaction is:

$SiO_2 + 4HF \rightarrow SiF_4 + 2H_2O$

This equation tells us that one mole of silicon dioxide ($SiO_2$) reacts with four moles of hydrofluoric acid ($HF$) to produce one mole of silicon tetrafluoride ($SiF_4$) and two moles of water ($H_2O$). The coefficients in the balanced chemical equation are crucial for stoichiometric calculations, as they provide the molar ratios between reactants and products. To solve the problem at hand, we will use these molar ratios, along with the molar masses of the compounds involved, to convert the given mass of $SiO_2$ into the mass of $HF$ required for the reaction. This process involves several steps, including calculating the moles of $SiO_2$, using the stoichiometric ratio to find the moles of $HF$, and finally converting the moles of $HF$ to grams.

This article aims to provide a comprehensive, step-by-step guide to solving this problem, making it easier for students and enthusiasts to grasp the fundamental concepts of stoichiometry. By the end of this article, you will not only understand how to calculate the mass of $HF$ needed for this specific reaction but also appreciate the broader applications of stoichiometry in various chemical calculations and reactions. Understanding these calculations is crucial not only for academic success in chemistry but also for various real-world applications, such as in industrial chemistry, environmental science, and materials science. So, let’s dive in and unravel the intricacies of this chemical reaction and the calculations involved.

Step 1: Calculate the Molar Mass of $SiO_2$ and $HF$

The first crucial step in solving any stoichiometry problem is to determine the molar masses of the compounds involved. The molar mass of a compound is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). To calculate the molar mass, we sum the atomic masses of all the atoms in the chemical formula. We obtain these atomic masses from the periodic table.

For silicon dioxide ($SiO_2$), the calculation is as follows:

• Silicon (Si): 1 atom × 28.0855 g/mol = 28.0855 g/mol
• Oxygen (O): 2 atoms × 15.999 g/mol = 31.998 g/mol

Adding these together, we get the molar mass of $SiO_2$:

$28.0855 \text{ g/mol} + 31.998 \text{ g/mol} = 60.0835 \text{ g/mol}$

Therefore, the molar mass of $SiO_2$ is approximately 60.08 g/mol. This value will be essential for converting the given mass of $SiO_2$ into moles.

Next, we calculate the molar mass of hydrofluoric acid ($HF$):

• Hydrogen (H): 1 atom × 1.008 g/mol = 1.008 g/mol
• Fluorine (F): 1 atom × 18.998 g/mol = 18.998 g/mol

Adding these together, we find the molar mass of $HF$:

$1.008 \text{ g/mol} + 18.998 \text{ g/mol} = 20.006 \text{ g/mol}$

Thus, the molar mass of $HF$ is approximately 20.01 g/mol. This value will be used to convert the moles of $HF$ needed for the reaction back into grams. Accurate molar masses are the foundation of stoichiometric calculations, ensuring that we can accurately convert between mass and moles, which is crucial for determining the correct amount of reactants and products in a chemical reaction.

Step 2: Convert Grams of $SiO_2$ to Moles

Now that we have the molar mass of $SiO_2$ (60.08 g/mol), we can convert the given mass of $SiO_2$ (182 grams) into moles. This conversion is a fundamental step in stoichiometry because the balanced chemical equation expresses the reaction in terms of moles, not grams. To convert from grams to moles, we use the formula:

$\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$

In this case, the mass of $SiO_2$ is 182 grams, and the molar mass is 60.08 g/mol. Plugging these values into the formula, we get:

$\text{Moles of } SiO_2 = \frac{182 \text{ g}}{60.08 \text{ g/mol}}$

Performing the division, we find:

$\text{Moles of } SiO_2 ≈ 3.03 \text{ mol}$

Therefore, 182 grams of $SiO_2$ is equivalent to approximately 3.03 moles. This value is critical because it allows us to use the stoichiometric ratio from the balanced chemical equation to determine the number of moles of $HF$ required for the reaction. Converting grams to moles is a common operation in chemistry, serving as a bridge between the macroscopic world (grams) and the microscopic world (moles and molecules). The accuracy of this conversion directly impacts the accuracy of subsequent calculations, making it an indispensable step in stoichiometric problem-solving. By understanding this conversion, we can accurately quantify the amounts of substances involved in a chemical reaction, ensuring that we have the correct proportions for the reaction to proceed as intended.

Step 3: Use the Stoichiometric Ratio to Find Moles of $HF$

The balanced chemical equation for the reaction between silicon dioxide ($SiO_2$) and hydrofluoric acid ($HF$) is:

$SiO_2 + 4HF \rightarrow SiF_4 + 2H_2O$

This equation provides us with the stoichiometric ratio between the reactants and products. The coefficients in front of each chemical formula indicate the number of moles of each substance involved in the reaction. In this case, the equation tells us that 1 mole of $SiO_2$ reacts with 4 moles of $HF$. This ratio is the key to determining how many moles of $HF$ are needed to react completely with the 3.03 moles of $SiO_2$ we calculated in the previous step.

The stoichiometric ratio between $SiO_2$ and $HF$ is 1:4. This means that for every 1 mole of $SiO_2$, we need 4 moles of $HF$. To find the moles of $HF$ required, we multiply the moles of $SiO_2$ by this ratio:

$\text{Moles of } HF = \text{Moles of } SiO_2 × \frac{4 \text{ moles } HF}{1 \text{ mole } SiO_2}$

Plugging in the value we calculated earlier (3.03 moles of $SiO_2$):

$\text{Moles of } HF = 3.03 \text{ mol } SiO_2 × \frac{4 \text{ moles } HF}{1 \text{ mole } SiO_2}$

Performing the multiplication, we get:

$\text{Moles of } HF = 12.12 \text{ mol}$

Therefore, 12.12 moles of $HF$ are required to react completely with 3.03 moles of $SiO_2$. This calculation highlights the power of stoichiometry in predicting the amounts of reactants needed in a chemical reaction. The stoichiometric ratio acts as a conversion factor, allowing us to move from the moles of one substance to the moles of another. Accurate application of these ratios is crucial in chemical synthesis, industrial processes, and laboratory experiments, where precise quantities of reactants are necessary for desired outcomes. By understanding and utilizing stoichiometric ratios, we can efficiently and accurately predict the amounts of substances involved in chemical reactions.

Step 4: Convert Moles of $HF$ to Grams

Having determined the number of moles of $HF$ required (12.12 moles), the final step is to convert this value back into grams. This conversion will give us the mass of $HF$ needed to react completely with 182 grams of $SiO_2$. To convert from moles to grams, we use the formula:

$\text{Mass} = \text{Moles} × \text{Molar Mass}$

We already calculated the molar mass of $HF$ in Step 1, which is approximately 20.01 g/mol. Now, we multiply the moles of $HF$ (12.12 mol) by its molar mass:

$\text{Mass of } HF = 12.12 \text{ mol} × 20.01 \text{ g/mol}$

Performing the multiplication, we get:

$\text{Mass of } HF ≈ 242.52 \text{ g}$

Therefore, approximately 242.52 grams of $HF$ are needed to react completely with 182 grams of $SiO_2$. However, the question asks for the answer to be expressed to three significant figures. Rounding 242.52 grams to three significant figures gives us 243 grams.

This final conversion provides a practical answer to the initial problem, telling us exactly how much $HF$ is required in a real-world measurement (grams). Converting moles back to grams is essential for laboratory work and industrial applications, where chemicals are typically measured by mass. This step completes the stoichiometric calculation, linking the initial mass of $SiO_2$ to the required mass of $HF$ through the balanced chemical equation and molar masses. By mastering these conversions, we can confidently perform stoichiometric calculations, ensuring accurate and efficient chemical reactions.

Final Answer

The reaction requires 243 grams of $HF$ for 182 grams of $SiO_2$ to react completely. This answer is expressed to three significant figures, as requested in the problem. This calculation demonstrates the practical application of stoichiometry in determining the required mass of reactants in a chemical reaction. By following the steps outlined—calculating molar masses, converting grams to moles, using stoichiometric ratios, and converting moles back to grams—we can accurately solve a wide range of stoichiometry problems. Understanding these principles is crucial for anyone studying chemistry or working in fields where chemical reactions are involved. The ability to perform these calculations accurately ensures efficient use of materials, safe handling of chemicals, and precise control over chemical processes. Stoichiometry is a fundamental tool in chemistry, providing a quantitative framework for understanding and predicting chemical reactions.

In conclusion, determining the amount of hydrofluoric acid ($HF$) needed to react completely with 182 grams of silicon dioxide ($SiO_2$) involves a series of stoichiometric calculations that are fundamental to the study and application of chemistry. By meticulously following the steps outlined, we've shown how to convert grams to moles, utilize stoichiometric ratios derived from balanced chemical equations, and convert moles back to grams. The final answer, 243 grams of $HF$, not only answers the specific question but also illustrates the broader principles of stoichiometry. Stoichiometry is not merely a mathematical exercise; it is a crucial tool in chemistry that allows us to predict and control the outcomes of chemical reactions. Whether in a laboratory setting, an industrial process, or an environmental study, understanding stoichiometry ensures that chemical reactions are carried out efficiently, safely, and with the desired results.

The ability to perform stoichiometric calculations is essential for chemists, engineers, and anyone working with chemical processes. It enables the accurate measurement of reactants and products, the prediction of reaction yields, and the optimization of chemical reactions. This article has provided a detailed, step-by-step guide to solving a specific stoichiometric problem, but the underlying principles apply to a wide range of chemical reactions. By mastering these principles, students and professionals alike can confidently approach chemical calculations and contribute to advancements in various fields, from materials science to pharmaceuticals. As we continue to explore the complexities of the chemical world, a solid understanding of stoichiometry remains a cornerstone of scientific progress and innovation. The reaction between $SiO_2$ and $HF$ serves as an excellent example of how these principles can be applied to solve practical problems and gain deeper insights into chemical interactions.