To determine how many grams of HF are needed for 182 grams of SiO_2 to react completely in the given chemical reaction:
[tex]\[ SiO_2 + 4 HF \rightarrow SiF_4 + 2 H_2O \][/tex]
we need to follow these steps:
1. Calculate the moles of SiO_2:
- The molar mass of SiO_2 is approximately 60.08 g/mol.
- Given mass of SiO_2 is 182 grams.
- Moles of SiO_2 = [tex]\(\frac{\text{mass of SiO}_2}{\text{molar mass of SiO}_2}\)[/tex]:
[tex]\[
\text{Moles of SiO}_2 = \frac{182 \text{ g}}{60.08 \text{ g/mol}} \approx 3.03 \text{ mol}
\][/tex]
2. Determine the moles of HF needed:
- According to the balanced chemical equation, 1 mole of SiO_2 reacts with 4 moles of HF.
- Therefore, moles of HF required = moles of SiO_2 × 4:
[tex]\[
\text{Moles of HF} = 3.03 \text{ mol} \times 4 = 12.12 \text{ mol}
\][/tex]
3. Calculate the mass of HF required:
- The molar mass of HF is approximately 20.01 g/mol.
- Mass of HF = moles of HF × molar mass of HF:
[tex]\[
\text{Mass of HF} = 12.12 \text{ mol} \times 20.01 \text{ g/mol} \approx 242.5 \text{ g}
\][/tex]
Therefore, the reaction requires 242.5 grams of HF.
