To determine the amount of hydrofluoric acid ([tex]\( \text{HF} \)[/tex]) needed for 182 grams of silicon dioxide ([tex]\( \text{SiO}_2 \)[/tex]) to fully react, we can follow these steps:
1. Determine the molar masses:
- The molar mass of [tex]\(\text{SiO}_2\)[/tex] is calculated as follows:
- Silicon (Si): 28.085 g/mol
- Oxygen (O): 16.00 g/mol (since there are two oxygen atoms, multiply by 2)
- Total molar mass of [tex]\(\text{SiO}_2\)[/tex] = 28.085 + (16.00 * 2) = 60.085 g/mol
- The molar mass of [tex]\(\text{HF}\)[/tex]:
- Hydrogen (H): 1.008 g/mol
- Fluorine (F): 19.00 g/mol
- Total molar mass of [tex]\(\text{HF}\)[/tex] = 1.008 + 19.00 = 20.008 g/mol
2. Calculate the number of moles of [tex]\(\text{SiO}_2\)[/tex]:
- Given mass of [tex]\(\text{SiO}_2\)[/tex] = 182 grams
- Number of moles of [tex]\(\text{SiO}_2\)[/tex] = [tex]\(\frac{\text{mass}}{\text{molar mass}}\)[/tex]
- Number of moles of [tex]\(\text{SiO}_2\)[/tex] = [tex]\(\frac{182}{60.085} \approx 3.029\)[/tex] moles
3. Establish the stoichiometric relationship:
- From the balanced chemical equation, 1 mole of [tex]\(\text{SiO}_2\)[/tex] reacts with 4 moles of [tex]\(\text{HF}\)[/tex].
4. Calculate the number of moles of [tex]\(\text{HF}\)[/tex] needed:
- Number of moles of [tex]\(\text{HF}\)[/tex] = [tex]\(3.029 \times 4 \approx 12.117\)[/tex] moles
5. Determine the mass of [tex]\(\text{HF}\)[/tex] needed:
- Mass of [tex]\(\text{HF}\)[/tex] = Number of moles of [tex]\(\text{HF}\)[/tex] [tex]\(\times\)[/tex] Molar mass of [tex]\(\text{HF}\)[/tex]
- Mass of [tex]\(\text{HF}\)[/tex] = [tex]\(12.117 \times 20.008 \approx 242.465\)[/tex] grams
Thus, the reaction requires 242.465 grams of HF to fully react with 182 grams of SiO[tex]\(_2\)[/tex].
