To determine how many grams of HF are needed for 182 grams of SiO[tex]\(_2\)[/tex] to react completely, follow these steps:
1. Calculate the moles of SiO[tex]\(_2\)[/tex]:
Given:
- Mass of SiO[tex]\(_2\)[/tex]: 182 grams
- Molar mass of SiO[tex]\(_2\)[/tex]: 60.0843 g/mol
Number of moles of SiO[tex]\(_2\)[/tex]:
[tex]\[
\text{moles of SiO\(_2\)} = \frac{\text{mass of SiO\(_2\)}}{\text{molar mass of SiO\(_2\)}}
\][/tex]
[tex]\[
\text{moles of SiO\(_2\)} = \frac{182 \text{ g}}{60.0843 \text{ g/mol}} = 3.029
\][/tex]
2. Use stoichiometry to determine the moles of HF needed:
From the balanced chemical equation:
[tex]\[
SiO_2 + 4 HF \rightarrow SiF_4 + 2 H_2O
\][/tex]
1 mole of SiO[tex]\(_2\)[/tex] reacts with 4 moles of HF.
Number of moles of HF needed:
[tex]\[
\text{moles of HF needed} = \text{moles of SiO\(_2\)} \times 4
\][/tex]
[tex]\[
\text{moles of HF needed} = 3.029 \times 4 = 12.116
\][/tex]
3. Calculate the mass of HF needed:
Given:
- Molar mass of HF: 20.0064 g/mol
Mass of HF needed:
[tex]\[
\text{mass of HF} = \text{moles of HF} \times \text{molar mass of HF}
\][/tex]
[tex]\[
\text{mass of HF} = 12.116 \times 20.0064 \text{ g/mol} = 242.404 \text{ g}
\][/tex]
Therefore, the reaction requires 242.404 grams of HF.
