To determine the number of grams of HF needed for 182 grams of SiO₂ to react completely in the given chemical reaction:
[tex]\[ SiO_2 + 4 HF \rightarrow SiF_4 + 2 H_2O \][/tex]
1. Calculate the moles of SiO₂:
First, find the molar mass of SiO₂. The molar mass of silicon dioxide (SiO₂) is:
[tex]\[
M_{\text{SiO}_2} = 28.085\ (\text{Si}) + 2 \times 15.999\ (\text{O}) = 60.08\ \text{g/mol}
\][/tex]
Next, compute the moles of SiO₂ using the given mass:
[tex]\[
\text{moles of SiO}_2 = \frac{\text{mass of SiO}_2}{\text{molar mass of SiO}_2} = \frac{182\ \text{g}}{60.08\ \text{g/mol}} \approx 3.029\ \text{mol}
\][/tex]
2. Determine the moles of HF needed:
The balanced equation shows that 1 mole of SiO₂ reacts with 4 moles of HF. Therefore, the moles of HF needed are:
[tex]\[
\text{moles of HF} = \text{moles of SiO}_2 \times 4 = 3.029\ \text{mol} \times 4 \approx 12.117\ \text{mol}
\][/tex]
3. Calculate the mass of HF needed:
The molar mass of hydrogen fluoride (HF) is:
[tex]\[
M_{\text{HF}} = 1.008\ (\text{H}) + 18.998\ (\text{F}) = 20.01\ \text{g/mol}
\][/tex]
Finally, compute the mass of HF required:
[tex]\[
\text{mass of HF} = \text{moles of HF} \times \text{molar mass of HF} = 12.117\ \text{mol} \times 20.01\ \text{g/mol} \approx 242.465\ \text{g}
\][/tex]
Thus, the reaction requires 242.465 grams of HF.
Expressed to three significant figures, the reaction requires:
242 grams of HF.
