To determine how many moles of silicon dioxide (SiO2) are needed to produce 13.5 moles of water (H2O), we can refer to the balanced chemical equation:
\[ \text{SiO}_2 + 4 \text{HF} \rightarrow \text{SiF}_4 + 2 \text{H}_2\text{O} \]
From the balanced equation, we see that 1 mole of SiO2 produces 2 moles of H2O.
To find out how many moles of SiO2 are required to produce 13.5 moles of H2O, we can set up the proportion:
\[ 1 \text{ mol SiO}_2 \text{ produces } 2 \text{ mol H}_2\text{O} \]
We need to find \( x \) moles of SiO2 to produce 13.5 moles of H2O.
Using the ratio from the balanced equation:
\[ x \text{ mol SiO}_2 = \frac{13.5 \text{ mol H}_2\text{O}}{2} \]
Calculating this gives:
\[ x = \frac{13.5}{2} = 6.75 \text{ mol SiO}_2 \]
Therefore, 6.75 moles of silicon dioxide (SiO2) are needed to produce 13.5 moles of water (H2O).
The correct response is 6.75 mol.