To determine how many grams of fluorine [tex]\( F_2 \)[/tex] are needed to generate 3.25 moles of carbon tetrafluoride [tex]\( CF_4 \)[/tex], we will follow these steps:
1. Understand the chemical reaction and mole ratio:
The balanced chemical equation is:
[tex]\[
C + 2 F_2 \rightarrow CF_4
\][/tex]
From this equation, note that 2 moles of [tex]\( F_2 \)[/tex] are required to produce 1 mole of [tex]\( CF_4 \)[/tex].
2. Determine the number of moles of [tex]\( F_2 \)[/tex] required:
We need to find out how many moles of [tex]\( F_2 \)[/tex] are required to produce 3.25 moles of [tex]\( CF_4 \)[/tex]. Using the mole ratio from the equation:
[tex]\[
\text{Moles of } F_2 = 2 \times \text{Moles of } CF_4
\][/tex]
Given that we have 3.25 moles of [tex]\( CF_4 \)[/tex]:
[tex]\[
\text{Moles of } F_2 = 2 \times 3.25 = 6.5 \text{ moles of } F_2
\][/tex]
3. Calculate the mass of [tex]\( F_2 \)[/tex] needed:
We know the molar mass of [tex]\( F_2 \)[/tex] is 38.00 g/mol. To find the mass, we use the formula:
[tex]\[
\text{Mass of } F_2 = \text{Moles of } F_2 \times \text{Molar mass of } F_2
\][/tex]
Substituting the values we have:
[tex]\[
\text{Mass of } F_2 = 6.5 \text{ moles} \times 38.00 \text{ g/mol} = 247.0 \text{ grams}
\][/tex]
Therefore, to generate 3.25 moles of carbon tetrafluoride [tex]\( CF_4 \)[/tex], you need 247.0 grams of fluorine [tex]\( F_2 \)[/tex].
