To determine how many grams of NaOH will react with 507 grams of FeCl[tex]\(_2\)[/tex], follow these steps:
1. Identify molar masses:
- The molar mass of FeCl[tex]\(_2\)[/tex] is 127.75 g/mol.
- The molar mass of NaOH is 40 g/mol.
2. Calculate moles of FeCl[tex]\(_2\)[/tex]:
[tex]\[
\text{Moles of FeCl\(_2\)} = \frac{\text{mass of FeCl\(_2\)}}{\text{molar mass of FeCl\(_2\)}} = \frac{507 \text{ grams}}{127.75 \text{ g/mol}}
\][/tex]
[tex]\[
\text{Moles of FeCl\(_2\)} \approx 3.97 \, \text{moles}
\][/tex]
3. Assess stoichiometric ratio:
According to the balanced chemical equation:
[tex]\[
\text{FeCl}_2 + 2\text{NaOH} \rightarrow \text{Fe(OH)}_2(\text{s}) + 2\text{NaCl}
\][/tex]
1 mole of FeCl[tex]\(_2\)[/tex] reacts with 2 moles of NaOH. Consequently, 3.97 moles of FeCl[tex]\(_2\)[/tex] will react with:
[tex]\[
\text{Moles of NaOH needed} = 3.97 \times 2 \approx 7.94 \, \text{moles}
\][/tex]
4. Calculate the mass of NaOH required:
[tex]\[
\text{Mass of NaOH needed} = \text{moles of NaOH} \times \text{molar mass of NaOH} = 7.94 \times 40 \, \text{g/mol}
\][/tex]
[tex]\[
\text{Mass of NaOH needed} \approx 317.50 \, \text{grams}
\][/tex]
5. Compare with given options:
The closest answer to 317.50 grams is:
B. 320 g NaOH
Thus, the answer is:
[tex]\[
\boxed{320 \text{ g NaOH}}
\][/tex]
