To determine the mass of [tex]\( \text{HgO} \)[/tex] required to produce [tex]\( 0.726 \text{ mol} \)[/tex] of [tex]\( \text{O}_2 \)[/tex], we can follow these steps:
1. Identify the stoichiometric ratio:
From the balanced chemical equation:
[tex]\[
2 \text{HgO} \rightarrow 2 \text{Hg} + \text{O}_2
\][/tex]
We see that 2 moles of [tex]\( \text{HgO} \)[/tex] produce 1 mole of [tex]\( \text{O}_2 \)[/tex]. Therefore, the molar ratio of [tex]\( \text{HgO} \)[/tex] to [tex]\( \text{O}_2 \)[/tex] is 2:1.
2. Calculate the moles of [tex]\(\text{HgO}\)[/tex] required:
Given that [tex]\( 0.726 \text{ mol} \)[/tex] of [tex]\( \text{O}_2 \)[/tex] is needed, we use the molar ratio to find the moles of [tex]\( \text{HgO} \)[/tex] required:
[tex]\[
\text{moles of } \text{HgO} = 2 \times \text{moles of } \text{O}_2 = 2 \times 0.726 = 1.452 \text{ mol}
\][/tex]
3. Determine the molar mass of [tex]\(\text{HgO}\)[/tex]:
The molar mass of [tex]\( \text{HgO} \)[/tex] is given as [tex]\( 216.59 \text{ g/mol} \)[/tex].
4. Calculate the mass of [tex]\(\text{HgO}\)[/tex] required:
Using the moles of [tex]\( \text{HgO} \)[/tex] and its molar mass, we can calculate the mass required:
[tex]\[
\text{mass of } \text{HgO} = \text{moles of } \text{HgO} \times \text{molar mass of } \text{HgO}
\][/tex]
[tex]\[
\text{mass of } \text{HgO} = 1.452 \text{ mol} \times 216.59 \text{ g/mol} = 314.48868 \text{ g}
\][/tex]
5. Compare to the provided choices:
The calculated mass of [tex]\( \text{HgO} \)[/tex] is [tex]\( 314.48868 \text{ g} \)[/tex]. Among the given choices:
- [tex]\( 314 \text{ g} \)[/tex]
- [tex]\( 0.003 \text{ g} \)[/tex]
- [tex]\( 628.16 \text{ g} \)[/tex]
- [tex]\( 0.410 \text{ g} \)[/tex]
The closest value is [tex]\( 314 \text{ g} \)[/tex].
Therefore, the mass of [tex]\( \text{HgO} \)[/tex] required to produce [tex]\( 0.726 \text{ mol} \)[/tex] of [tex]\( \text{O}_2 \)[/tex] is [tex]\( \boxed{314 \text{ g}} \)[/tex].
