To determine the mass of HgO required to produce 0.726 moles of [tex]\( O_2 \)[/tex], let's follow these step-by-step calculations:
1. Understanding the Reaction Stoichiometry:
The balanced chemical equation is:
[tex]\[
2 \, \text{HgO} \rightarrow 2 \, \text{Hg} + O_2
\][/tex]
This tells us that 2 moles of HgO produce 1 mole of [tex]\( O_2 \)[/tex].
2. Determining the Mole Ratio:
From the balanced equation, we can see that the mole ratio of HgO to [tex]\( O_2 \)[/tex] is 2:1. This means that to produce 1 mole of [tex]\( O_2 \)[/tex], 2 moles of HgO are needed.
3. Calculating Moles of HgO Needed:
We are given that we need to produce 0.726 moles of [tex]\( O_2 \)[/tex]. Using the mole ratio:
[tex]\[
\text{Moles of HgO needed} = 0.726 \, \text{mol} \times 2 = 1.452 \, \text{mol} \, \text{HgO}
\][/tex]
4. Finding the Molar Mass of HgO:
The molar mass of HgO is given as 216.59 g/mol.
5. Calculating the Mass of HgO Required:
Now, we use the moles of HgO needed and the molar mass of HgO to find the mass required:
[tex]\[
\text{Mass of HgO required} = 1.452 \, \text{mol} \times 216.59 \, \text{g/mol} = 314.48868 \, \text{g}
\][/tex]
Given this detailed calculation, the mass of HgO required to produce 0.726 moles of [tex]\( O_2 \)[/tex] is approximately 314 g.
