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What mass of [tex][tex]$HgO$[/tex][/tex] is required to produce [tex][tex]$0.726 \, \text{mol}$[/tex][/tex] of [tex][tex]$O_2$[/tex][/tex]?

[tex]
2 \, \text{HgO} \rightarrow 2 \, \text{Hg} + O_2
[/tex]

A. [tex]314 \, \text{g}[/tex]
B. [tex]0.003 \, \text{g}[/tex]
C. [tex]628.16 \, \text{g}[/tex]
D. [tex]0.410 \, \text{g}[/tex]



Answer :

GinnyAnswer
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].

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