Answer :
Let's break down the given chemical reaction:
[tex]\[ S_8 + 12 O_2 \rightarrow 8 SO_3 \][/tex]
From this balanced chemical equation, we can derive several mole ratios. A mole ratio comes from the coefficients of the reactants and products in a balanced chemical equation.
1. Ratio of [tex]\( S_8 \)[/tex] to [tex]\( O_2 \)[/tex]:
- According to the equation, 1 mole of [tex]\( S_8 \)[/tex] reacts with 12 moles of [tex]\( O_2 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{1 \text{ mole } S_8}{12 \text{ moles } O_2} = 0.08333333333333333 \][/tex]
This ratio matches one of the given choices.
2. Ratio of [tex]\( SO_3 \)[/tex] to [tex]\( S_8 \)[/tex]:
- According to the equation, 8 moles of [tex]\( SO_3 \)[/tex] are produced from 1 mole of [tex]\( S_8 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{8 \text{ moles } SO_3}{1 \text{ mole } S_8} = 8.0 \][/tex]
This ratio matches one of the given choices.
3. Ratio of [tex]\( O_2 \)[/tex] to [tex]\( S_8 \)[/tex]:
- According to the equation, 12 moles of [tex]\( O_2 \)[/tex] react with 1 mole of [tex]\( S_8 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{12 \text{ moles } O_2}{1 \text{ mole } S_8} = 12.0 \][/tex]
This ratio matches one of the given choices.
4. Ratio of [tex]\( S_8 \)[/tex] to [tex]\( SO_3 \)[/tex]:
- According to the equation, 1 mole of [tex]\( S_8 \)[/tex] produces 8 moles of [tex]\( SO_3 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{1 \text{ mole } S_8}{8 \text{ moles } SO_3} = 0.125 \][/tex]
This ratio matches one of the given choices.
Now, let's match these with the given options:
- [tex]\(\frac{1 \text{ mole Sf }}{12 \text{ mole } O _2}\)[/tex]:
- This matches the ratio [tex]\(\frac{1 \text{ mole } S_8}{12 \text{ moles } O_2}\)[/tex] which is 0.08333333333333333.
- [tex]\(\frac{8 \text{ mole } 50_1}{1 \ text{ mole } S _4}\)[/tex]:
- This seems to be a typo and probably meant [tex]\(\frac{8 \text{ mole } SO_3}{1 \text{ mole } S_8}\)[/tex] which is 8.0.
- [tex]\(\frac{12 \text{ mole } S_1}{1 \text { mole } O _2}\)[/tex]:
- This does not match any of the ratios.
- [tex]\(\frac{1 \text{ mole } S_1}{8 \text { mole } 50_3}\)[/tex]:
- This seems to be a typo and probably meant [tex]\(\frac{1 \text{ mole } S_8}{8 \text{ mole } SO_3}\)[/tex] which is 0.125.
Based on the corrected mole ratios, the accurate matches from the above are:
- [tex]\(\frac{1 \text { mole } S_8}{12 \text { mole } O_2}\)[/tex]
- [tex]\(\frac{8 \text { mole } SO_3}{1 \text{ mole } S_8}\)[/tex]
- [tex]\(\frac{1 \text{ mole } S_8}{8 \text{ mole } SO_3}\)[/tex]
Therefore, the correct options are:
- [tex]\(\frac{1 \text { mole Sf }}{12 \text { mole } O _2}\)[/tex]
- [tex]\(\frac{8 \text { mole } 50_1}{1 \text { mole } S _4}\)[/tex] (corrected to [tex]\(\frac{8 \text{ mole } SO_3}{1 \text{ mole } S_8}\)[/tex])
- [tex]\(\frac{1 \text { mole } S_1}{8 \text { mole } 50_3}\)[/tex] (corrected to [tex]\(\frac{1 \text{ mole } S_8}{8 \text{ mole } SO_3}\)[/tex]).
[tex]\[ S_8 + 12 O_2 \rightarrow 8 SO_3 \][/tex]
From this balanced chemical equation, we can derive several mole ratios. A mole ratio comes from the coefficients of the reactants and products in a balanced chemical equation.
1. Ratio of [tex]\( S_8 \)[/tex] to [tex]\( O_2 \)[/tex]:
- According to the equation, 1 mole of [tex]\( S_8 \)[/tex] reacts with 12 moles of [tex]\( O_2 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{1 \text{ mole } S_8}{12 \text{ moles } O_2} = 0.08333333333333333 \][/tex]
This ratio matches one of the given choices.
2. Ratio of [tex]\( SO_3 \)[/tex] to [tex]\( S_8 \)[/tex]:
- According to the equation, 8 moles of [tex]\( SO_3 \)[/tex] are produced from 1 mole of [tex]\( S_8 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{8 \text{ moles } SO_3}{1 \text{ mole } S_8} = 8.0 \][/tex]
This ratio matches one of the given choices.
3. Ratio of [tex]\( O_2 \)[/tex] to [tex]\( S_8 \)[/tex]:
- According to the equation, 12 moles of [tex]\( O_2 \)[/tex] react with 1 mole of [tex]\( S_8 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{12 \text{ moles } O_2}{1 \text{ mole } S_8} = 12.0 \][/tex]
This ratio matches one of the given choices.
4. Ratio of [tex]\( S_8 \)[/tex] to [tex]\( SO_3 \)[/tex]:
- According to the equation, 1 mole of [tex]\( S_8 \)[/tex] produces 8 moles of [tex]\( SO_3 \)[/tex].
- The mole ratio is:
[tex]\[ \frac{1 \text{ mole } S_8}{8 \text{ moles } SO_3} = 0.125 \][/tex]
This ratio matches one of the given choices.
Now, let's match these with the given options:
- [tex]\(\frac{1 \text{ mole Sf }}{12 \text{ mole } O _2}\)[/tex]:
- This matches the ratio [tex]\(\frac{1 \text{ mole } S_8}{12 \text{ moles } O_2}\)[/tex] which is 0.08333333333333333.
- [tex]\(\frac{8 \text{ mole } 50_1}{1 \ text{ mole } S _4}\)[/tex]:
- This seems to be a typo and probably meant [tex]\(\frac{8 \text{ mole } SO_3}{1 \text{ mole } S_8}\)[/tex] which is 8.0.
- [tex]\(\frac{12 \text{ mole } S_1}{1 \text { mole } O _2}\)[/tex]:
- This does not match any of the ratios.
- [tex]\(\frac{1 \text{ mole } S_1}{8 \text { mole } 50_3}\)[/tex]:
- This seems to be a typo and probably meant [tex]\(\frac{1 \text{ mole } S_8}{8 \text{ mole } SO_3}\)[/tex] which is 0.125.
Based on the corrected mole ratios, the accurate matches from the above are:
- [tex]\(\frac{1 \text { mole } S_8}{12 \text { mole } O_2}\)[/tex]
- [tex]\(\frac{8 \text { mole } SO_3}{1 \text{ mole } S_8}\)[/tex]
- [tex]\(\frac{1 \text{ mole } S_8}{8 \text{ mole } SO_3}\)[/tex]
Therefore, the correct options are:
- [tex]\(\frac{1 \text { mole Sf }}{12 \text { mole } O _2}\)[/tex]
- [tex]\(\frac{8 \text { mole } 50_1}{1 \text { mole } S _4}\)[/tex] (corrected to [tex]\(\frac{8 \text{ mole } SO_3}{1 \text{ mole } S_8}\)[/tex])
- [tex]\(\frac{1 \text { mole } S_1}{8 \text { mole } 50_3}\)[/tex] (corrected to [tex]\(\frac{1 \text{ mole } S_8}{8 \text{ mole } SO_3}\)[/tex]).
