To determine the valid mole ratio from the given balanced chemical equation:
[tex]\[ 2 C_3H_6 + 9 O_2 \rightarrow 6 CO_2 + 6 H_2O \][/tex]
We'll compare each of the provided ratios with the stoichiometric coefficients in the balanced equation. Here's the step-by-step analysis:
1. Option 1: [tex]\(\frac{1 \text{ mol } C_3H_6}{2 \text{ mol } CO_2}\)[/tex]
- According to the balanced equation, 2 moles of [tex]\(C_3H_6\)[/tex] produce 6 moles of [tex]\(CO_2\)[/tex].
- Simplifying the ratio, [tex]\(\frac{2 \text{ moles } C_3H_6}{6 \text{ moles } CO_2} = \frac{1 \text{ mol } C_3H_6}{3 \text{ moles } CO_2}\)[/tex].
- Therefore, [tex]\(\frac{1 \text{ mol } C_3H_6}{2 \text{ moles } CO_2}\)[/tex] does not match this ratio.
2. Option 2: [tex]\(\frac{6 \text{ mol } H_2O}{9 \text{ mol } O_2}\)[/tex]
- According to the balanced equation, 9 moles of [tex]\(O_2\)[/tex] react to produce 6 moles of [tex]\(H_2O\)[/tex].
- The ratio [tex]\(\frac{6 \text{ mol } H_2O}{9 \text{ mol } O_2}\)[/tex] correctly reflects the stoichiometry in the given balanced equation.
- This ratio is valid.
3. Option 3: [tex]\(\frac{2 \text{ mol } C_3H_6}{6 \text{ mol } O_2}\)[/tex]
- According to the balanced equation, 2 moles of [tex]\(C_3H_6\)[/tex] react with 9 moles of [tex]\(O_2\)[/tex].
- Simplifying the ratio, [tex]\(\frac{2 \text{ moles } C_3H_6}{9 \text{ moles } O_2}\)[/tex].
- Therefore, [tex]\(\frac{2 \text{ moles } C_3H_6}{6 \text{ moles } O_2}\)[/tex] does not match this ratio.
4. Option 4: [tex]\(\frac{3 \text{ mol } H_2O}{2 \text{ mol } CO_2}\)[/tex]
- According to the balanced equation, 6 moles of [tex]\(CO_2\)[/tex] are produced alongside 6 moles of [tex]\(H_2O\)[/tex].
- Simplifying the ratio, [tex]\(\frac{6 \text{ moles } H_2O}{6 \text{ moles } CO_2} = \frac{1 \text{ mol } H_2O}{1 \text{ mol } CO_2}\)[/tex].
- Therefore, [tex]\(\frac{3 \text{ moles } H_2O}{2 \text{ moles } CO_2}\)[/tex] does not match this ratio.
Among the given options, the valid mole ratio from the balanced equation is:
[tex]\[ \boxed{\frac{6 \text{ mol } H_2O}{9 \text{ mol } O_2}} \][/tex]
