Certainly! To determine the amount of water produced when 4.0 moles of [tex]\( O_2 \)[/tex] are completely reacted, we can follow a step-by-step approach.
1. Identify the balanced chemical equation:
The balanced chemical equation is:
[tex]\[
2 C_3H_6(g) + 9 O_2(g) \rightarrow 6 CO_2(g) + 6 H_2O(g)
\][/tex]
2. Determine the mole ratio from the balanced equation:
From the balanced equation, 9 moles of [tex]\( O_2 \)[/tex] react to produce 6 moles of [tex]\( H_2O \)[/tex]. This means the ratio of moles of [tex]\( H_2O \)[/tex] produced to moles of [tex]\( O_2 \)[/tex] used is:
[tex]\[
\frac{6 \text{ moles } H_2O}{9 \text{ moles } O_2} = \frac{6}{9} = \frac{2}{3}
\][/tex]
3. Calculate the moles of [tex]\( H_2O \)[/tex] produced:
If we start with 4.0 moles of [tex]\( O_2 \)[/tex], we can use the ratio to find the moles of [tex]\( H_2O \)[/tex] produced:
[tex]\[
\text{Moles of } H_2O = 4.0 \text{ moles } O_2 \times \frac{2}{3}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Moles of } H_2O = 4.0 \times \frac{2}{3} = \frac{8}{3} = 2.6666666666666665
\][/tex]
Thus, the amount of water produced is approximately [tex]\( 2.7 \)[/tex] moles when rounded to one decimal place.
Considering the options provided:
- 4.8 mol
- 1.5 mol
- 1.9 mol
- 2.7 mol
The correct answer is:
[tex]\[
2.7 \text{ mol}
\][/tex]
