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How many moles of [tex]\(O_2\)[/tex] are required to produce 10 moles of [tex]\(H_2O\)[/tex]?

Given the reaction:
[tex]\[C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O\][/tex]

A. 10
B. 20
C. 25
D. 30

Sagot :

To determine how many moles of [tex]\( O_2 \)[/tex] are required to produce 10 moles of [tex]\( H_2O \)[/tex], we need to refer to the balanced chemical equation given:

[tex]\[ C_3H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O \][/tex]

From this equation, it is clear that:

- 5 moles of [tex]\( O_2 \)[/tex] produce 4 moles of [tex]\( H_2O \)[/tex].

We need to find how many moles of [tex]\( O_2 \)[/tex] are needed to produce 10 moles of [tex]\( H_2O \)[/tex]. We can set up a proportion to solve for the unknown number of moles of [tex]\( O_2 \)[/tex]:

[tex]\[ \frac{5 \text{ moles of } O_2}{4 \text{ moles of } H_2O} = \frac{x \text{ moles of } O_2}{10 \text{ moles of } H_2O} \][/tex]

Cross-multiplying to solve for [tex]\( x \)[/tex]:

[tex]\[ 4x = 5 \times 10 \][/tex]

So,

[tex]\[ 4x = 50 \][/tex]

Dividing both sides by 4:

[tex]\[ x = \frac{50}{4} = 12.5 \][/tex]

Therefore, 12.5 moles of [tex]\( O_2 \)[/tex] are required to produce 10 moles of [tex]\( H_2O \)[/tex].

The correct answer is:

[tex]\[ \boxed{12.5} \][/tex]