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How many moles of [tex]$O_2$[/tex] are needed to react with 24 moles of [tex]$C_2H_6$[/tex]?

[tex]2C_2H_6 + 7O_2 \rightarrow 4CO_2 + 6H_2O[/tex]

Given:
[tex]\[ \begin{array}{l}
\begin{array}{c|c}
24 \text{ moles } C_2H_6 & \text{? moles } O_2 \\
\hline
2 \text{ moles } C_2H_6 & 7 \text{ moles } O_2 \\
\end{array}
\end{array} \][/tex]

Calculate:
[tex]\[ \frac{24 \text{ moles } C_2H_6 \times 7 \text{ moles } O_2}{2 \text{ moles } C_2H_6} = 84 \text{ moles } O_2 \][/tex]

So, 84 moles of [tex]$O_2$[/tex] are needed.


Sagot :

To determine how many moles of [tex]\( O_2 \)[/tex] are needed to react with 24 moles of [tex]\( C_2H_6 \)[/tex], we will use stoichiometry based on the provided balanced chemical equation:
[tex]\[ 2 C_2H_6 + 7 O_2 \rightarrow 4 CO_2 + 6 H_2O \][/tex]

1. Identify the stoichiometric ratio:
From the balanced equation, we see that 2 moles of [tex]\( C_2H_6 \)[/tex] react with 7 moles of [tex]\( O_2 \)[/tex].

2. Set up the proportion:
If 2 moles of [tex]\( C_2H_6 \)[/tex] require 7 moles of [tex]\( O_2 \)[/tex], then 24 moles of [tex]\( C_2H_6 \)[/tex] would need:
[tex]\[ \frac{7 \text{ moles of } O_2}{2 \text{ moles of } C_2H_6} \][/tex]
This represents the stoichiometric ratio.

3. Calculate the moles of [tex]\( O_2 \)[/tex] required for 24 moles of [tex]\( C_2H_6 \)[/tex]:
Using the proportion, we get:
[tex]\[ \text{Moles of } O_2 = \left( \frac{7 \text{ moles of } O_2}{2 \text{ moles of } C_2H_6} \right) \times 24 \text{ moles of } C_2H_6 \][/tex]

Solving this:
[tex]\[ \text{Moles of } O_2 = \left( \frac{7}{2} \right) \times 24 = 3.5 \times 24 = 84 \][/tex]

Therefore, 84.0 moles of [tex]\( O_2 \)[/tex] are needed to react with 24 moles of [tex]\( C_2H_6 \)[/tex].