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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]

[tex]\[ \begin{array}{l}
\begin{array}{l|l}
24 \text{ moles } C_2H_6 & 7 \text{ moles } O_2 \\
\hline
& 2 \text{ moles } C_2H_6
\end{array} = \frac{168}{2} \\
= 84 \text{ mol } O_2 \\
\end{array} \][/tex]



Answer :

GinnyAnswer
To determine how many moles of [tex]\( O_2 \)[/tex] are needed to react with 24 moles of [tex]\( C_2H_6 \)[/tex], we can use the stoichiometric relationship provided by the balanced chemical equation:

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

Step-by-Step Solution:

1. Identify the given information:
- We have [tex]\( 24 \)[/tex] moles of [tex]\( C_2H_6 \)[/tex].

2. Determine the mole ratio from the balanced equation:
- According to the equation, [tex]\( 2 \)[/tex] moles of [tex]\( C_2H_6 \)[/tex] react with [tex]\( 7 \)[/tex] moles of [tex]\( O_2 \)[/tex].

3. Set up the proportion using the given and required moles:

[tex]\[ \frac{24 \text{ moles of } C_2H_6}{X \text{ moles of } O_2} = \frac{2 \text{ moles of } C_2H_6}{7 \text{ moles of } O_2} \][/tex]

4. Solve for [tex]\( X \)[/tex] which represents the moles of [tex]\( O_2 \)[/tex] needed:

[tex]\[ \frac{24}{X} = \frac{2}{7} \][/tex]

To solve for [tex]\( X \)[/tex], cross-multiply:

[tex]\[ 24 \times 7 = 2 \times X \][/tex]

[tex]\[ 168 = 2X \][/tex]

Now, divide both sides by 2:

[tex]\[ X = \frac{168}{2} \][/tex]

[tex]\[ X = 84 \][/tex]

Thus, the moles of [tex]\( O_2 \)[/tex] needed to react with 24 moles of [tex]\( C_2H_6 \)[/tex] are [tex]\( 84 \)[/tex] moles.

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