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Multiply across the bottom of the unit conversion. What is the product of the denominator?

[tex]\[
\begin{array}{c|c}
24 \text{ moles } C_2H_6 & 7 \text{ moles } O_2 \\
\hline
& 2 \text{ moles } C_2H_6
\end{array}
=
\begin{array}{c}
168 \\
\hline
[?]
\end{array}
\][/tex]

What is the product of the denominator?



Answer :

GinnyAnswer
To find the product of the denominator when multiplying across the unit conversion table, we need to handle the denominator's components separately.

Here's a detailed, step-by-step solution for this problem:

Given:
- [tex]\(moles\_ C _2 H _6\_initial = 24\)[/tex]
- [tex]\(moles\_ O _2\_needed = 7\)[/tex]
- [tex]\(moles\_ C _2 H _6\_reacting = 2\)[/tex]

We are dealing with the denominator here, so we specifically focus on multiplying the components in the denominator:

The denominator components are:
- [tex]\(moles\_ O _2\_needed = 7\)[/tex]
- [tex]\(moles\_ C _2 H _6\_reacting = 2\)[/tex]

To find the product of the denominator, multiply these components:

[tex]\[ 7 \text{ moles } O_2 \times 2 \text{ moles } C_2H_6 \][/tex]

Calculating this:

[tex]\[ 7 \times 2 = 14 \][/tex]

Thus, the product of the denominator is [tex]\(\boxed{14}\)[/tex].

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