Sure, let's work through this step-by-step.
We are given the task to multiply across the top of a unit conversion. Let's lay out the given values:
[tex]\[
24 \text{ moles } \text{C}_2\text{H}_6
\][/tex]
and
[tex]\[
7 \text{ moles } \text{O}_2
\][/tex]
To find the product of these values in the numerator, we'll multiply them together:
[tex]\[
24 \text{ moles } \text{C}_2\text{H}_6 \times 7 \text{ moles } \text{O}_2
\][/tex]
Carrying out the multiplication gives us:
[tex]\[
24 \times 7 = 168
\][/tex]
So, the product of the numerator is:
[tex]\[
168 \text{ moles}^{2} (\text{C}_2\text{H}_6 \cdot \text{O}_2)
\][/tex]
Therefore, the final product across the numerator is [tex]\(168\)[/tex].
