To determine the number of moles of aluminum acetate in the sample, we need to understand the relationship between the hydrogen atoms and the molecular structure of aluminum acetate, [tex]$Al \left( C _2 H _3 O _2 \right)_3$[/tex].
1. Identify the number of hydrogen atoms per molecule of aluminum acetate:
- The chemical formula for aluminum acetate is [tex]$Al \left( C _2 H _3 O _2 \right)_3$[/tex].
- Each [tex]$C _2 H _3 O _2$[/tex] (acetate) group contains 3 hydrogen atoms.
- Since there are three acetate groups in each molecule of aluminum acetate, we calculate the total number of hydrogen atoms per molecule of aluminum acetate:
[tex]\[
3 \text{ acetate groups} \times 3 \text{ hydrogen atoms per acetate group} = 9 \text{ hydrogen atoms}
\][/tex]
2. Calculate the number of moles of aluminum acetate:
- We know there are 2.5 moles of hydrogen atoms in the sample.
- From the structure of aluminum acetate determined above, each mole of aluminum acetate contains 9 moles of hydrogen atoms.
- To find the number of moles of aluminum acetate, we divide the number of moles of hydrogen by the number of moles of hydrogen atoms per mole of aluminum acetate:
[tex]\[
\frac{2.5 \text{ moles of hydrogen}}{9 \text{ hydrogen atoms per molecule of aluminum acetate}} \approx 0.277777778 \text{ moles of aluminum acetate}
\][/tex]
Therefore, the number of moles of aluminum acetate in the sample is approximately:
[tex]\[
0.277777778 \text{ moles of } Al \left( C _2 H _3 O _2 \right)_3
\][/tex]
