To determine the mole ratio of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] to [tex]\( \text{H}_2\text{O} \)[/tex] in the given reaction, we first need to balance the chemical equation. Here’s a step-by-step hand-calculation of the balanced equation and the mole ratio:
1. Write the skeleton equation:
[tex]\[
\text{H}_2\text{SO}_4 + \text{Al(OH)}_3 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \text{H}_2\text{O}
\][/tex]
2. Balance the aluminum (Al) atoms first:
There are 2 aluminum atoms on the right side in [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex]. So, we need 2 moles of [tex]\( \text{Al(OH)}_3 \)[/tex] on the left side:
[tex]\[
\text{H}_2\text{SO}_4 + 2 \text{Al(OH)}_3 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \text{H}_2\text{O}
\][/tex]
3. Balance the sulfate (SO[tex]\(_4\)[/tex]) ions:
There are 3 sulfate ions on the right side in [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex]. So, we need 3 moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] on the left side:
[tex]\[
3 \text{H}_2\text{SO}_4 + 2 \text{Al(OH)}_3 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \text{H}_2\text{O}
\][/tex]
4. Balance the hydrogen (H) atoms:
On the left side, we have:
- [tex]\(3 \text{H}_2\text{SO}_4 \)[/tex]: 3 \times 2 = 6 hydrogen atoms
- [tex]\(2 \text{Al(OH)}_3 \)[/tex]: 2 \times 3 = 6 hydrogen atoms
This gives us a total of 6 + 6 = 12 hydrogen atoms on the left side. Each water molecule [tex]\( \text{H}_2\text{O} \)[/tex] on the right side has 2 hydrogen atoms, so we need 6 moles of [tex]\( \text{H}_2\text{O} \)[/tex] to balance:
[tex]\[
3 \text{H}_2\text{SO}_4 + 2 \text{Al(OH)}_3 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 6 \text{H}_2\text{O}
\][/tex]
5. Therefore, the balanced equation is:
[tex]\[
3 \text{H}_2\text{SO}_4 + 2 \text{Al(OH)}_3 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 6 \text{H}_2\text{O}
\][/tex]
6. Determine the mole ratio [tex]\( \text{H}_2\text{SO}_4 : \text{H}_2\text{O} \)[/tex]:
From the balanced equation, for every 3 moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex], there are 6 moles of [tex]\( \text{H}_2\text{O} \)[/tex]. Therefore, the ratio is:
[tex]\[
\frac{3 \text{H}_2\text{SO}_4}{6 \text{H}_2\text{O}} = \frac{1}{2} = 0.5
\][/tex]
7. The mole ratio [tex]\( H_2SO_4:H_2O \)[/tex] corresponds to:
[tex]\[
3:6
\][/tex]
Thus, the correct answer is:
D. [tex]\( 3:6 \)[/tex]
