To determine which combination of acid (X) and base (Y) reacts to produce [tex]\( \text{Mg}_3(\text{PO}_4)_2 \)[/tex], we need to identify the correct acid and base from the given options.
Let's consider each option step-by-step:
1. Option 1: [tex]\( X = \text{H}_3\text{PO}_3 \)[/tex]; [tex]\( Y = \text{Mg(OH)}_2 \)[/tex]
Reaction:
[tex]\[
\text{H}_3\text{PO}_3 + \text{Mg(OH)}_2 \rightarrow \text{Mg}_3(\text{PO}_4)_2
\][/tex]
This reaction does not balance properly because [tex]\(\text{H}_3\text{PO}_3\)[/tex] (Phosphorous Acid) has a different chemical formula and structure compared to [tex]\(\text{H}_3\text{PO}_4\)[/tex] (Phosphoric Acid).
2. Option 2: [tex]\( X = \text{H}_3\text{PO}_4 \)[/tex]; [tex]\( Y = \text{Mg(OH)}_2 \)[/tex]
Reaction:
[tex]\[
2 \text{H}_3\text{PO}_4 + 3 \text{Mg(OH)}_2 \rightarrow \text{Mg}_3(\text{PO}_4)_2 + 6 \text{H}_2\text{O}
\][/tex]
This reaction balances correctly. The reaction between phosphoric acid [tex]\((\text{H}_3\text{PO}_4)\)[/tex] and magnesium hydroxide [tex]\((\text{Mg(OH)}_2)\)[/tex] forms magnesium phosphate [tex]\((\text{Mg}_3(\text{PO}_4)_2)\)[/tex] and water [tex]\((\text{H}_2\text{O})\)[/tex].
3. Option 3: [tex]\( X = \text{H}_3\text{PO}_4 \)[/tex]; [tex]\( Y = \text{Ca(OH)}_2 \)[/tex]
Reaction:
[tex]\[
2 \text{H}_3\text{PO}_4 + 3 \text{Ca(OH)}_2 \rightarrow \text{Ca}_3(\text{PO}_4)_2 + 6 \text{H}_2\text{O}
\][/tex]
This reaction forms calcium phosphate [tex]\((\text{Ca}_3(\text{PO}_4)_2)\)[/tex], not magnesium phosphate [tex]\((\text{Mg}_3(\text{PO}_4)_2)\)[/tex].
4. Option 4: [tex]\( X = \text{H}_3\text{PO}_3 \)[/tex]; [tex]\( Y = \text{Ca(OH)}_2 \)[/tex]
Reaction:
[tex]\[
\text{H}_3\text{PO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca}_3(\text{PO}_4)_2
\][/tex]
This reaction also does not form magnesium phosphate [tex]\((\text{Mg}_3(\text{PO}_4)_2)\)[/tex].
After evaluating all the options, we see that only Option 2 correctly balances the chemical equation and matches the required product. Thus, the correct answer is:
[tex]\[
X = \text{H}_3\text{PO}_4 ; Y = \text{Mg(OH)}_2
\][/tex]
Therefore, the acid [tex]\(X\)[/tex] and base [tex]\(Y\)[/tex] that react to produce [tex]\(\text{Mg}_3(\text{PO}_4)_2\)[/tex] are:
[tex]\[
\boxed{2}
\][/tex]
