To determine the acid [tex]\(X\)[/tex] and the base [tex]\(Y\)[/tex] which produce [tex]\(Mg_3(PO_4)_2\)[/tex], let's analyze each pair of reactants given in the options:
1. [tex]\(X = H_3PO_3\)[/tex], [tex]\(Y = Mg(OH)_2\)[/tex]
2. [tex]\(X = H_3PO_4\)[/tex], [tex]\(Y = Mg(OH)_2\)[/tex]
3. [tex]\(X = H_3PO_4\)[/tex], [tex]\(Y = Ca(OH)_2\)[/tex]
4. [tex]\(X = H_3PO_3\)[/tex], [tex]\(Y = Ca(OH)_2\)[/tex]
Our goal is to identify the correct pair that produces [tex]\(Mg_3(PO_4)_2\)[/tex], magnesium phosphate.
### Step-by-step Analysis:
#### Option 1:
[tex]\(X = H_3PO_3\)[/tex], [tex]\(Y = Mg(OH)_2\)[/tex]
- [tex]\(H_3PO_3\)[/tex] is phosphorous acid.
- Basic form of phosphorous acid does not typically lead to [tex]\(Mg_3(PO_4)_2\)[/tex].
- Phosphorous acid primarily leads to phosphites, not phosphates.
Therefore, this combination is less likely to correctly produce [tex]\(Mg_3(PO_4)_2\)[/tex].
#### Option 2:
[tex]\(X = H_3PO_4\)[/tex], [tex]\(Y = Mg(OH)_2\)[/tex]
- [tex]\(H_3PO_4\)[/tex] is phosphoric acid, which is commonly used to create phosphates.
- [tex]\(Mg(OH)_2\)[/tex] is magnesium hydroxide, a strong base.
The reaction between phosphoric acid and magnesium hydroxide can form magnesium phosphate:
[tex]\[ 2H_3PO_4 + 3Mg(OH)_2 \rightarrow Mg_3(PO_4)_2 + 6H_2O \][/tex]
This reaction fits perfectly, producing magnesium phosphate [tex]\( ( Mg_3(PO_4)_2) \)[/tex].
#### Option 3:
[tex]\(X = H_3PO_4\)[/tex], [tex]\(Y = Ca(OH)_2\)[/tex]
- [tex]\(H_3PO_4\)[/tex] is phosphoric acid.
- [tex]\(Ca(OH)_2\)[/tex] is calcium hydroxide, another strong base.
The reaction would form calcium phosphate instead of magnesium phosphate:
[tex]\[ 2H_3PO_4 + 3Ca(OH)_2 \rightarrow Ca_3(PO_4)_2 + 6H_2O \][/tex]
Since the product in this case is calcium phosphate [tex]\((Ca_3(PO_4)_2)\)[/tex], not magnesium phosphate [tex]\((Mg_3(PO_4)_2)\)[/tex], this option is incorrect.
#### Option 4:
[tex]\(X = H_3PO_3\)[/tex], [tex]\(Y = Ca(OH)_2\)[/tex]
- [tex]\(H_3PO_3\)[/tex] is phosphorous acid.
- [tex]\(Ca(OH)_2\)[/tex] is calcium hydroxide.
This reaction would also not lead to the correct product. It would form calcium phosphite, and we need to form a phosphate.
### Conclusion:
- Only the second option:
[tex]\[ X = H_3PO_4, Y = Mg(OH)_2 \][/tex]
leads to the formation of [tex]\(Mg_3(PO_4)_2\)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{X=H_3PO_4; Y=Mg(OH)_2} \][/tex]
