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An acid [tex]\((X)\)[/tex] reacts with a base [tex]\((Y)\)[/tex] to produce [tex]\(Mg_3(PO_4)_2\)[/tex]. What are [tex]\(X\)[/tex] and [tex]\(Y\)[/tex]?

A. [tex]\(X = H_3PO_3\)[/tex]; [tex]\(Y = Mg(OH)_2\)[/tex]
B. [tex]\(X = H_3PO_4\)[/tex]; [tex]\(Y = Mg(OH)_2\)[/tex]
C. [tex]\(X = H_3PO_4\)[/tex]; [tex]\(Y = Ca(OH)_2\)[/tex]
D. [tex]\(X = H_3PO_3\)[/tex]; [tex]\(Y = Ca(OH)_2\)[/tex]

Sagot :

GinnyAnswer
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]
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