Answer :
To determine the correct balanced hydration equation for the dissociation of sodium sulfate [tex]\((\text{Na}_2\text{SO}_4)\)[/tex] in water, we need to analyze the given equations and compare them to the typical dissociation behavior of this compound in aqueous solution.
### Equation 1:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} \text{Na}^+(aq) + 2 \text{SO}_4^{2-}(aq) \][/tex]
- Upon examining this equation, we see that it suggests [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociates into one [tex]\(\text{Na}^+\)[/tex] ion and two [tex]\(\text{SO}_4^{2-}\)[/tex] ions.
- However, this is incorrect because [tex]\(\text{Na}_2\text{SO}_4\)[/tex] should produce two [tex]\(\text{Na}^+\)[/tex] ions and one [tex]\(\text{SO}_4^{2-}\)[/tex] ion.
### Equation 2:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} 2 \text{Na}^{2+}(aq) + \text{S}^{2-}(aq) + \text{O}_4^{2-}(aq) \][/tex]
- This equation suggests [tex]\( \text{Na}_2\text{SO}_4 \)[/tex] dissociates into ions with unusual oxidation states: two [tex]\(\text{Na}^{2+}\)[/tex] ions (instead of [tex]\(\text{Na}^+\)[/tex] ions), one [tex]\(\text{S}^{2-}\)[/tex] ion, and one [tex]\(\text{O}_4^{2-}\)[/tex] ion.
- These species are not typical products of [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociation and are chemically unrealistic.
### Equation 3:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} \text{Na}_2^{2+}(aq) + \text{SO}_4^{2-}(aq) \][/tex]
- This equation proposes that [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociates into a [tex]\(\text{Na}_2^{2+}\)[/tex] ion and a [tex]\(\text{SO}_4^{2-}\)[/tex] ion.
- A [tex]\(\text{Na}_2^{2+}\)[/tex] ion is not a recognized or stable species in aqueous solution.
### Equation 4:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} 2 \text{Na}^+(aq) + \text{SO}_4^{2-}(aq) \][/tex]
- This equation correctly indicates that [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociates into two [tex]\(\text{Na}^+\)[/tex] ions and one [tex]\(\text{SO}_4^{2-}\)[/tex] ion.
- This is consistent with known chemical behavior and balances both mass and charge.
Thus, the correct balanced hydration equation for [tex]\(\text{Na}_2\text{SO}_4\)[/tex] in water is:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} 2 \text{Na}^+(aq) + \text{SO}_4^{2-}(aq) \][/tex]
Therefore, the correct equation is given by option 4.
### Equation 1:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} \text{Na}^+(aq) + 2 \text{SO}_4^{2-}(aq) \][/tex]
- Upon examining this equation, we see that it suggests [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociates into one [tex]\(\text{Na}^+\)[/tex] ion and two [tex]\(\text{SO}_4^{2-}\)[/tex] ions.
- However, this is incorrect because [tex]\(\text{Na}_2\text{SO}_4\)[/tex] should produce two [tex]\(\text{Na}^+\)[/tex] ions and one [tex]\(\text{SO}_4^{2-}\)[/tex] ion.
### Equation 2:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} 2 \text{Na}^{2+}(aq) + \text{S}^{2-}(aq) + \text{O}_4^{2-}(aq) \][/tex]
- This equation suggests [tex]\( \text{Na}_2\text{SO}_4 \)[/tex] dissociates into ions with unusual oxidation states: two [tex]\(\text{Na}^{2+}\)[/tex] ions (instead of [tex]\(\text{Na}^+\)[/tex] ions), one [tex]\(\text{S}^{2-}\)[/tex] ion, and one [tex]\(\text{O}_4^{2-}\)[/tex] ion.
- These species are not typical products of [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociation and are chemically unrealistic.
### Equation 3:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} \text{Na}_2^{2+}(aq) + \text{SO}_4^{2-}(aq) \][/tex]
- This equation proposes that [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociates into a [tex]\(\text{Na}_2^{2+}\)[/tex] ion and a [tex]\(\text{SO}_4^{2-}\)[/tex] ion.
- A [tex]\(\text{Na}_2^{2+}\)[/tex] ion is not a recognized or stable species in aqueous solution.
### Equation 4:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} 2 \text{Na}^+(aq) + \text{SO}_4^{2-}(aq) \][/tex]
- This equation correctly indicates that [tex]\(\text{Na}_2\text{SO}_4\)[/tex] dissociates into two [tex]\(\text{Na}^+\)[/tex] ions and one [tex]\(\text{SO}_4^{2-}\)[/tex] ion.
- This is consistent with known chemical behavior and balances both mass and charge.
Thus, the correct balanced hydration equation for [tex]\(\text{Na}_2\text{SO}_4\)[/tex] in water is:
[tex]\[ \text{Na}_2\text{SO}_4(s) \xrightarrow{H_2O} 2 \text{Na}^+(aq) + \text{SO}_4^{2-}(aq) \][/tex]
Therefore, the correct equation is given by option 4.
