To solve this question, let's analyze each of the given options in the context of solubility:
Magnesium sulfate ([tex]\(MgSO_4\)[/tex]) is an ionic compound, and ionic compounds typically dissolve well in polar solvents due to the strong interaction between the ions and the dipole moments of the polar solvent molecules.
### Option A: A higher polarity than [tex]\(C_6H_{14}\)[/tex].
Water ([tex]\(H_2O\)[/tex]) is a highly polar molecule with a strong dipole moment due to the significant difference in electronegativity between hydrogen and oxygen atoms, and the resulting asymmetric shape of the molecule. This polarity allows water to interact effectively with the ions in [tex]\(MgSO_4\)[/tex] through ion-dipole interactions, leading to its high solubility in water. On the other hand, hexane ([tex]\(C_6H_{14}\)[/tex]) is a nonpolar molecule composed entirely of carbon and hydrogen atoms with very similar electronegativities, which means hexane cannot provide the necessary interactions to dissolve [tex]\(MgSO_4\)[/tex]. Therefore, the correct reason why [tex]\(MgSO_4\)[/tex] is soluble in water but not in hexane is the polarity difference.
### Option B: A higher heat capacity than [tex]\(C_6H_{14}\)[/tex].
Heat capacity is a measure of the amount of heat required to raise the temperature of a substance. While water does have a higher specific heat capacity compared to hexane, this property is not directly related to the solubility of [tex]\(MgSO_4\)[/tex]. Solubility primarily depends on the nature of the solute and the solvent, especially their polarity.
### Option C: A higher viscosity than [tex]\(C_6H_{14}\)[/tex].
Viscosity refers to the resistance of a fluid to flow. Although water has a higher viscosity compared to hexane, this property does not explain the solubility of [tex]\(MgSO_4\)[/tex] in water. Viscosity influences the flow properties of liquids rather than their ability to dissolve substances.
### Option D: A higher melting point than [tex]\(C_6H_{14}\)[/tex].
Water's melting point is indeed higher than that of hexane. However, the melting point of a solvent is not a relevant factor in determining the solubility of [tex]\(MgSO_4\)[/tex]. Solubility is influenced by the interactions between solvent molecules and the solute, rather than the temperature at which the solvent changes from solid to liquid.
Based on this analysis, the correct answer is:
A. A higher polarity than [tex]\(C_6H_{14}\)[/tex].
