A 3.45 g sample of hydrated magnesium sulfate (MgSO4.xH2O) is dissolved in 250 cm3 of solution. Calculate the value of x.

We are given the mass of hydrated magnesium sulfate, $\text{MgSO}_4 \cdot x\text{H}_2\text{O}$, as $3.45 \text{ g}$. This mass is dissolved in $250 \text{ cm}^3$ of solution. The goal is to calculate the value of $x$, which represents the number of moles of water of crystallization.

To determine $x$, we would need to find the ratio of moles of water to moles of anhydrous $\text{MgSO}_4$. This requires knowing the molar masses of the components.

• Molar mass of $\text{Mg}$ = $24.305 \text{ g/mol}$
• Molar mass of $\text{S}$ = $32.06 \text{ g/mol}$
• Molar mass of $\text{O}$ = $16.00 \text{ g/mol}$
• Molar mass of $\text{H}$ = $1.008 \text{ g/mol}$

Molar mass of $\text{MgSO}_4$:

Molar mass of $\text{H}_2\text{O}$:

The molar mass of $\text{MgSO}_4 \cdot x\text{H}_2\text{O}$ would be $120.365 + x(18.016) \text{ g/mol}$.

To calculate $x$, we need to determine the mass of anhydrous $\text{MgSO}_4$ and the mass of water present in the $3.45 \text{ g}$ sample. This information is typically obtained by heating the hydrated salt to remove the water of crystallization, or by knowing the concentration of the $\text{MgSO}_4$ in the solution.

The given information (mass of hydrated salt and volume of solution) is insufficient to calculate the value of $x$. Additional data, such as the concentration of the $\text{MgSO}_4$ solution or the mass of anhydrous $\text{MgSO}_4$ obtained from the $3.45 \text{ g}$ sample, is required.