Questions: If you want to make a 0.5 M solution of MgSO4, how many grams of MgSO4 would you need? Assume the volume of the solution is one liter.

Transcript text: If you want to make a 0.5 M solution of $\mathrm{MgSO}_{4}$, how many grams of $\mathrm{MgSO}_{4}$ would you need? Assume the volume of the solution is one liter.

Solution

Solution Steps

Step 1: Determine the Molar Mass of $\mathrm{MgSO}_{4}$

To find the molar mass of $\mathrm{MgSO}_{4}$, we need to sum the atomic masses of each element in the compound:

Magnesium (Mg): $24.305 \, \text{g/mol}$
Sulfur (S): $32.065 \, \text{g/mol}$
Oxygen (O): $16.00 \, \text{g/mol}$ (since there are four oxygen atoms, multiply by 4)

\[ \text{Molar mass of } \mathrm{MgSO}_{4} = 24.305 + 32.065 + (16.00 \times 4) = 120.365 \, \text{g/mol} \]

Step 2: Calculate the Mass Required for a 0.5 M Solution

A 0.5 M solution means there are 0.5 moles of $\mathrm{MgSO}_{4}$ per liter of solution. To find the mass needed, multiply the number of moles by the molar mass:

\[ \text{Mass} = 0.5 \, \text{mol/L} \times 120.365 \, \text{g/mol} = 60.1825 \, \text{g} \]

Step 3: Round to the Nearest Option

The calculated mass is approximately 60.1825 g, which rounds to 60 g. This matches one of the given multiple-choice options.