Given:
Substitute 5 g for a mass of solute and 295 g for the mass of solvent and calculate the mass of solution.
As we know,
Mass of solution = mass of solute + mass of solvent
Mass of solution = 5 g +295 g = 300 g
Now, we have a mass solution and also we have given the density of the solution so, calculate the volume of the solution as follows:
Density \(=\frac{\text { mass }}{\text { volume }}\)
volume \(=\frac{\text { mass }}{\text { Density }}\)
Substitute 300 g for a mass of solution and 1.5g/cc for the density of the solution and calculate the volume of the solution.
volume of solution \(=\frac{300 \mathrm{~g}}{1.5 \mathrm{~g} / \mathrm{cc}}\)
volume of solution \(=200 \mathrm{cc}\)
Now, to calculate the moles of solute using the volume of solution and molarity of solution convert the volume of solution in L.
\(1 \mathrm{~L}=1000 \mathrm{cc}\)
\(200 \mathrm{cc} \times \frac{1 \mathrm{~L}}{1000 \mathrm{cc}}=0.2 \mathrm{~L}\)
Substitute 0.05 M for molarity and 0.2 L for the volume of solution and calculate the moles of solute as follows:
Molarity \(=\frac{\text { moles of solute }}{\mathrm{L} \text { of solution }}\)
Moles of solute \(=\) Molarity \(\times \mathrm{L}\) of solution
Moles of solute \(=0.05 \mathrm{M} \times 0.2 L=0.01 \mathrm{~mol}\)
Now, we have moles of solute and mass of solute so calculate the molecular weight of solute as follows:
molecular weight \(=\frac{\text { mass }}{\text { mole }}\)
Substitute 0.01 mol for moles of solute and 5 g for a mass of solution and calculate the molecular weight of the unknown solute.
Molecular weight \(=\frac{5 \mathrm{~g}}{0.01 \mathrm{~mol}}\)
Molecular weight \(=\frac{5 \mathrm{~g}}{0.01 \mathrm{~mol}}\)
Molecular weight \(=500 \mathrm{~g} / \mathrm{mol}\)
Thus, the molecular weight of the unknown solute is 500 g/mol.