Question

A solution of magnesium sulfate is 0.0500 molal. Calculate the mass percentage of MgSO4 in this solution

Answer 1

The molar concentration of a solution is defined as the number of the moles divided by the volume of the solution:

$c = \frac{n (MgSO_4)}{V(solution)}$ ,

while the mass percentage is the ratio of the mass of the solute to the mass of the solution, times 100%:

$w = \frac{m(MgSO_4)}{m(solution)}\cdot100\%$ .

The mass of magnesium sulfate is its number of the moles times its molar mass, 120.37 g/mol:

$m = n\cdot M$ .

Also, the volume of the solution and the mass of the solution are related through the density:

$m(solution) = d(solution)\cdot V(solution)$ .

Using these relations, the link between the molar concentration and the mass percentage can be established:

$w = \frac{c\cdot V(solution)\cdot M(MgSO_4)}{m(soltion)}\cdot 100\%$

$w = \frac{c \cdot M(MgSO_4)}{d(solution)}\cdot 100\%$ .

Assuming the density of the solution equal to 1 g/mL, or 1000 g/L, the mass percentage of MgSO₄ is:

$w = \frac{0.0500\cdot 120.37}{1000}\cdot 100\% = 0.602\%$

Answer: the mass percentage of MgSO₄ in this solution is 0.602%.