Question

A solid consists of a mixture of$NaN{O}_3$ and $Mg{\left(N{O}_3\right)}_2$. When 6.50 g of the solid is dissolved in 50.0 g of water, the freezing point of the solution is lowered by $5.23°C$. What is the composition by mass of the solid mixture?

Short answer

Mass of$NaN{O}_3$is $42.5\%$

Step-by-step solution

Step 1:

$NaN{O}_3$in solution dissociates into one $N{A}^{+}$ ion and one $N{O_3}^{-}$ion, while $Mg{\left(N{O}_3\right)}_2$ dissociates into one $M{g}^{2+}$ ion and two $N{O_3}^{-}$ ion.

Write the equation.

$$\begin{gathered} 2\times n\left(NaN{O}_3\right)+3\times n\left(Mg{\left(N{O}_3\right)}_2\right)=i\times nTOT=0.1406 \\ 2\times \frac{x}{84.995}+3\times \frac{6.50-x}{148.3}=2.76 \end{gathered}$$

Step 2:

Calculate mass.

Mass=$\frac{2.76g}{6.50g}=42.5\%$