Question

Consider an aqueous solution containing sodium chloride that has a density of 1.01 g/mL. Assume that the solution behaves ideally. The freezing point of this solution at 1.00 atm is -1.28 ⁰C. Calculate the percent composition of this solution (by mass).

Short answer

Percent composition of the solution by mass = 8.30%

Step-by-step solution

Step 1:

Percentage composition of the solution by mass = $\frac{\text{massofsolute}}{\text{massofsolution}}\times 100$

Assuming that the solution behaves ideally

$\begin{array}{l}\Delta T_f=m{K}_f\\ \Delta T_f=0^{0}C-(-{1.28}^{0}C)={1.28}^{0}C\left[given\right]\end{array}$

K_f= 0.512 [for water]

molality = $\frac{\Delta T_f}{K_f}=\frac{1.28}{0.512}$ =2.5m

Step 2:

Assuming that the mass of the water is 1kg

Moles of solute = molality mass of solvent = 2.5mol

Mass of solute = moles of solute molar mass of solute

Molar mass of NaCl = 36.5g

Mass of solute = 36.5 2.5 = 90.625g

Mass of the solution = mass of solute + mass of solvent = (90.625 + 1000) g

= 1090.625g

Percentage composition of the solution by mass = $\frac{90.625}{1090.625}\times 100=8.30\text{\%}$