A saline solution begins to freeze at -1.13 °C.Express the concentration of NaCl in this solution in mass %.K_f for water is 1.86 °C m^-1. A)3.48% B)1.74% C)0.870% D)17.8% E)8.90%

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Quizplus · Accepted Answer

The freezing point depression formula is $\Delta T_f = K_f \cdot m$, where $\Delta T_f$ is the change in freezing point, $K_f$ is the cryoscopic constant (1.86 °C·kg/mol for water), and $m$ is the molality of the solution. Given $\Delta T_f = 1.13$ °C, we solve for $m$: $m = \frac{\Delta T_f}{K_f} = \frac{1.13}{1.86} = 0.608$ mol/kg. The molar mass of NaCl is approximately 58.44 g/mol, so the mass of NaCl in 1 kg of water is $0.608 \times 58.44 = 35.53$ g. The mass percent of NaCl is then $\frac{35.53}{1000 + 35.53} \times 100\% \approx 1.74\%$.

A Saline Solution Begins to Freeze at -1