A mixture of solid NaCl and CaCl₂ contains 10.0 g of NaCl, and an unknown amount of CaCl₂. When the entire mixture is dissolved in 1.00 kg of water, the boiling point changes by 0.25 $\degree$C. What mass of CaCl₂ was in the original mixture? K_b for water is 0.512 K^.kg ^.mol^-1. A) 5.4 g B) 8.1 g C) 35.2 g D) Not enough data to answer the question E) None of the above

Question

Quizplus · Accepted Answer

The change in boiling point is given by the equation:$$\Delta T_b = K_b 	imes m 	imes i$$where:$$\Delta T_b$$ is the change in boiling point$$K_b$$ is the boiling point elevation constant$$m$$ is the molality of the solution$$i$$ is the van't Hoff factorWe know that the change in boiling point is 0.25 °C, the boiling point elevation constant for water is 0.512 K·kg·mol-1, and the mass of NaCl is 10.0 g. We can calculate the molality of the NaCl solution:$$m = \frac{moles \ NaCl}{kg \ H_2O}$$$$moles \ NaCl = \frac{10.0 g}{58.44 g/mol} = 0.171 mol$$$$m = \frac{0.171 mol}{1.00 kg} = 0.171 mol/kg$$We also know that the van't Hoff factor for NaCl is 2, since it dissociates into two ions in water. Therefore, the change in boiling point due to the NaCl is:$$\Delta T_b = K_b 	imes m 	imes i$$$$\Delta T_b = 0.512 K·kg·mol-1 	imes 0.171 mol/kg 	imes 2$$$$\Delta T_b = 0.174 °C$$The remaining change in boiling point must be due to the CaCl2. We can calculate the molality of the CaCl2 solution:$$\Delta T_b = K_b 	imes m 	imes i$$$$0.25 °C - 0.174 °C = 0.512 K·kg·mol-1 	imes m 	imes 3$$$$m = \frac{0.076 °C}{0.512 K·kg·mol-1 	imes 3}$$$$m = 0.049 mol/kg$$We also know that the van't Hoff factor for CaCl2 is 3, since it dissociates into three ions in water. Therefore, the moles of CaCl2 in the solution is:$$moles \ CaCl_2 = m 	imes kg \ H_2O$$$$moles \ CaCl_2 = 0.049 mol/kg 	imes 1.00 kg$$$$moles \ CaCl_2 = 0.049 mol$$Finally, we can calculate the mass of CaCl2 in the original mixture:$$mass \ CaCl_2 = moles \ CaCl_2 	imes molar \ mass \ CaCl_2$$$$mass \ CaCl_2 = 0.049 mol 	imes 110.98 g/mol$$$$mass \ CaCl_2 = 5.4 g$$Therefore, the mass of CaCl2 in the original mixture was 5.4 g.

A Mixture of Solid NaCl and CaCl2 Contains 10 °\degree° C What Mass of CaCl2 Was in the Original Mixture

A Mixture of Solid NaCl and CaCl₂ Contains 10 $\degree$ C What Mass of CaCl₂ Was in the Original Mixture