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 ºC. What mass of CaCl₂ was in the original mixture? Kb for water is 0.512 K. kg . mol⁻¹.

Question

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 ºC.  What mass of CaCl₂ was in the original mixture? Kb for water is 0.512 K. kg . mol⁻¹.

Quizplus · Accepted Answer

The change in boiling point is given by:ΔTb = Kb * molalitywhere Kb is the boiling point elevation constant for water (0.512 K kg mol-1) and molality is the number of moles of solute per kilogram of solvent.We can calculate the molality of the solution by dividing the number of moles of solute by the mass of the solvent in kilograms:molality = moles of solute / mass of solvent (kg)We know that the mass of the solvent is 1.00 kg, and we can calculate the number of moles of NaCl by dividing the mass of NaCl by its molar mass (58.44 g mol-1):moles of NaCl = 10.0 g / 58.44 g mol-1 = 0.171 molWe can also calculate the change in boiling point by subtracting the boiling point of pure water (100.00 ºC) from the boiling point of the solution (100.25 ºC):ΔTb = 100.25 ºC - 100.00 ºC = 0.25 ºCNow we can substitute these values into the equation for ΔTb and solve for the molality of the solution:0.25 ºC = 0.512 K kg mol-1 * molalitymolality = 0.25 ºC / 0.512 K kg mol-1 = 0.488 mol kg-1Finally, we can calculate the number of moles of CaCl2 in the solution by subtracting the number of moles of NaCl from the total molality:moles of CaCl2 = molality - moles of NaClmoles of CaCl2 = 0.488 mol kg-1 - 0.171 mol = 0.317 molNow we can calculate the mass of CaCl2 in the original mixture by multiplying the number of moles of CaCl2 by its molar mass (110.98 g mol-1):mass of CaCl2 = 0.317 mol * 110.98 g mol-1 = 35.2 gTherefore, the mass of CaCl2 in the original mixture was 35.2 g.

A Mixture of Solid NaCl and CaCl₂ Contains 10