A 100.0-mL aqueous sodium chloride solution is 13.5% NaCl by mass and has a density of 1.12 g/mL. What would you add (solute or solvent) and what mass of it to make the boiling point of the solution 104.4 °C? (Use i = 1.8 for NaCl.)

Video transcript

Hi everyone here we have a question telling us magnesium chloride is dissolved in 150.0 mL of water to make a 12.5% magnesium chloride solution by mass. The solution has a density of 1.105 g per centimeter cube. And our goal here is to calculate the mass of solute or solvent that must be added in order to make the boiling point of the solution 108.2 degrees Celsius. The van Hoff factor of magnesium chloride is 2.70. So our change and boiling point equals our boiling point of our solution minus the boiling point of our solvent. The change in boiling point equals the van halt factor times are boiling point constant times. Our morality. The boiling point constant equal 0.512 degrees Celsius divided by morality. And our morality equals moles of solute over kilograms of solvent At boiling point. We know that we are at 108.2°C. So our change in boiling point equals 108.2°C -100°C Equals 8.2°C M equals the change in boiling point, divided by our van Hoff factor times are boiling point constant. So a morality Equals 8. degrees Celsius Times 2. Times 0.512°C Divided by Morality, Which equals 5. 317 Morality Or 5. moles per kilogram. Yeah. and 1.105g per cm cubed Equals 1. grams per mil leader. The mass of our solution Equals 150 0. mL Times 1.105 grams per mil leader Equals 165. g Solution. Our mass of magnesium chloride Equals 165. g solution times 12. grams of magnesium chloride over 100 g of solution. So our grams of solution are canceling out here and that equals 20. g of magnesium chloride. Our mass of magnesium chloride Equals 24. grams per mole Plus 35.45 g per mole times two equals 95. g per mole. Our moles magnesium chloride equals .71875 g Times 95.205g over one mole Equals 0. moles of magnesium chloride. Our kilograms of water equals our moles of solute, divided by our morality. So are kilograms of water Equals 0. moles. A magnesium chloride Divided by 5.9 moles per kilogram That equals 0.366, nine Times 10 to the 3rd g over one kg Equals 36.69. And for our original solution, our morality of our solution is going to equal the morality of sodium chloride plus the morality of water. So the morality of our water Equals 165.75g of our solution -20. g of magnesium chloride Equals 145.03125g of water At boiling point at 108.2°C 20. grams of magnesium chloride Per 36. grams of water, .71875g of magnesium chloride, Divided by 36. grams of water. In our final solution equals x grams. A magnesium chloride Divided by 145.03125g of water. And our final solution x grams of magnesium chloride Equals 81.8988 magnesium chloride. So the magnesium chloride to be added is 81. -20.71875, Which equals 61.18 which we're going to round 261.2 g. And that is our final answer. Thank you for watching. Bye.