{"type":"doc","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"{\"type\":\"doc\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1. Calculate the molality, freezing point, and boiling point for a solution made by dissolving 144 g of C6H12O6 in 1000 g of H2O.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Molality, Freezing Point Depression, Boiling Point Elevation)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate molality and use it to determine the freezing point depression and boiling point elevation for a solution of a nonionizing solute in water.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of C6H12O6. First, find its molar mass by adding the atomic masses: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{C}_6\\\\text{H}_{12}\\\\text{O}_6\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use the mass of C6H12O6 (144 g) and the molar mass to find the number of moles: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{\\\\text{mass}}{\\\\text{molar mass}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\") using the number of moles and the mass of water in kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{1.0\\\\ \\\\text{kg of solvent}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Apply the freezing point depression formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\" (with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\" for nonionizing solute).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Apply the boiling point elevation formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\" (again, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\").\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 0.8\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Freezing point} = 0 - (1 \\\\times 1.86 \\\\times 0.8) = -1.49\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Boiling point} = 100 + (1 \\\\times 0.52 \\\\times 0.8) = 100.42\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We calculated the molality, then used the colligative property equations to find the new freezing and boiling points.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2. Calculate the molality, freezing point, and boiling point for a solution made by dissolving 48 g of CH3OH in 200 g of H2O.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Molality, Freezing Point Depression, Boiling Point Elevation)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate molality and use it to determine the freezing and boiling points for a solution of a nonionizing solute in water.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the molar mass of CH3OH (methanol).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of CH3OH using \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{\\\\text{mass}}{\\\\text{molar mass}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Convert the mass of water to kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"200\\\\ \\\\text{g} = 0.200\\\\ \\\\text{kg}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{0.200\\\\ \\\\text{kg}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\" to set up the freezing and boiling point calculations.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 7.5\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Freezing point} = 0 - (1 \\\\times 1.86 \\\\times 7.5) = -13.95\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Boiling point} = 100 + (1 \\\\times 0.52 \\\\times 7.5) = 103.9\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We calculated the molality and then used the colligative property equations to find the new freezing and boiling points.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q3. Calculate the molality, freezing point, and boiling point for a solution made by dissolving 184 g of C2H5OH in 400 g of H2O.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Molality, Freezing Point Depression, Boiling Point Elevation)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate molality and use it to determine the freezing and boiling points for a solution of a nonionizing solute in water.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the molar mass of C2H5OH (ethanol).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of C2H5OH using \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{\\\\text{mass}}{\\\\text{molar mass}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Convert the mass of water to kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"400\\\\ \\\\text{g} = 0.400\\\\ \\\\text{kg}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{0.400\\\\ \\\\text{kg}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\" to set up the freezing and boiling point calculations.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 10\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Freezing point} = 0 - (1 \\\\times 1.86 \\\\times 10) = -18.6\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Boiling point} = 100 + (1 \\\\times 0.52 \\\\times 10) = 105.2\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We calculated the molality and then used the colligative property equations to find the new freezing and boiling points.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q4. Calculate the molality, freezing point, and boiling point for a solution made by dissolving 600 g of C3H7OH in 600 g of H2O.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Molality, Freezing Point Depression, Boiling Point Elevation)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate molality and use it to determine the freezing and boiling points for a solution of a nonionizing solute in water.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the molar mass of C3H7OH (propanol).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of C3H7OH using \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{\\\\text{mass}}{\\\\text{molar mass}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Convert the mass of water to kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"600\\\\ \\\\text{g} = 0.600\\\\ \\\\text{kg}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{0.600\\\\ \\\\text{kg}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\" to set up the freezing and boiling point calculations.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 13.0\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Freezing point} = 0 - (1 \\\\times 1.86 \\\\times 13.0) = -24.18\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Boiling point} = 100 + (1 \\\\times 0.52 \\\\times 13.0) = 106.76\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We calculated the molality and then used the colligative property equations to find the new freezing and boiling points.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q5. Calculate the molality, freezing point, and boiling point for a solution made by dissolving 100 g of C2H6O2 in 200 g of H2O.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Molality, Freezing Point Depression, Boiling Point Elevation)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate molality and use it to determine the freezing and boiling points for a solution of a nonionizing solute in water.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the molar mass of C2H6O2 (ethylene glycol).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of C2H6O2 using \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{\\\\text{mass}}{\\\\text{molar mass}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Convert the mass of water to kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"200\\\\ \\\\text{g} = 0.200\\\\ \\\\text{kg}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{0.200\\\\ \\\\text{kg}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\" to set up the freezing and boiling point calculations.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 8.1\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Freezing point} = 0 - (1 \\\\times 1.86 \\\\times 8.1) = -15.07\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Boiling point} = 100 + (1 \\\\times 0.52 \\\\times 8.1) = 104.21\\\\ ^\\\\circ\\\\text{C}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We calculated the molality and then used the colligative property equations to find the new freezing and boiling points.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q6. Calculate the molality of a water solution if the freezing point is -9.3°C.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Freezing Point Depression)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the freezing point depression equation to determine the molality of a solution given its freezing point.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the change in freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = 0 - (-9.3) = 9.3\\\\ ^\\\\circ\\\\text{C}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rearrange to solve for molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\Delta T_f}{i K_f}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug in the values: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = 9.3\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 5.0\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We used the freezing point depression equation and solved for molality.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q7. Calculate the molality of a water solution if the freezing point is -27.9°C.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Freezing Point Depression)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the freezing point depression equation to determine the molality of a solution given its freezing point.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the change in freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = 0 - (-27.9) = 27.9\\\\ ^\\\\circ\\\\text{C}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rearrange to solve for molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\Delta T_f}{i K_f}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug in the values: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = 27.9\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 15.0\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We used the freezing point depression equation and solved for molality.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q8. Calculate the molality of a water solution if the freezing point is -7.44°C.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Freezing Point Depression)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the freezing point depression equation to determine the molality of a solution given its freezing point.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the change in freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = 0 - (-7.44) = 7.44\\\\ ^\\\\circ\\\\text{C}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rearrange to solve for molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\Delta T_f}{i K_f}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug in the values: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = 7.44\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 4.0\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We used the freezing point depression equation and solved for molality.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q9. Calculate the molality of a water solution if the boiling point is 103.12°C.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Boiling Point Elevation)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the boiling point elevation equation to determine the molality of a solution given its boiling point.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the change in boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = 103.12 - 100 = 3.12\\\\ ^\\\\circ\\\\text{C}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rearrange to solve for molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\Delta T_b}{i K_b}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug in the values: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = 3.12\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 6.0\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We used the boiling point elevation equation and solved for molality.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q10. Calculate the molality of a water solution if the boiling point is 108.32°C.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Boiling Point Elevation)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the boiling point elevation equation to determine the molality of a solution given its boiling point.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the change in boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = 108.32 - 100 = 8.32\\\\ ^\\\\circ\\\\text{C}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rearrange to solve for molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\Delta T_b}{i K_b}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug in the values: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = 8.32\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = 16.0\\\\ \\\\text{mol/kg}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We used the boiling point elevation equation and solved for molality.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q11. What is the boiling point of a solution made by dissolving 31 g of NaCl in 559 g of water? (Assume 100% ionization of NaCl.)\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Boiling Point Elevation, Ionic Solute)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate boiling point elevation for an ionic solute, including the use of the van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\") for ionization.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For NaCl, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 2\"}},{\"type\":\"text\",\"text\":\" (Na\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"^+\"}},{\"type\":\"text\",\"text\":\" and Cl\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"^-\"}},{\"type\":\"text\",\"text\":\")\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the molar mass of NaCl.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of NaCl: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{31}{\\\\text{molar mass of NaCl}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Convert the mass of water to kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"559\\\\ \\\\text{g} = 0.559\\\\ \\\\text{kg}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of NaCl}}{0.559\\\\ \\\\text{kg}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\" with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 2\"}},{\"type\":\"text\",\"text\":\" to set up the boiling point calculation.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Boiling point} = 100 + (2 \\\\times 0.52 \\\\times m)\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We calculated the molality and used the van't Hoff factor for NaCl to find the boiling point elevation.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q12. Calculate the freezing point of a nonionizing antifreeze solution containing 388 g ethylene glycol (C2H6O2) and 409 g of water.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Freezing Point Depression, Nonionizing Solute)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate freezing point depression for a nonionizing solute in water.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing Point Depression: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_f = 1.86\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For nonionizing solutes, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the molar mass of C2H6O2 (ethylene glycol).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of C2H6O2: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{388}{\\\\text{molar mass of C2H6O2}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Convert the mass of water to kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"409\\\\ \\\\text{g} = 0.409\\\\ \\\\text{kg}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of C2H6O2}}{0.409\\\\ \\\\text{kg}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_f = i K_f m\"}},{\"type\":\"text\",\"text\":\" with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 1\"}},{\"type\":\"text\",\"text\":\" to set up the freezing point calculation.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Freezing point: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Freezing point} = 0 - (1 \\\\times 1.86 \\\\times m)\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"We calculated the molality and used the colligative property equation for freezing point depression.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q13. Calculate the boiling point of an ionic solution containing 29.7 g Na2SO4 and 84.4 g water. (Assume 100% ionization.)\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Colligative Properties (Boiling Point Elevation, Ionic Solute)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate boiling point elevation for an ionic solute, including the use of the van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\") for ionization.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boiling Point Elevation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For water: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"K_b = 0.52\\\\ ^\\\\circ\\\\text{C}/m\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Van't Hoff factor (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\"): For Na2SO4, \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 3\"}},{\"type\":\"text\",\"text\":\" (Na\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"^+\"}},{\"type\":\"text\",\"text\":\", Na"},{"type":"inlineMath","attrs":{"latex":"^+"}},{"type":"text","text":", SO\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"_4^{2-}\"}},{\"type\":\"text\",\"text\":\")\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Molality (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\"): \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of solute}}{\\\\text{kg of solvent}}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the molar mass of Na2SO4.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of moles of Na2SO4: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{moles} = \\\\frac{29.7}{\\\\text{molar mass of Na2SO4}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Convert the mass of water to kilograms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"84.4\\\\ \\\\text{g} = 0.0844\\\\ \\\\text{kg}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate molality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m = \\\\frac{\\\\text{moles of Na2SO4}}{0.0844\\\\ \\\\text{kg}}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\Delta T_b = i K_b m\"}},{\"type\":\"text\",\"text\":\" with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i = 3\"}},{\"type\":\"text\",\"text\":\" to set up the boiling point calculation.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\"