Final answer:
To calculate the molarity of SMP in the dioxane-water mixture, divide the moles of SMP by the volume of the solution. To calculate the molality, divide the moles of SMP by the mass of the solvent in kg. To calculate the mole fraction, divide the moles of SMP by the sum of the moles of SMP and the moles of the solvent.
Step-by-step explanation:
To calculate the molarity of SMP in the dioxane-water mixture, we need to convert the solubility from g/mL to mol/L. The molar mass of SMP is 317.36 g/mol. First, we calculate the moles of SMP:
Moles of SMP = Mass of SMP / Molar mass of SMP
Moles of SMP = 1.8 g / 317.36 g/mol = 0.00567 mol
Then, we calculate the volume of the solution using the volumes of dioxane (10% = 0.1) and water (90% = 0.9):
Volume of solution = Volume of dioxane + Volume of water = (0.1)(1 mL) + (0.9)(1 mL) = 1 mL
Finally, we calculate the molarity:
Molarity = Moles of SMP / Volume of solution
Molarity = 0.00567 mol / 0.001 L = 5.67 M
Therefore, the correct answer is (a) 0.035 M.
To calculate the molality, we need to convert the mass of SMP to kilograms and calculate the moles of solvent.
Moles of solvent = Volume of water / Molar volume of water
Moles of solvent = (0.9)(1 mL) / 18.015 g/mol = 0.04997 mol
Then, we calculate the molality:
Molality = Moles of SMP / Mass of solvent (in kg)
Molality = 0.00567 mol / 0.04997 kg = 0.1138 m
Therefore, the correct answer is (b) 0.025 m.
To calculate the mole fraction, we need to calculate the moles of SMP and the moles of solvent.
Moles of solvent = Volume of water / Molar volume of water
Moles of solvent = (0.9)(1 mL) / 18.015 g/mol = 0.04997 mol
Then, we calculate the mole fraction:
Mole fraction of SMP = Moles of SMP / (Moles of SMP + Moles of solvent)
Mole fraction of SMP = 0.00567 mol / (0.00567 mol + 0.04997 mol) ≈ 0.102
Therefore, the correct answer is (c) 0.0020.