Step-by-step explanation:
To calculate the molarity and molality of the student's solution, we'll follow these steps:
Step 1: Calculate the moles of styrene (C8H8).
Step 2: Calculate the volume of the solvent in liters.
Step 3: Calculate the molarity (M).
Step 4: Calculate the molality (m).
Step 1: Calculate the moles of styrene (C8H8):
Molar mass of styrene (C8H8):
Carbon (C) has a molar mass of approximately 12.01 g/mol.
Hydrogen (H) has a molar mass of approximately 1.01 g/mol.
Molar mass of C8H8 = (8 × 12.01 g/mol) + (8 × 1.01 g/mol) = 96.08 g/mol
Now, calculate moles:
Moles of styrene = Mass (g) / Molar mass (g/mol)
Moles of styrene = 8.1 g / 96.08 g/mol ≈ 0.0843 mol
Step 2: Calculate the volume of the solvent in liters:
Given density of the solvent = 0.90 g/mL
Volume of the solvent = 250 mL = 0.25 L (since 1 mL = 0.001 L)
Step 3: Calculate the molarity (M):
Molarity (M) = Moles of solute / Volume of solution (in liters)
Molarity (M) = 0.0843 mol / 0.25 L ≈ 0.337 M
Step 4: Calculate the molality (m):
Molality (m) = Moles of solute / Mass of solvent (in kg)
Mass of solvent = Volume of solvent (in L) × Density of solvent (in g/mL) / 1000 (to convert g to kg)
Mass of solvent = 0.25 L × 0.90 g/mL / 1000 = 0.225 kg
Molality (m) = 0.0843 mol / 0.225 kg ≈ 0.374 mol/kg
So, the molarity of the solution is approximately 0.337 M, and the molality of the solution is approximately 0.374 mol/kg.