Question

when 4.74 g of a nonelectrolyte solute is dissolved in water to make 155 ml of solution at 25 °c, the solution exerts an osmotic pressure of 967 torr.
what is the molar concentration of the solution?
concentration: ______ m
how many moles of solute are in the solution?
moles of solute: ______ mol
what is the molar mass of the solute?
molar mass: ______ g/mol

Explanation:

Step1: Convert units to SI standards

Osmotic pressure: $967\ \text{torr} = \frac{967}{760}\ \text{atm} \approx 1.272\ \text{atm}$
Temperature: $25^\circ\text{C} = 25 + 273.15 = 298.15\ \text{K}$
Volume: $155\ \text{mL} = 0.155\ \text{L}$

Step2: Calculate molar concentration

Use osmotic pressure formula $\Pi = MRT$, rearrange to $M = \frac{\Pi}{RT}$.
$M = \frac{1.272\ \text{atm}}{0.0821\ \frac{\text{L·atm}}{\text{mol·K}} \times 298.15\ \text{K}} \approx 0.0520\ \text{M}$

Step3: Calculate moles of solute

Use $n = M \times V$.
$n = 0.0520\ \text{mol/L} \times 0.155\ \text{L} \approx 0.00806\ \text{mol}$

Step4: Calculate molar mass of solute

Use $MM = \frac{m}{n}$.
$MM = \frac{4.74\ \text{g}}{0.00806\ \text{mol}} \approx 588\ \text{g/mol}$

Answer:

concentration: $0.0520$ M
moles of solute: $0.00806$ mol
molar mass: $588$ g/mol