when 3.20 g of a nonelectrolyte solute is dissolved in water to make 765 ml of solution at 23 °c, the…

Explanation:

Step1: Convert units

First, convert osmotic - pressure from torr to atm and temperature from Celsius to Kelvin. $809\ torr\times\frac{1\ atm}{760\ torr}=1.0645\ atm$ $T=(23 + 273.15)\ K=296.15\ K$

Step2: Use the osmotic - pressure formula to find molar concentration

The osmotic - pressure formula is $\Pi = MRT$, where $\Pi$ is osmotic pressure, $M$ is molar concentration, $R$ is the ideal gas constant ($R = 0.0821\ L\cdot atm/(mol\cdot K)$), and $T$ is temperature. We can solve for $M$: $M=\frac{\Pi}{RT}$ $M=\frac{1.0645\ atm}{0.0821\ L\cdot atm/(mol\cdot K)\times296.15\ K}=0.0437\ mol/L$

Step3: Calculate moles of solute

The volume of the solution $V = 765\ mL=0.765\ L$. The number of moles $n$ of solute is given by $n = M\times V$. $n=0.0437\ mol/L\times0.765\ L = 0.0334\ mol$

Step4: Calculate molar mass

The mass of the solute $m = 3.20\ g$. The molar mass $MM$ is given by $MM=\frac{m}{n}$. $MM=\frac{3.20\ g}{0.0334\ mol}=95.8\ g/mol$

Answer:

concentration: $0.0437\ M$ moles of solute: $0.0334\ mol$ molar mass: $95.8\ g/mol$