A solution is prepared by dissolving 49.0 g of glucose (C6H12O6) in 225.0 g of water. The density of the resulting solution is 1.23 g/mL. Determine the osmotic pressure (in Pa) of this solution at 25.0 oC.
pi = MRT
Calculate the molarity of the solution and substitute into the above equation. The osmotic pressure (pi) will be in atmospheres. Convert to Pa. Don't forget to use T in Kelvin. Post your work if you get stuck.
To determine the osmotic pressure of a solution, we first need to calculate the concentration of the solution in moles per liter (mol/L).
1. Calculate the number of moles of glucose (C6H12O6):
- The molar mass of glucose = 6(12.01 g/mol) + 12(1.01 g/mol) + 6(16.00 g/mol) = 180.18 g/mol
- Moles of glucose = mass of glucose / molar mass of glucose
= 49.0 g / 180.18 g/mol
2. Calculate the volume of the solution:
- The density of the solution = mass of the solution / volume of the solution
- Volume of the solution = mass of the solution / density of the solution
3. Convert the volume to liters:
- Volume of the solution in liters = volume of the solution in mL / 1000
4. Calculate the concentration of glucose in the solution:
- Concentration of glucose (C) = moles of glucose / volume of the solution in liters
Now, we can use the Van't Hoff equation to calculate the osmotic pressure:
π = nCRT
Where:
- π is the osmotic pressure in Pascals (Pa)
- n is the concentration of solute in mol/L
- R is the ideal gas constant (8.314 Pa⋅m³/(mol⋅K))
- T is the temperature in Kelvin (K)
5. Convert the temperature to Kelvin:
- Temperature in Kelvin = temperature in Celsius + 273.15
6. Plug the values into the equation and calculate the osmotic pressure (π).
Note: Make sure the units of all variables are consistent in order to obtain the correct result.