Calculating Osmotic Pressure With an Example Problem

The osmotic pressure of a solution is the minimum amount of pressure needed to prevent water from flowing into it across a semipermeable membrane. Osmotic pressure also reflects how readily water can enter the solution via osmosis, as across a cell membrane. For a dilute solution, osmotic pressure obeys a form of the ideal gas law and can be calculated provided  you know the concentration of the solution and the temperature. Osmotic Pressure Problem What is the osmotic pressure of a solution prepared by adding 13.65 g of sucrose (C12H22O11) to enough water to make 250 mL of solution at 25  °C?Solution:Osmosis and osmotic pressure are related. Osmosis is the flow of a solvent into a solution through a semipermeable membrane. Osmotic pressure is the pressure that stops the process of osmosis. Osmotic pressure is a colligative property of a substance since it depends on the concentration of the solute and not its chemical nature.Osmotic pressure is expressed by the formula:ÃŽ   iMRT (note how it resembles the PV nRT form of the Ideal Gas Law)whereÃŽ   is the osmotic pressure in atmi van t Hoff factor of the soluteM molar concentration in mol/LR universal gas constant 0.08206 L ·atm/mol ·KT absolute temperature in K Step 1,Find the Concentration of Sucrose To do this, look up the atomic weights of the elements in the compound:From the periodic table:C 12 g/molH 1 g/molO 16 g/mol Use the atomic weights to find the molar mass of the compound. Multiply the subscripts in the formula times the atomic weight of the element. If there is no subscript, it means one atom is present.molar mass of sucrose 12(12) 22(1) 11(16)molar mass of sucrose 144 22 176molar mass of sucrose 342nsucrose 13.65 g x 1 mol/342 gnsucrose 0.04 molMsucrose nsucrose/VolumesolutionMsucrose 0.04 mol/(250 mL x 1 L/1000 mL)Msucrose 0.04 mol/0.25 LMsucrose 0.16 mol/L Step 2,Find absolute temperature Remember, absolute temperature is always given in Kelvin. If the temperature is given in Celsius or Fahrenheit, convert it to Kelvin. T  °C 273T 25 273T 298 K Step 3,Determine the van t Hoff factor Sucrose does not dissociate in water; therefore the van t Hoff factor 1. Step 4,Find the Osmotic Pressure To find the osmotic pressure, plug the values into the equation. ÃŽ   iMRTÃŽ   1 x 0.16 mol/L x 0.08206 L ·atm/mol ·K x 298 KÃŽ   3.9 atmAnswer:The osmotic pressure of the sucrose solution is 3.9 atm. Tips for Solving Osmotic Pressure Problems The biggest issue when solving the problem is knowing the vant Hoff factor and using the correct units for terms in the equation. If a solution dissolves in water (e.g., sodium chloride), its necessary to either have the vant Hoff factor given or else look it up. Work in units of atmospheres for pressure, Kelvin for temperature, moles for mass, and liters for volume. Watch significant figures if unit conversions are required.