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How do you calculate the osmotic pressure of sucrose?

Published in Osmotic Pressure 3 mins read

You calculate the osmotic pressure of sucrose using the following formula derived from the ideal gas law: π = iMRT, where π is the osmotic pressure, i is the van't Hoff factor, M is the molarity of the solution, R is the ideal gas constant, and T is the absolute temperature.

Here's a breakdown of the steps and an example:

Understanding the Formula

The osmotic pressure formula is:

π = iMRT

Where:

  • π = Osmotic pressure (typically in atm)
  • i = van't Hoff factor (number of particles the solute dissociates into in solution). For sucrose, i = 1 because it does not dissociate in water.
  • M = Molarity of the solution (mol/L)
  • R = Ideal gas constant (0.0821 L atm / (mol K))
  • T = Absolute temperature (in Kelvin)

Steps to Calculate Osmotic Pressure of Sucrose

  1. Determine the Molarity (M) of the Sucrose Solution:

    • Molarity is defined as moles of solute per liter of solution.

    • Example: If you have 342 grams of sucrose (C12H22O11) in 1000 ml (1 Liter) of solution:

      • The molar mass of sucrose is 342 g/mol.
      • Moles of sucrose = (mass of sucrose) / (molar mass of sucrose) = 342 g / 342 g/mol = 1 mol.
      • Molarity (M) = moles of sucrose / volume of solution = 1 mol / 1 L = 1 M

  2. Determine the van't Hoff Factor (i):

    • Sucrose is a non-electrolyte, meaning it does not dissociate into ions when dissolved in water.
    • Therefore, the van't Hoff factor (i) for sucrose is 1.

  3. Determine the Absolute Temperature (T):

    • Convert the temperature from Celsius to Kelvin.
    • T (K) = Temperature (°C) + 273.15
    • Example: If the temperature is 27°C, then T (K) = 27 + 273.15 = 300.15 K (approximately 300 K for simplicity).

  4. Choose the Ideal Gas Constant (R):

    • Use R = 0.0821 L atm / (mol K) when the osmotic pressure is desired in atmospheres (atm).

  5. Calculate the Osmotic Pressure (π):

    • Plug the values into the formula: π = iMRT
    • Example: Using the values from above:
      • π = (1) (1 mol/L) (0.0821 L atm / (mol K)) * (300 K)
      • π = 24.63 atm

Example Calculation

Let's recalculate using the reference information.

  • 342 gm of sucrose in 1000 ml (1L) at 27°C.
  • Molarity (M) = 1 M (as calculated above)
  • i = 1
  • R = 0.0821 L atm / (mol K)
  • T = 27°C = 300 K

π = (1) (1 M) (0.0821 L atm / (mol K)) * (300 K) = 24.63 atm

Therefore, the osmotic pressure of the sucrose solution is approximately 24.63 atm.

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