Based on the provided reference, the osmotic pressure of sucrose, calculated under specific conditions of concentration and temperature using the van 't Hoff equation (Π=cRT), is 37.6 atm.
Osmotic pressure is a colligative property, meaning it depends on the concentration of solute particles in a solution, not on the identity of the solute itself. For sucrose solutions, this pressure arises from the tendency of solvent molecules (like water) to move across a semipermeable membrane from an area of lower solute concentration to an area of higher solute concentration.
The reference highlights that calculating osmotic pressure relies on the van 't Hoff equation:
Π = cRT
Where:
- Π is the osmotic pressure.
- c is the molar concentration of the solute (sucrose) in mol/L.
- R is the ideal gas constant.
- T is the absolute temperature in Kelvin.
The value of 37.6 atm is obtained when specific values for the concentration (c), temperature (T), and the universal gas constant (R) are used in this formula. While the exact concentration and temperature used to achieve this value are not detailed in the provided snippet, the reference explicitly states this is the result of the calculation under those specific (correct) conditions.
Factors Influencing Sucrose Osmotic Pressure
The osmotic pressure of a sucrose solution is directly affected by:
- Concentration (c): A higher molar concentration of sucrose leads to a higher osmotic pressure. The reference notes that calculating the correct concentration, often involving the molar mass of sucrose (Msucrose) and potentially the density of the solution (ρ) which is temperature-dependent, is crucial for accurate calculation.
- Temperature (T): Osmotic pressure increases with increasing absolute temperature. The reference points out that while concentration and density are temperature-dependent, molality (moles of solute per kilogram of solvent) is not. However, the van 't Hoff equation uses molar concentration (moles per liter of solution), which is temperature-dependent due to volume expansion/contraction.
- The Gas Constant (R): This is a constant value relating energy scales to temperature scales.
Therefore, stating a single "osmotic pressure of sucrose" is technically incomplete without specifying the concentration and temperature. However, the reference provides a concrete example of 37.6 atm resulting from a specific set of conditions.
Key Takeaways from the Reference
- The osmotic pressure (Π) can be calculated using the van 't Hoff equation (Π = cRT).
- A specific calculation resulted in an osmotic pressure of 37.6 atm for sucrose under particular concentration and temperature conditions.
- Accurate calculation requires the correct molar concentration (c), which involves factors like the molar mass of sucrose (Msucrose) and solution density (ρ).
- Concentration (c), density (ρ), and temperature (T) are interrelated and affect the outcome, unlike molality which is independent of temperature.
Understanding these factors is essential for working with solutions and predicting their behavior across membranes.
