Calculation of Temperature for Osmotic Pressure

Introduction:
Osmotic pressure is defined as the pressure required to stop the flow of solvent molecules from a region of high solvent concentration to a region of low solvent concentration through a semi-permeable membrane. The osmotic pressure is directly proportional to the concentration of the solute. In this question, we need to find the temperature at which a 10% aqueous solution of glucose will exhibit the osmotic pressure of 16.4 atm.

Formula:
The osmotic pressure (π) of a solution is given by the formula
π = CRT
where C is the molar concentration of the solute, R is the gas constant, and T is the temperature.

Calculation:
Given that the concentration of the glucose solution is 10% (w/v). This means that 10 g of glucose is dissolved in 100 mL of water. The molar mass of glucose is 180 g/mol. Therefore, the molarity of the solution can be calculated as follows:

Molarity (M) = (10 g / 180 g/mol) / (0.1 L) = 0.5555 M

We need to find the temperature at which the osmotic pressure of this solution is 16.4 atm. The gas constant R is 0.0821 L*atm/(mol*K).

π = CRT
16.4 atm = (0.5555 M) (0.0821 L*atm/mol*K) T
T = (16.4 atm) / [(0.5555 M) (0.0821 L*atm/mol*K)]
T = 367 K

Therefore, the temperature at which a 10% aqueous solution of glucose will exhibit the osmotic pressure of 16.4 atm is 367 K (93.85°C).

Explanation:
The osmotic pressure is a colligative property of solutions, which means it depends only on the number of solute particles present in the solution and not on the nature of the solute particles. The higher the concentration of solute particles, the higher the osmotic pressure. In this question, we have calculated the molar concentration of the glucose solution and used the formula for osmotic pressure to calculate the temperature at which the given osmotic pressure will be exhibited. The gas constant is used to convert the units of concentration and pressure into the appropriate units for the temperature. This calculation is important in fields such as biology, where the osmotic pressure plays a crucial role in maintaining the cell structure and function.