The Osmotic Pressure of a Solution

Osmotic pressure is a colligative property of a solution that depends on the concentration of solute particles in the solution. It is defined as the pressure required to prevent the net flow of solvent across a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. In other words, osmotic pressure is the pressure needed to stop osmosis from occurring.

Calculating Osmotic Pressure

The osmotic pressure of a solution can be calculated using the formula:

Osmotic pressure (π) = (n/V)RT

Where:
- n is the number of moles of solute in the solution
- V is the volume of the solution
- R is the ideal gas constant (0.0821 L·atm/mol·K)
- T is the temperature in Kelvin

Determining the Number of Moles of Glucose

To calculate the osmotic pressure of the given solution, we first need to determine the number of moles of glucose present.

Given:
- Density of the solution = 1 g/mL
- Mass of glucose = 3 g
- Mass of water = 60 g

Using the density formula, we can determine the volume of the solution:

Volume of solution = Mass of solution / Density of solution
Volume of solution = (3 g + 60 g) / 1 g/mL
Volume of solution = 63 mL

Next, we convert the volume of the solution to liters:

Volume of solution = 63 mL * (1 L / 1000 mL)
Volume of solution = 0.063 L

To determine the number of moles of glucose, we need to use the molar mass of glucose:

Molar mass of glucose = 180.16 g/mol

Number of moles of glucose = Mass of glucose / Molar mass of glucose
Number of moles of glucose = 3 g / 180.16 g/mol
Number of moles of glucose ≈ 0.01666 mol

Calculating Osmotic Pressure

Now that we have the number of moles of glucose (n) and the volume of the solution (V), we can calculate the osmotic pressure (π) using the formula mentioned earlier:

Osmotic pressure (π) = (n/V)RT

Temperature (T) = 15°C = 15 + 273.15 K = 288.15 K

Osmotic pressure (π) = (0.01666 mol / 0.063 L) * (0.0821 L·atm/mol·K) * 288.15 K
Osmotic pressure (π) ≈ 35.1 atm

Therefore, the osmotic pressure of the given solution at 15°C is approximately 35.1 atm.

6.56