Osmotic Pressure: Study with Video Lessons, Practice Problems & Examples

Osmotic pressure drives water movement from lower to higher solute concentrations, influenced by concentration and temperature. The formula for osmotic pressure (π) is given by: ${\pi }^{=}IMRT$, where I is the van't Hoff factor, M is molarity (moles per liter), R is the gas constant (0.08206 L·atm/(mol·K)), and T is temperature in Kelvin. Understanding these relationships is crucial for applications in biology and chemistry.

Osmotic Pressure Concept 1

Now recall that osmotic pressure is the force that drives the movement of water from a lower concentration to a higher concentration. And remember that the osmotic pressure of a solution can be influenced by its concentration and temperature. So if we take a look here, we have our osmotic pressure formula. Here we're going to say that osmotic pressure, which is represented by this pi symbol, is in units of atmospheres, and it equals I, which is your van't Hoff factor, capital M, which is your molarity or concentration or solubility. Okay. And that will be in moles per liter, so moles of solute over liters of solution, times R. R is your gas constant, which is 0.08206, liters times atmospheres over moles times K. And then here, finally, T is our temperature and that would be in units of Kelvin. So just remember, when it comes to osmotic pressure, concentration and temperature can play a role in influencing the osmotic pressure of any solution.

π = I ⁢ M ⁢ R = 0.08206 ⁢ T

Osmotic Pressure Example 1

Here it says calculate the osmotic pressure of the solution that is 18.30 milligrams of zinc oxide and 15.1 ml of solution at 26 degrees Celsius. Alright. So osmotic pressure equals I⋅M⋅R⋅T. Zinc oxide is an ionic solute that breaks up into zinc ion and oxide ion. That's 2 ions, so I=2. M (capital) is our molarity which is moles over liters. Here, when I convert the 15 ml into liters, that's 0.015 liters. Then I can change the 18.30 milligrams of Zinc into moles. So remember 1 milligram is 10-3 grams and 1 mole of zinc, the weight of zinc oxide the mole the weight of zinc oxide, when we figure that out is, well, the mass is 81.38 grams. So when we work that out, the moles is 2.2487⋅10-4 moles. So then that's going to give us our moles over liters. R is our gas constant, which we don't have to do anything, we just have to plug it in. And then our temperature needs to be in Kelvin, so add 273.15 to this number here and that gives us 299.15 Kelvin. So then what cancels out? Kelvins cancel out, moles cancel out, liters cancel out, and we're left with atmospheres at the end. So when we plug this in, we're going to get 0.731 atmospheres as the osmotic pressure for this given solution.

The osmotic pressure of blood is 5950.8 mmHg at 41ºC. What mass of glucose, C₆H₁₂O₆, is needed to prepare 5.51 L of solution. The osmotic pressure of the glucose solution is equal to the osmotic pressure of blood.

• A. 54.7 g
• B. 0.304 g
• C. 419 g
• D. 302 g

The osmotic pressure of a solution containing 7.0 g of insulin per liter is 23 torr at 25ºC. What is the molar mass of insulin? (1 atm = 760 torr)

• A. 474.5 g/mol
• B. 6x10³ g/mol
• C. 5.2x10³ g/mol
• D. 5.7x10³ g/mol

Here’s what students ask on this topic:

What is the formula for calculating osmotic pressure?

The formula for calculating osmotic pressure (π) is given by:

$\pi =I\cdot M\cdot R\cdot T$

where:

• $I$ is the van't Hoff factor, which accounts for the number of particles the solute dissociates into.
• $M$ is the molarity of the solution, measured in moles per liter (mol/L).
• $R$ is the gas constant, which is 0.08206 L·atm/(mol·K).
• $T$ is the temperature in Kelvin (K).

This formula helps in understanding how concentration and temperature influence the osmotic pressure of a solution.

How does temperature affect osmotic pressure?

Temperature directly affects osmotic pressure. According to the formula $\pi =I\cdot M\cdot R\cdot T$, osmotic pressure (π) is proportional to temperature (T). As temperature increases, the kinetic energy of the molecules also increases, leading to a higher osmotic pressure. Conversely, a decrease in temperature results in a lower osmotic pressure. This relationship is crucial in biological and chemical processes where temperature control is essential for maintaining proper osmotic balance.

What is the van't Hoff factor and how does it influence osmotic pressure?

The van't Hoff factor (I) represents the number of particles into which a solute dissociates in solution. For example, NaCl dissociates into two ions (Na⁺ and Cl⁻), so its van't Hoff factor is 2. The van't Hoff factor influences osmotic pressure by determining the number of particles contributing to the pressure. According to the formula $\pi =I\cdot M\cdot R\cdot T$, a higher van't Hoff factor results in a higher osmotic pressure, assuming constant molarity, gas constant, and temperature. This factor is essential for accurately predicting osmotic pressure in solutions with electrolytes.

Why is osmotic pressure important in biological systems?

Osmotic pressure is crucial in biological systems because it regulates the movement of water across cell membranes. Cells maintain osmotic balance to ensure proper hydration, nutrient uptake, and waste removal. For example, in human cells, osmotic pressure helps maintain blood pressure and volume. Disruptions in osmotic pressure can lead to conditions like dehydration or edema. Understanding osmotic pressure is essential for fields like medicine and physiology, where maintaining cellular homeostasis is vital for health and function.

How do you convert temperature to Kelvin for osmotic pressure calculations?

To convert temperature from Celsius to Kelvin for osmotic pressure calculations, you use the formula:

$T=T{C}_{°}+273.15$

where $T{C}_{°}$ is the temperature in Celsius. For example, if the temperature is 25°C, the temperature in Kelvin would be:

$25+273.15=298.15$ K

This conversion is necessary because the osmotic pressure formula requires temperature in Kelvin to ensure accurate calculations.