Calculate the osmotic pressure of a solution containing 24.6 g of glycerin (C3H8O3) in 250.0 mL of solution at 298 K.

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Calculate the molar mass of glycerin (C_3H_8O_3) by adding the atomic masses of its constituent atoms: 3 carbon atoms, 8 hydrogen atoms, and 3 oxygen atoms.

Convert the mass of glycerin (24.6 g) to moles using its molar mass.

Determine the molarity of the solution by dividing the number of moles of glycerin by the volume of the solution in liters (0.250 L).

Use the formula for osmotic pressure: \( \Pi = iMRT \), where \( i \) is the van't Hoff factor (which is 1 for glycerin, a non-electrolyte), \( M \) is the molarity, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin (298 K).

Substitute the values into the osmotic pressure formula to calculate \( \Pi \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is calculated by dividing the number of grams of solute by its molar mass to find moles, and then dividing by the volume of the solution in liters. Understanding molarity is essential for determining how concentrated a solution is, which directly affects osmotic pressure.

Glycerin Properties

Glycerin, or glycerol (C3H8O3), is a simple polyol compound that is hygroscopic and soluble in water. Its molecular weight is approximately 92.09 g/mol, which is necessary for calculating the number of moles in a given mass. Knowing the properties of glycerin helps in accurately determining its contribution to the osmotic pressure of the solution.

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