Question

Calculate the osmotic pressure of the following solutions of urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO},\) at \(22^{\circ} \mathrm{C}\). (a) \(0.217 \mathrm{M}\) urea (b) \(25.0 \mathrm{~g}\) urea dissolved in enough water to make \(685 \mathrm{~mL}\) of solution. (c) \(15.0 \%\) urea by mass (density of the solution = \(1.12 \mathrm{~g} / \mathrm{mL})\)

Short answer

Question: Calculate the osmotic pressure of the following urea solutions at 22°C: (a) 0.217 M, (b) 25.0 g urea in 685 mL of solution, and (c) 15.0% urea by mass (density = 1.12 g/mL). Answer: The osmotic pressure for the given urea solutions is: (a) 5.04 atm, (b) 14.7 atm, and (c) 68.0 atm.

Step-by-step solution

Convert Celsius to Kelvin

First, convert the given temperature of 22°C to Kelvin. To do this, add 273.15 to the Celsius temperature. T = 22 + 273.15 = 295.15 K.

Determine the van't Hoff factor for urea

As urea is a non-electrolyte and doesn't dissociate into ions in solution, the van't Hoff factor (i) is 1.

Calculate osmotic pressure for (a) 0.217 M urea solution

Given the molarity (n) as 0.217 M, we use the formula: \(\Pi = \text{i} \cdot \text{n} \cdot R \cdot T = 1 \cdot 0.217 \cdot 0.0821 \cdot 295.15\). Thus, the osmotic pressure is approximately 5.04 atm.

Calculate the molarity of (b) 25.0 g urea in 685 mL of solution

Dissolving 25.0 g of urea in enough water to make 685 mL of solution, first, calculate the moles of urea. Urea has a molar mass of 60.06 g/mol. Moles of urea = 25.0 g / 60.06 g/mol = 0.4162 mol. The volume of the solution is 685 mL, which is equal to 0.685 L. Therefore, the molarity of the solution is 0.4162 mol / 0.685 L = 0.607 M.

Calculate osmotic pressure for (b)

Using the formula and the molarity of 0.607 M for the urea solution in part (b), compute osmotic pressure: \(\Pi = 1 \cdot 0.607 \cdot 0.0821 \cdot 295.15\). Thus, the osmotic pressure is approximately 14.7 atm.

Calculate the molarity of (c) 15.0% urea by mass (density = 1.12 g/mL)

Given a 15.0% urea by mass solution with a density of 1.12 g/mL, we can determine the mass of urea and water in 1 L (1000 mL) of the solution. Mass of solution = Density × Volume = 1.12 g/mL × 1000 mL = 1120 g. Mass of urea = 0.15 × 1120 g = 168 g. Mass of water = 1120 g - 168 g = 952 g. Now, calculate the moles of urea: Moles of urea = 168 g / 60.06 g/mol = 2.80 mol. As the total volume is 1000 mL (1 L), molarity of the solution is 2.80 mol / 1 L = 2.80 M.

Calculate osmotic pressure for (c)

Using the formula and the molarity of 2.80 M for the urea solution in part (c), compute osmotic pressure: \(\Pi = 1 \cdot 2.80 \cdot 0.0821 \cdot 295.15\). Thus, the osmotic pressure is approximately 68.0 atm.

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution, expressed as the number of moles of solute per liter of solution. It's important to understand that molarity, denoted with the unit M, is different from molality, which is moles per kilogram of solvent. In solutions chemistry, molarity is significant because it allows us to predict the number of solute particles available in a solution, which in turn affects properties such as osmotic pressure, boiling point, and freezing point.

van't Hoff factor

The van't Hoff factor, represented by the symbol 'i', is essential in solutions chemistry, particularly when dealing with colligative properties such as osmotic pressure, boiling point elevation, and freezing point depression. This factor indicates the number of particles a compound dissociates into when it dissolves. For non-electrolytes, like urea, which do not dissociate, the van't Hoff factor is 1. For electrolytes, it can be greater than 1. This means that the effect of the solute on colligative properties is proportional not to the concentration of the solute itself but to the concentration of the particles it forms in solution.

Solutions Chemistry

Solutions chemistry deals with the study of chemical solutions which comprise a solute dispersed within a solvent. The properties of a solution can significantly differ from those of its components when separate. To fully comprehend solutions and their behavior—such as osmotic pressure, it's crucial to understand various concentration measures like molarity, factors affecting solute-solvent interactions, and how a solute influences colligative properties through the van't Hoff factor. These concepts are integral to predicting and controlling the characteristics of a solution in different chemical processes and applications.
For instance, calculating osmotic pressure requires knowledge of not just the solution's molarity but also its temperature and the nature of the solute, seen in the use of the van't Hoff factor.