Colligative Properties Worksheet Answers Explained
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Colligative properties are a fascinating topic in chemistry that delve into how the presence of solute particles affects the physical properties of a solvent. Understanding these properties is crucial for students as they prepare for exams or engage in practical applications. In this blog post, we will explain the answers to common worksheets on colligative properties, providing clarity on key concepts.
What are Colligative Properties? 🤔
Colligative properties are properties that depend on the number of solute particles in a solution rather than the identity of the solute itself. The four primary colligative properties include:
- Vapor Pressure Lowering
- Boiling Point Elevation
- Freezing Point Depression
- Osmotic Pressure
These properties are crucial in various real-world applications, from cooking to pharmaceuticals.
Vapor Pressure Lowering 🌡️
When a non-volatile solute is dissolved in a solvent, the vapor pressure of the solvent decreases. This phenomenon occurs because the solute particles occupy space at the surface of the liquid, reducing the number of solvent molecules that can escape into the vapor phase.
Example Calculation
Suppose we have a solution containing 2 moles of a non-volatile solute (e.g., salt) dissolved in 1 liter of water. The vapor pressure of pure water at a given temperature is 23.8 mmHg.
Using Raoult's Law:
[ P_{\text{solution}} = X_{\text{solvent}} \cdot P_{\text{solvent}}^0 ]
Where:
- (P_{\text{solution}}) = vapor pressure of the solution
- (X_{\text{solvent}}) = mole fraction of the solvent
- (P_{\text{solvent}}^0) = vapor pressure of the pure solvent
Assuming 2 moles of solute and 55.5 moles of water (the approximate number of moles in 1 liter), the mole fraction can be calculated:
[ X_{\text{solvent}} = \frac{55.5}{55.5 + 2} \approx 0.964 ]
Thus:
[ P_{\text{solution}} = 0.964 \cdot 23.8 \approx 22.94 \text{ mmHg} ]
This reduction in vapor pressure is a classic example of colligative properties.
Boiling Point Elevation 🔥
The addition of a solute to a solvent raises the boiling point of that solvent. This elevation can be calculated using the formula:
[ \Delta T_b = i \cdot K_b \cdot m ]
Where:
- (\Delta T_b) = change in boiling point
- (i) = van 't Hoff factor (number of particles the solute dissociates into)
- (K_b) = ebullioscopic constant of the solvent
- (m) = molality of the solution
Example Calculation
If we dissolve 1 mole of NaCl (which dissociates into 2 particles: Na⁺ and Cl⁻) in 1 kg of water, with (K_b) for water being 0.512 °C kg/mol, we can calculate:
[ \Delta T_b = 2 \cdot 0.512 \cdot 1 \approx 1.024 °C ]
Thus, the boiling point of the solution would be approximately 100.6 °C.
Freezing Point Depression ❄️
Similar to boiling point elevation, freezing point depression occurs when a solute is added to a solvent. The formula for calculating the change in freezing point is:
[ \Delta T_f = i \cdot K_f \cdot m ]
Where:
- (\Delta T_f) = change in freezing point
- (i) = van 't Hoff factor
- (K_f) = cryoscopic constant of the solvent
- (m) = molality of the solution
Example Calculation
For the same NaCl solution, where (K_f) for water is 1.86 °C kg/mol, the change in freezing point is:
[ \Delta T_f = 2 \cdot 1.86 \cdot 1 \approx 3.72 °C ]
This means the freezing point of the solution would decrease to approximately -3.72 °C.
Osmotic Pressure 💧
Osmotic pressure is another colligative property that refers to the pressure required to stop the flow of solvent into a solution through a semipermeable membrane. It can be calculated using the formula:
[ \Pi = i \cdot C \cdot R \cdot T ]
Where:
- (\Pi) = osmotic pressure
- (C) = molar concentration of the solute
- (R) = ideal gas constant (0.0821 L·atm/K·mol)
- (T) = temperature in Kelvin
Example Calculation
If 1 mole of NaCl is dissolved in 1 liter of solution at 298 K (25°C), we can calculate the osmotic pressure as follows:
[ \Pi = 2 \cdot 1 \cdot 0.0821 \cdot 298 \approx 49.3 \text{ atm} ]
This calculation shows how colligative properties play a role in biological systems, such as cellular osmotic pressure.
Summary Table of Colligative Properties
<table> <tr> <th>Property</th> <th>Effect of Solute</th> <th>Formula</th> </tr> <tr> <td>Vapor Pressure Lowering</td> <td>Decreases</td> <td>P<sub>solution</sub> = X<sub>solvent</sub> * P<sub>solvent</sub><sup>0</sup></td> </tr> <tr> <td>Boiling Point Elevation</td> <td>Increases</td> <td>ΔT<sub>b</sub> = i * K<sub>b</sub> * m</td> </tr> <tr> <td>Freezing Point Depression</td> <td>Decreases</td> <td>ΔT<sub>f</sub> = i * K<sub>f</sub> * m</td> </tr> <tr> <td>Osmotic Pressure</td> <td>Increases</td> <td>Π = i * C * R * T</td> </tr> </table>
Conclusion
Understanding colligative properties is vital for anyone studying chemistry or working in related fields. These concepts not only apply to theoretical aspects but are also crucial in practical applications, from food preservation to medication formulation. With these explanations and examples, worksheets on colligative properties can become an easy tool for mastering this subject. Remember, the key to mastering colligative properties lies in practicing calculations and conceptual understanding!