Isopropyl Alcohol 70% Ethyl Alcohol 70% Calculate the freezing point depression
The Correct Answer and Explanation is :
To calculate the freezing point depression ((\Delta T_f)) for 70% isopropyl alcohol and 70% ethyl alcohol, we use the freezing point depression equation:
[
\Delta T_f = i \cdot K_f \cdot m
]
Where:
- ( i ) = van’t Hoff factor (for non-electrolytes like alcohols, ( i = 1 ))
- ( K_f ) = cryoscopic constant (for water, ( K_f = 1.86 \,^{\circ}C \cdot \text{kg/mol} ))
- ( m ) = molality (moles of solute per kg of solvent)
Step 1: Define Given Data
- 70% isopropyl alcohol (C₃H₇OH) and 70% ethyl alcohol (C₂H₅OH) indicate 70 g of alcohol per 100 g of solution.
- Water is the solvent; hence, solvent mass = 100 g – 70 g = 30 g = 0.030 kg.
- Molar masses: Isopropyl alcohol = 60.1 g/mol, Ethyl alcohol = 46.1 g/mol.
Step 2: Calculate Molality (m)
[
m = \frac{\text{mass of solute}}{\text{molar mass} \times \text{mass of solvent in kg}}
]
For Isopropyl Alcohol:
[
m = \frac{70}{60.1 \times 0.030} = 38.8 \text{ mol/kg}
]
For Ethyl Alcohol:
[
m = \frac{70}{46.1 \times 0.030} = 50.6 \text{ mol/kg}
]
Step 3: Calculate Freezing Point Depression
[
\Delta T_f = 1 \times 1.86 \times m
]
For Isopropyl Alcohol:
[
\Delta T_f = 1.86 \times 38.8 = 72.2^{\circ}C
]
For Ethyl Alcohol:
[
\Delta T_f = 1.86 \times 50.6 = 94.1^{\circ}C
]
Step 4: Determine New Freezing Points
Water’s normal freezing point = 0°C.
- Isopropyl alcohol solution: ( 0 – 72.2 = -72.2^{\circ}C )
- Ethyl alcohol solution: ( 0 – 94.1 = -94.1^{\circ}C )
Explanation (300 Words)
Freezing point depression occurs when a solute is dissolved in a solvent, lowering its freezing temperature. This happens because the solute particles disrupt the solvent’s ability to form a solid structure, requiring a lower temperature to freeze.
For isopropyl alcohol (70%), the large number of solute molecules in a small amount of water significantly decreases the freezing point to -72.2°C. Similarly, ethyl alcohol (70%) lowers the freezing point even more to -94.1°C due to its higher molality.
This principle is widely used in antifreeze solutions, preventing liquids from freezing in cold temperatures. In real-life applications, alcohol-based solutions like rubbing alcohol remain in liquid form at sub-zero temperatures, making them useful for medical, industrial, and de-icing purposes.
Now, I will generate an image illustrating freezing point depression for both alcohols.
Here is the scientific illustration showing the freezing point depression of 70% isopropyl alcohol (-72.2°C) and 70% ethyl alcohol (-94.1°C) compared to pure water (0°C). The image includes thermometers, labeled test tubes, and a cold environment representation. Let me know if you need any modifications or further explanations!
