Pure water freezes at $273 \,K$ and $1$ bar. The addition of $34.5\, g$ of ethanol to $500\, g$ of water changes the freezing point of the solution. Use the freezing point depression constant of water as $2\,K\, kg\,mol^{-1}$. The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is $46\, g\,mol^{-1}$]
Among the following, the option representing change in the freezing point is
The Correct Option is C
Solution and Explanation
$=2 \times \frac{34.5 \times 2}{46}$
$=2 \times 1.5$
$=3$
Freezing point of ethanol $+$ water mixture
$=273-3=270$
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Concepts Used:
Colligative Properties
Colligative Property of any substance is entirely dependent on the ratio of the number of solute particles to the total number of solvent particles but does not depend on the nature of particles. There are four colligative properties: vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.
Examples of Colligative Properties
We can notice the colligative properties of arrangements by going through the accompanying examples:
- On the off chance that we add a spot of salt to a glass full of water, its freezing temperature is brought down impressively than its normal temperature. On the other hand, the boiling temperature is likewise increased and the arrangement will have a lower vapor pressure. There are also changes observed in its osmotic pressure.
- In the same way, if we add alcohol to water, the solution’s freezing point goes down below the normal temperature that is usually observed for either pure alcohol or water.
Types of Colligative Properties
- Freezing point depression: ΔTf =1000 x kf x m2 /(M2 x m1)
- Boiling point elevation: ΔTb = kb m
- Osmotic pressure: π = (n2/V) RT
- Relative lowering of vapor pressure: (Po - Ps)/Po