Table of contents  
Who discovered Raoult's Law?  
What is Raoult’s Law?  
Finding Vapour Composition  
Raoult's Law as a special case of Henry's law  
Limitations of Raoult’s Law  
Solved Examples 
Raoult’s law states that:
For a solution of volatile liquids, the partial vapour pressure of each component of the solution
is directly proportional to its mole fraction present in solution.
Let's understand this by looking at the example below
Ideal Solution of Two Volatile Liquids
Let two volatile liquids A and B dissolve each other to form an ideal solution. Then the vapours above the solution will contain the vapours of A and B. Applying Dalton’s law of partial pressure the total vapour pressure of the solution will be
P_{solution} = P_{A} + P_{B}
Where,
P_{A} and P_{B} are the partial vapour pressures of A and B.
P_{A} = P^{º}_{A} X_{A}
P_{B} = P^{º}_{B} X_{B}
Where:
Hence, 𝑃 (Solution) 𝑜𝑟 P_{s} = P_{A}^{0} X_{A} + P_{B}^{0} X_{B}
Also, P_{s} = P^{0}_{A}(1X_{B}) + P^{0}_{B}X_{B}
⇒ P_{s} = P^{0}_{A}+(P^{0}_{B}  P^{0}_{A})X_{B}
This equation is of the form y = mx + c. The value of m (slope) may be (+ve) or (–ve) depending upon whether P^{0}_{B} > P^{0}_{A} (m = + ve) or P^{0}_{B} < P^{0}_{A} (m = –ve).
Hence a plot of a graph of P_{s} versus X_{B} will be a straight line with an intercept on the yaxis equal to p_{A} and a slope equal to (P^{0}_{B}  P^{0}_{A})
Plot of Vapour Pressure and Mole Fraction
The total Pressure of a Solution will be:
where y_{A} and y_{B} are mole fractions of ‘A’ and ‘B’ in the vapour phase and y_{A} + y_{B} = 1
SPECIAL NOTE:
x_{A} and x_{B} are mole fraction of ‘A’ and ‘B’ in the solution phase and x_{A} + x_{B} =1y_{A} and y_{B} are mole fraction of ‘A’ and ‘B’ in the vapour phase and y_{A} + y_{B} =1
There are a few limitations to Raoult’s law:
There is either a negative or a positive deviation:
Positive and Negative Deviation
Example 1. The vapour pressure of ethanol and methanol are 44.5 mm and 88.7 mm Hg respectively. An ideal solution is formed at the same temperature by mixing 60 g of ethanol with 40g of methanol. Calculate the total vapour pressure of the solution.
Solution.
Number of moles of ethanol = 60/40 = 1.5
Number of moles of methanol = 40/32 = 1.25
X_{A }= 1.25/1.25 + 1.3 = 0.4545 and X_{B} = 1 – 0.4545 = 0.545
Let A = CH_{3}OH, B = C_{2}H_{5}OH
Total pressure of the solution
P_{T} = X_{A}P^{0}_{A} + X_{B}P^{0}B
= 0.4545 × 88.7 + 0.545 × 44.5 = 40.31 + 24.27
= 64.58 mm Hg
Example 2. The composition of vapour over a binary ideal solution is determined by the composition of the liquid. If X_{A} and Y_{A} are the mole fraction of A in the liquid and vapour, respectively find the value of X_{A} for which Y_{A} − X_{A }has a minimum. What is the value of the pressure at this composition?
Solution.
Subtracting x_{A} from both sides, we get
Now differentiating w.r.t. x_{A}, we get
The value of x_{A} at which y_{A} − x_{A} has a minimum value can be obtained by putting the above derivative equal to zero. Thus we have
Solving for x_{A}, we get
hence
Example 3. A very small amount of nonvolatile solute (that does not dissociate) is dissolved in 56.8 cm^{3} of benzene (density 0.889 g cm^{3}). At room temperature, the vapour pressure of this solution is 99.88 mm Hg while that of benzene is 100mm Hg. Find the molality of this solution. If the freezing temperature of this solution is 0.73 degrees lower than that of benzene. What is the value of the molal freezing point depression constant of benzene?
Solution.
Also,
ΔT_{f} = K_{f} × molality f
∴ 0.73 = K × 0.1452
f_{K} = 5.028 K. molality
Example 4. What is the composition of the vapour which is in equilibrium at 30°C with a benzenetoluene solution with a mole fraction of benzene of 0.400?
(P^{o}_{B} = 119 torr and P_{T}^{o} = 37.0 torr)
Solution.
The Total pressure of the solution is given by
P_{T} = X_{B} P^{0}_{B} + X_{T}P^{0}_{T}
= 0.4 × 119 + 0.6 × 37
= 47.6 + 22.2
= 69.8 torr
Applying Dalton’s law for mole fraction in the vapour phase.
Y_{B} = P_{B}/P_{T} = 47.6/62.4
= 0.763
Y_{T} = 1– 0.763
= 0.237
135 videos348 docs182 tests

1. Who discovered Raoult's Law? 
2. What is Raoult’s Law? 
3. How can we find vapor composition using Raoult's Law? 
4. How is Raoult's Law related to Henry's Law? 
5. What are the limitations of Raoult’s Law? 

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