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Heptane and octane form an ideal solution. At 373 K, the vapour pressure of the two liquid components are 105.2 kPa and 46.8 kPa respectively. What will be the vapour pressure of a mixture of 26.0 g of heptane and 35 g of octane?

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Hint: According to Raoult’s law, 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 the solution.
Thus, P1X1
Or,P1=P10×X1, where
P1=Partial vapour pressure of heptane
P10=Pure vapour pressure of heptane
X1=Mole fraction of heptane

Similarly,P2=P20×X2,
where
P2=Partial vapour pressure of octane
P20=Pure vapour pressure of octane
X2=Mole fraction of octane
According to Dalton’s law of partial pressure, the total pressure of the mixture will be the sum of the partial pressure of each component of the solution.
Ptotal=P1+P2

Complete step by step answer:
Here it is given that,
Vapour pressure of heptane in pure form (P10) = 105.2 kPa
Vapour pressure of octane in pure form (P20) = 46.8 kPa
We will calculate the moles of heptane and octane to find their mole fraction.
Molar mass of heptane (C7H16) = 12 x 7 + 16 x 1 = 100 g/mol

Number of moles = GivenmassMolarmass

Molesofheptane=26 g100 g/mol = 0.26 mol
Molar mass of octane (C8H18) = 12 x 8 + 18 x 1 = 114 g/mol

Molesofoctane=35 g114 g/mol = 0.30 mol

Total number of moles = 0.26 + 0.30 = 0.56 mol
ThereforeMole fraction of heptane (XC7H16) = 0.26 0.56= 0.46
And Mole fraction of octane (XC8H18) = 0.30 0.56 = 0.54
According to Dalton’s law, Ptotal=P1+P2
Or, Ptotal=P10×X1+P20×X2 (According to Raoult’s law P1=P10×X1 and P2=P20×X2)
Or, Ptotal=P10XC7H16+P20XC8H18
Now we will put the values of variables in above equation,
Ptotal=105.2 kPa × 0.46 + 46.8 kPa × 0.54
Ptotal= 73.66 kPa
Hence the vapour pressure of mixture containing 26 g of heptane and 35 g of octane is 73.66 kPa.

Note: To solve this question we should know to calculate the molecular masses of heptane and octane and the formula for calculating their mole fraction. Some time should make mistakes by getting confused in partial pressure and total pressure but one should remember that in Raoult’s law and Dalton’s law partial pressure is used and then after getting the values of partial pressure we can further calculate total pressure
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Heptane and octane form an ideal solution. At 373 K, the vapour pressure of the two liquid components are 105.2 kPa and 46.8 kPa respectively. What will be the vapour pressure of a mixture of 26.0 g of heptane and 35 g of octane?

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SOLUTIONS Chemistry Class 12 - NCERT EXERCISE 1.16 | Class 12 Chemistry Chapter 1 | Nandini Ma'am
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