Question

On mixing, heptane and octane form an ideal solution. At 373 K , the vapour pressures of two liquid components (heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressures of solution obtained by mixing 25.0 g of heptane and 35.0 g of octane will be: (Molar mass of heptane 100 g/mol and of octane 114 g/mol).
A) 72.0 kPa
B) 36.1 kPa
C) 96.2 kPa
D) 144.5 kPa

Answer 1

Hint: In a binary solution, the sum of the mole fractions of two components is equal to one.
Total pressure of a binary solution is the sum of the partial pressures of two components.

Complete step by step answer:
Mass of heptane is 25.0 g.
The molar mass of heptane is 100 g/mol.
Divide mass of heptane with molar mass of heptane to obtain a number of moles of heptane.
\[\dfrac{{{\text{25 g}}}}{{{\text{100 g/mol}}}}\] = 0.25 mol
Now we have to calculate Moles of octane,
Mass of octane is 35.0 g.
The molar mass of octane is 114 g/mol.
Divide mass of octane with molar mass of octane to obtain number of moles of octane.
\[\dfrac{{{\text{35 g}}}}{{{\text{114 g/mol}}}}\] = 0.307 mol.
The mole fraction of heptane is the ratio of the number of moles of heptane to total number of moles of heptane and octane.
Calculate the mole fraction of heptane
\[{X_H} = \dfrac{{{\text{0}}{\text{.25 mol}}}}{{{\text{0}}{\text{.25 mol + 0}}{\text{.307 mol}}}}
= \dfrac{{0.25}}{{0.557}} \\
= 0.45 \\\]
In a binary solution, the sum of the mole fractions of two components is equal to one. Thus, the sum of the mole fractions of heptane and octane is one. To obtain the mole fraction of octane, subtract the mole fraction of heptane from one.
\[{X_O} = 1 - {X_H} \\
= 1 - 0.45 \\
= 0.55 \\\]
Hence, the mole fraction of octane is 0.55.
Total pressure of a binary solution is the sum of the partial pressures of two components.
Thus, the total pressure of mixture of heptane and octane is equal to the sum of the partial pressures of heptane and octane.
Partial pressure of heptane is equal to the product of the mole fraction of heptane and the vapour pressure of pure heptane.
Partial pressure of octane is equal to the product of the mole fraction of octane and the vapour pressure of pure octane.
\[{P_{total}} = \left( {105 \times 0.45} \right) + \left( {45 \times 0.55} \right){\text{ kPa}} \\
= 72.0{\text{ kPa}} \\\]
Hence, the total pressure is \[72.0{\text{ kPa}}\]

Thus, the option A ) is the correct answer.

Note: For an ideal solution, total pressure of a binary solution is the sum of the partial pressures of two components which is given by Raoult's law.