Question

On mixing heptanes and octane form an ideal solution. At 373 K, the vapor pressures of the two liquid components (heptanes and octane) are 105 kPa and 45 kPa respectively. Vapor pressure of the solution obtained by mixing 25.0 gm of heptanes and 35 gm of octane will be: (molar mass of heptanes = 100$gmo{{l}^{-1}}$ and of octane = 114$gmo{{l}^{-1}}$)
A.72.0 kPa
B. 36.1 kPa
C. 96.2 kPa
D. 144.5 kPa

Answer 1

Partial pressure is directly proportional to the mole fraction into vapor pressure. Mole fraction is the number of moles of one component upon total number of moles of all components. Number of moles is calculated by the given mass upon molar mass of an element. So, here we can use the number of moles as given mass by molar mass ratio.
Formula used:
Partial pressure = vapor pressure $\times$ mole fraction = ${{P}_{A}}={{P}^{o}}_{A}.{{\chi }_{A}}$
Vapor pressure = ${{P}_{A}}+{{P}_{B}}$

Complete answer:
We have an ideal solution of heptanes and octane, given the vapor pressures of both of them. To calculate total vapor pressure we will use total pressure is equal to the sum of partial pressures. For this mole fraction are needed as partial pressure is the product of vapor pressure and mole fractions, so mole fractions will be:
Taking number of moles =$\dfrac{given\,mass}{molar\,mass}$
Mole fraction of heptane, ${{\chi }_{hep\tan e}}=\dfrac{{{n}_{hep\tan e}}}{{{n}_{hep\tan e}}+{{n}_{oc\tan e}}}$
${{\chi }_{hep\tan e}}=\dfrac{\dfrac{25}{100}}{\dfrac{25}{100}+\dfrac{35}{114}}=\dfrac{0.25}{0.557}$
${{\chi }_{heptane}}=0.45$
So, mole fraction of octane = 1 – 0.45 = 0.55
Now, keeping the vapor pressure and mole fractions in the total pressure formula we have,
${{P}_{total}}={{P}^{o}}_{hep\tan e}{{\chi }_{hep\tan e}}+{{P}^{o}}_{oc\tan e}{{\chi }_{oc\tan e}}$
${{P}_{total}}=105\times 0.45+45\times 0.55$
Pressure = 72.0 kPa

So, the total vapor pressure of the solution is 72.0 kPa so option A is correct.

Note:
Total pressure is based on Dalton’s law of partial pressure that total pressure is the sum of partial pressure of all components. As the sum of mole fraction of all components is unity, we can only take out one component then subtract that component from 1 to get the other component mole fraction. As mole fraction is a ratio, so it has no units.