Heptane and octane form an ideal solution. At 373 K, the vapour pressures 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?

Heptane and octane form an ideal solution. At 373 K, the vapour pressures 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?

Solution:- 

Step-1 Find the given values

Vapour pressureof pure heptane = 105.2 kPa

Vapour pressure of pure octane  = 46.8 kPa

Mass of heptane                            = 26g

Mass of octane                                =35g

Step -2 What to find

Here we have to find total pressure of the mixture

And total pressure of solution =  sum of their partial pressures

P total                   = P heptane +  P octane                     ... (1)

Used Formula and understanding of problem

partial pressure  =  pressure of our liquid × mole fraction

Partial pressure P = P_pure × X                                                   … (2)

Now we have the pressure of gas but need to find their moles fraction

                                 ...(3)

So we need to find number of moles there

                                                      ...(4)

Mass of component is given in problem and we need to find molar mass here 

Step – 3   calculations 

Molar mass of heptane (C₇H₁₆) = 7×12 + 16×1   = 100 gram / mol

Molar mass of octane (C₈H₁₈)   = 8×12 + 18×1   = 114 gram / mol

Plug these value in equation (4)we get

Number of moles of heptanes = 26/100 = 0.26 mol

Number of moles of octane = 35/114 =0.31 mol

Plug these values in equation (3) we get

Mole fraction of heptanes  = (0.26/(0.26+0.31)) =0.456

Mole fraction of octane = 0.31/(0.26+0.31) =0.544

Now plug these values in equation (2) we get

Partial pressure of heptane = 105.2×0.456=47.97 kPa

Partial pressure of octane =46.8×0.544 = 25.46 kPa

Now plug these value in equation (1) we get

Total pressure = 47.97+25.46 =73.43 Kpa