Question

At 20 degrees C, the VP of benzene is 75 torr and that of toluene is 22 torr. Assume that benzene and toluene form an ideal solution.What is the composition in mol fraction of a solution that has a vapor pressure of 35 torr at 20 degrees C?

I see that the answer explanation is posted but I dont understand where the 1-x comes from?!?

Answer 1

Solution:-

The vapor pressure of the solution is the sum of the partial pressure of the components of the solution.

The partial pressure of each component of the solution is dependent on the mole fraction and pure vapor pressure of each component.

The formula to calculate the vapor pressure of the solution is as follows,

P solution = P benzene + P toluene

P solution = x*P^o benzene + x*P^o toluene

Where,

x=mole fraction

P^o = pure vapor pressure.

Now let's say mole fraction of the benzene is x and mole fraction of toluene is y

Then x +y = 1

Because sum of the mole fractions of the component of the mixture is always 1

Then we can write it as

y=1-x

now lets put this in the above equation

P solution = x*P^o benzene + x*P^o toluene

35 torr = (x*75 torr)+(1-x*22torr)

35=75x+22-22x

35-22=75x-22x

13=53x

13/53 =x

0.25 =x

Since the x is assumed as the mole fraction of benzene therefore now we can find the mole fraction of toluene

Mole fraction of toluene = 1-x

                                             =1-0.25

                                             =0.75

Therefore the answers are as follows

Mole fraction of each liquid in the solution is as follows

Mole fraction of benzene = 0.25

Mole fraction of toluene = 0.75

The explanation of the why (1-x) is used is that because since we have only two components in the solution, therefore, sum of mole fractions of two components equals 1. So when we assume a mole fraction of benzene as x and toluene as y then to substitute the value in the equation we use it (1-x) for y.