Question

Consider a mixture of 30% n-butane, 35% n-hexane, 35% n-heptane. If the pressure is 202 kPa, calculate the bubble point temperature in ?C and the unknown mole fractions. Specify whether the unknown mole fractions are vapor or liquid. .

Answer 1

Now we are asked to find the bubble point temperature hence the mixture as of now is in liquid state.

So the given mole fraction are of liquid and we will have to find the mole fraction of vapors along with temperature

Now

Let n-butane --->1 , n-hexane ---> 2, n-heptane --->3

Let us write Raoult's law for all these 3 components

For component 1

Y1*P =X1*P1sat ..........1

For component 2

Y2*P =X2*P2sat .....2

For component 3

Y3*P =X3*P3sat .......3

Adding equation 1, 2 and 3

(Y1 + Y2 + Y3)*P = X1*P1sat +X2*P2sat +X3*P3sat ..4

For a ternary composition mixture

Y1 + Y2 + Y3 = 1

Hence equation 4 now becomes

P = X1*P1sat + X2*P2sat +X3*P3sat

Now we will substitute the known mole fraction

P =0.3*P1sat + 0.35*P2sat + 0.35*P3sat

Now we will make use of Antoine equation and substitute the value of saturation pressure in terms of temperature and solve the above equation to obtain the values of temperatures

P = 202 KPa = 1515.125 mmHg

Solving the above equation for T, we get T = 55.68 ^oC

Substituting this Temperature in Antoine equation to obtain saturation pressures

P1sat =4265 mmHg

P2sat =494.6 mmHg

P3sat = 177.9 mmHg

Now recalling equation 1

Y1*P =X1*P1sat

Y1*1515.125 = 0.3*4265

Y1 =0.844

From equation 2

Y2*P =X2*P2sat

Y2*1515.125 = 0.35*494.6

Y2 =0.114

Now

Y1 +Y2 + Y3 = 1

Y3 = 1 - Y1 - Y2 = 1- 0.844 - 0.114 = 0.042