Question

Aclosed system contains an equimolar mixture of n-pentane and isopentane. Suppose the system is initially all liquid at 120°C and a high pressure, and the pressure is gradually reduced at a constant temperature. Estimate the pressures at which the first bubble of vapor forms and at which the last drop of liquid evaporates. Also calculate the liquid and vapor compositions (mole fractions) at those two conditions.

Answer 1

Explanation:

The given data is as follows.

      T = $120^{o}C$ = (120 + 273.15)K = 393.15 K,  

As it is given that it is an equimolar mixture of n-pentane and isopentane.

So,            $x_{1}$ = 0.5   and   $x_{2}$ = 0.5

According to the Antoine data, vapor pressure of two components at 393.15 K is as follows.

               $p^{sat}_{1}$ (393.15 K) = 9.2 bar

               $p^{sat}_{1}$ (393.15 K) = 10.5 bar

Hence, we will calculate the partial pressure of each component as follows.

                 $p_{1} = x_{1} \times p^{sat}_{1}$

                            = $0.5 \times 9.2 bar$

                             = 4.6 bar

and,           $p_{2} = x_{2} \times p^{sat}_{2}$

                         = $0.5 \times 10.5 bar$

                         = 5.25 bar

Therefore, the bubble pressure will be as follows.

                           P = $p_{1} + p_{2}$            

                              = 4.6 bar + 5.25 bar

                              = 9.85 bar

Now, we will calculate the vapor composition as follows.

                      $y_{1} = \frac{p_{1}}{p}$

                                = $\frac{4.6}{9.85}$

                                = 0.467

and,                $y_{2} = \frac{p_{2}}{p}$

                                = $\frac{5.25}{9.85}$

                                = 0.527  

Calculate the dew point as follows.

                     $y_{1}$ = 0.5,      $y_{2}$ = 0.5  

          $\frac{1}{P} = \sum \frac{y_{1}}{p^{sat}_{1}}$

           $\frac{1}{P} = \frac{0.5}{9.2} + \frac{0.5}{10.2}$

             $\frac{1}{P}$ = 0.101966 $bar^{-1}$              

                             P = 9.807

Composition of the liquid phase is $x_{i}$ and its formula is as follows.

                   $x_{i} = \frac{y_{i} \times P}{p^{sat}_{1}}$

                               = $\frac{0.5 \times 9.807}{9.2}$

                               = 0.5329

                    $x_{z} = \frac{y_{i} \times P}{p^{sat}_{1}}$

                               = $\frac{0.5 \times 9.807}{10.5}$

                               = 0.467