Question

In: Chemistry

Physical Chemistry Estimate the bubble point and dew point temperatures of a 25 mol % n-pentane,...

Physical Chemistry

Estimate the bubble point and dew point temperatures of a 25 mol % n-pentane, 45 mol % n-hexane, and 30 mol % n-heptane mixture at 1.013 bar.

Data:

lnP5vap = 10.422 - 26,799 / RT δ5 = 7.02 (Cal/cc)(1/2)

lnP6vap = 10.456 - 29,676 / RT δ6 = 7.27 (Cal/cc)(1/2)

lnPvap7 = 11.431 - 35,200 / RT δ7 = 7.43 (Cal/cc)(1/2)

For P in bar, T in K, and R = 8.314 J/(mol * K); The subscripts 5,6,7 designate pentane, hexane, and heptane, respectfully

Solutions

Expert Solution

Ans:

By short-cut vapor pressure eqn.

Though not required, the table below also shows bubble T and dew T calculations at 70 bar.

For the bubble calculations, in each column, the temperature at the top of the column is used to calculate the K-ratio. Then yi = xiKi. The temperature is adjusted until the sum of y’s is unity. This is an iterature calculation.

For the dew T calculations, in each column, the temperature at the top of the column is used to calculate the K-ratio. Then xi = yi/Ki. The temperature is adjusted until the sum of x’s is unity. This is an iterative calculation. For the isothermal flash calculation, the T = 233K and the pressure is 70 bar, so the K-ratio is fixed, as tabulated in the column under ‘233’. Equation 9.63 is programmed in the cells below the value of L/F=0.181 below the ‘Flash’ title. Each row holds the value of the term ‘Di = zi(1-Ki)/[Ki + (L/F)(1-Ki)]’ from equation 9.63. These values are summed at the bottom of the column. The criteria for the isothermal flash is that L/F is adjusted until the sum goes to zero, as is shown at L/F = 0.181. Once the value of L/F is found, the xi values and yi values in the last columns are generated separately using equations 9.57 and 9.58 respectively.

The bubble point of a liquid is the point where the liquid just starts to evaporate (boil), that is, when the first vapor bubble is formed.

If the temperature is given, then we must lower the pressure until the first bubble is formed. If the pressure is given, then we must increase the temperature until the first bubble is formed.

In both cases, this corresponds to adjusting T or p until the computed sum of vapor fractions is just 1, Σyi = 1 or ΣiKixi = 1 where xi is given.

For the ideal case where Raoult’s law holds this gives Σi xipi sat (T ) = p


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