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Consider a mixture of hydrocarbons that consists of 60 percent (by volume) methane, 30 percent ethane, and 10 percent propane. After passing through a separator, the mole fraction of the propane is reduced to 1 percent. the mixture pressure before and after the separation is 100 kPa. Determine the change in the partial pressures of all the constituents in the mixture.

Respuesta :

Answer:

[tex]\Delta P_m=6\text{kPa}\\\Delta P_e=3\text{kPa}\\\Delta P_p=-9\text{kPa}[/tex]

Explanation:

mole fraction of propane after passing through the separator is [tex]\beta_p[/tex]

[tex]\frac{\beta}{0.6+0.3+\beta}=0.01[/tex]

[tex]\beta =9.09\times 10^-^3[/tex]

mole fractions of ethane [tex]\beta _e[/tex] and methane [tex]\beta_m[/tex] after passing through separator are:

[tex]\beta_e =\frac{0.3}{0.3+0.6+0.00909}=0.66\\\beta_m=\frac{0.6}{0.3+0.6+0.00909}=0.33[/tex]

Change in partial pressures then can be written as:

[tex]\Delta P=(y_2-y_1)\cdot P[/tex]  where [tex]y_2[/tex] and [tex]y_1[/tex] are mole fractions after and before passing through the separator

Hence,

[tex]\Delta P_m=(0.66-0.6)\cdot 100\text{k}=6\text{kPa}\\\Delta P_e=(0.33-0.3)\cdot 100\text{k}=3\text{kPa}\\\Delta P_p=(0.01-0.1)\cdot 100\text{k}=-9\text{kPa}[/tex]

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