It is desired to represent the vapor pressure of an organic substance by an equa

Question

It is desired to represent the vapor pressure of an organic substance by an equation of the form: P* = (p_0*)e^m/T Where p* is the vapor pressure in atm, T is absolute temperature in kelvin. 100 m^3 dry air a1 1 atm and 0degree C is required to vaporize 0.5 kmole of the organic material at a temperature of 290 k and a pressure of 1 atm. At 340 k and 1 atm, 50 m^3 of air at 1 atm and 0degree C are required to vaporize 0.5 kmole. Calculate the constant p_0* and m in the given units and write the actual equation. Problem 8.34: Do the following only!! Derive an equation for C_p as a function of T Use this equation to calculate deltaH (analytical solution) Calculate deltaH using trapezoidal rule (use an increment of 150degree C ) Show all your steps ans work on the paper you are submitting and you are expected to do it on your own!!

Explanation / Answer

100 m3 = 100 / 22.4 = 4.46 Kmol
Partial pressure of Vapor = (0.5 / (0.5 + 4.46 ) ) * 1 = 0.1007 atm

50 m3 = 50 / 22.4 = 2.23 Kmol
Partial pressure of Vapor = 0.183 atm

P*= Po*e^m/T
0.1007 = Po * e^ m/290
0.183 = Po * e^m/340

dividing the above two, we get

0.585 = (e^ m/290) / (e^ m/340)
=> 0.585 = e^(m/290 - m/340) = e^m * 5.07 * 10^-4
=> ln 0.585 = m * 5.07 * 10^-4
=> m = -1057.3

now,
0.1007 = Po * e^ m/290
=>Po = 0.1007 / e^ (-1057.3 / 290) = 3.858 atm

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