A more universal and accurate way of evaluating l/(y - x) is through the use of Simpson's rule

Area = V» A[y0 + y„ + 4(yi + y3...) + 2 (y2 +yi-..)]

where h = width of an even number of equally spaced segments y = height

Using this method,

Area = Y3 (0.1)[4.10 + 4(3.86 + 4.55) + 2(3.94) + 6.94] = 1.75

_Still_

Start End Receiver

Benzene 50 1.73 48.27

Toluene _50 15,57 34.43

Mole-fraction benzene 0.500 0.100 0.584

which produces results essentially identical to the previous calculation. (In the interest of conciseness, Simpson's rule will be used in all subsequent examples.) Clearly, simple distillation is not a good method for either removing or concentrating the benzene. Of the original 100 moles, 82.7 moles had to be distilled off to reduce the original benzene concentration to 10 mole percent, and the concentration of the recovered benzene only increased from 50 to 58 mole percent.

When relative volatility is constant, Eq. (5.6) can be substituted for y in Eq. (5.12), and the Rayleigh equation can be integrated to obtain

Example 5.2 The initial concentration of benzene in a benzene-toluene mixture is 5 mole percent. Calculate the material balance for the separation when the residual benzene concentration is 1 mole percent, again using an original charge of 100 moles of mixture.

solution

1 JÏZ 1 , [0.01(1 - 0.05)] (1 - 0.05) 100 (2.90 - 1) [0.05(1 - 0.01)] <1 - 0.01)

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