The VLE data for formic acid (left(mathrm{CH}_{2} mathrm{O}_{2} ight))-water are presented in Table 8-6. a. Determine the

The VLE data for formic acid \(\left(\mathrm{CH}_{2} \mathrm{O}_{2}\right)\)-water are presented in Table 8-6.

a. Determine the value of \(\alpha\) at each data point from \(\mathrm{x}_{\mathrm{A}}=0.042\) to \(\mathrm{x}_{\mathrm{A}}=\) 0.485 with Eq. (2-7a), and then calculate the geometric average value of \(\alpha\) using all data points. Use the geometric average value of \(\alpha\) in the Fenske equation to find \(\mathrm{N}_{\text {min }}\) at total reflux for a distillation column with a total condenser and a partial reboiler operating at \(750 \mathrm{~mm} \mathrm{Hg}\) if we want to have a distillate that is 0.015 mole fraction formic acid and a bottoms that is 0.54 mole fraction formic acid.

Equation (2-7a)

b. Plot Eq. (2-10a) with the geometric average value of \(\alpha\) from \(\mathrm{x}_{\mathrm{A}}=0\) to \(\mathrm{x}_{\mathrm{A}}=\mathrm{x}_{\mathrm{A}, \mathrm{az}}=0.560\left(\mathrm{~A}=\right.\) formic acid and \(\left.\mathrm{x}_{\mathrm{A}, \mathrm{az}}=0.560\right)\), and step off stages at total reflux.

Equation (2-10a)

c. Plot the experimental equilibrium data from \(\mathrm{x}_{\mathrm{A}}=0\) to \(\mathrm{x}_{\mathrm{A}}=0.560\) on a McCabe-Thiele plot, draw a smooth curve through the data, and step off stages at total reflux.

d. Determine the linear equation for relative volatility, and use this equation to estimate the value of \(\mathrm{y}\) formic acid for the \(\mathrm{x}\) values from 0.042 to 0.485 in Table 8-6. Use the linearized equation for alpha to calculate an average relative volatility for the total reflux distillation problem in part \(\mathrm{a}\). Then calculate the value of \(\mathrm{N}_{\text {min }}\) with this \(\alpha_{\text {avg }}\).

e. Compare the results for the calculation of \(\mathrm{N}_{\text {min }}\) from parts \(\mathrm{a}, \mathrm{b}, \mathrm{c}\), and

d. Because \(\alpha\) is not constant, exact matches of part \(d\) with parts \

(a, b\), and \(\mathrm{c}\) are not expected.

At \(1.0 \mathrm{~atm}\) formic acid boils at \(100.8^{\circ} \mathrm{C}\). It forms a maximum boiling azeotrope with water that can be separated with a two-pressure distillation system. In the range of the distillation in this problem, formic acid is the less volatile component, which should not cause difficulties in use of the Fenske equation.

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TABLE 8-6. VLE Data for formic acid-water at 750 mm Hg y formic acid 0 0.016 0.040 0.070 0.110 0.172 0.298 0.425 x formic acid 0 y formic acid 0.042 0.090 0.145 0.205 0.300 0.375 0.485 0.560 0.650 0.870 1.00 x formic acid 0.560 0.615 0.780 1.00 -