Estimation of the Vapor Pressure at an Arbitrary Temperature You are employed in a firm that manufactures Pharmaceuticals. For some products the firm uses pyridine as a solvent. Pyridine (C5H5N, CAS 110-86-1) is a colorless, toxic (PEL = 5 PPM), flammable liquid with an unpleasant odor.For purposes

Question

Estimation of the Vapor Pressure at an Arbitrary Temperature
You are employed in a firm that manufactures Pharmaceuticals. For some products the firm uses pyridine as a solvent. Pyridine ([latex]C_5H_5N[/latex], CAS 110-86-1) is a colorless, toxic (PEL = 5 PPM), flammable liquid with an unpleasant odor. For purposes of design you need to know the vapor pressure at 38. °C and 75. °C. The data can be obtained from tables of thermophysical data available on the internet (see Chapter 1) or perhaps Perry et al. (1984), but unfortunately all you have at your disposal is an old data sheet which states that the vapor pressure at 77. °F is 20.0 mm Hg, and the BP (boiling point at atmospheric pressure) is 240. °F.
To do: Estimate the vapor pressure of pyridine at 38. and 75. °C using the Clausius-Clapeyron equation, and compare to exact values.

Accepted Answer

For clarification, the four temperatures used in this problem are numbered as follows:
- [latex]T_1[/latex] = 77. °F(=25.°C = 298.15 K)
- [latex]T_2[/latex] = 38.°C(=311.15 K)
- [latex]T_3[/latex] = 75. °C(=348.15 K)
- [latex]T_4[/latex] = 240. °F(= 115.56 °C = 388.71 K)
In thermodynamic terms the data correspond to [latex]P_\mathbf{v}[/latex](at 25. °C) = 20.0 mm Hg and [latex]P_\mathbf{v}[/latex](at 115.56 °C) = 760. mm Hg. To use Eq. (4-28), it is necessary to know the average value of the enthalpy of vaporization per mol between temperatures [latex]T_1[/latex] and [latex]T_2[/latex]. If this cannot be found in the available literature, an approximate average value can be computed by applying Eq. (4-28) between the temperatures 298.15 K and 388.71 K.

[latex]\ln \left(\frac{P_{\mathbf{v},2}}{P_{\mathbf{v},1}} \right) =\left(\frac{M\hat{a} h_{fg}}{R_u} \right) \left(\frac{T_2-T_1}{T_2T_1} \right)[/latex] (4-28)

[latex]\frac{M\hat{h}_{fg}}{R_u} =\ln \left(\frac{P_\mathbf{v},4}{P_{\mathbf{v},1}} \right) \left[\frac{T_4T_1}{T_4-T_1} \right] =\ln \left(\frac{760.}{20.0} \right) \left[\frac{(388.71 K)(289.15 K)}{(388.71 K - 289.15 K)} \right] =5655. K[/latex]

Note that [latex]\hat{h} _{fg}[/latex] can be calculated by multiplying the above value by [latex]R_U[/latex]/M, but it is not necessary to do so. The vapor pressure [latex]P_\mathbf{v}[/latex] (at 311.15 K) can now be found by applying Eq. (4-28) between 298.15 K and 311.15 K, using the above ratio:

[latex]\ln \left(\frac{P_{\mathbf{v},2}}{P_{\mathbf{v},1}} \right) =\frac{M\hat{h}_{fg} }{R_u} \left[\frac{T_2-T_1}{(T_2)(T_1)} \right] =(4655. K)\left[\frac{311.15 K-298.15 K}{(311.15 K)(298.15 K)} \right] =0.6523 [/latex]

from which

[latex]P_{\mathbf{v},2}(at 38. °C) = P_{\mathbf{v},1} .e^{0.6523} [/latex] = (20.0 mm Hg)(1.920) = 38.4 mm Hg

To find the vapor pressure at 75. °C, the calculation can be repeated using temperatures [latex]T_3[/latex] and [latex]T_4[/latex]. The computation yields

[latex]P_{\mathbf{v},3}[/latex] (at 348.15 K) = 188. mm Hg

For comparison, exact values of pyridine vapor pressure are found from Appendix A.8:

method	38. °C	75. °C
estimation from Eq. (4-28)	38.4 mm Hg	188. mmHg
exact value from Appendix A.8	40.0 mm Hg	200. mm Hg
percentage error	4.0%	5.9%

Discussion: The errors arise because the estimations use two temperatures that are quite different from one another (25. °C and 115.56 °C). The value of M[latex]\hat{h} _{fg}[/latex] for pyridine at 114.1 °C is 8,492.2 cal/gmol (Perry et al., 1984). If this value were used in the above calculation, the computed values of [latex]P_\mathbf{v}[/latex] (at 38. °C) and [latex]P_\mathbf{v}[/latex] (at 75. °C) would be even less than those shown in the table. These disparities illustrate the sensitivity of predictions obtained from the Clausius-Clapeyron equation.

Question 4.8: Estimation of the Vapor Pressure at an Arbitrary Temperature...

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