Question

ethyl alcohol has a vapor pressure of 20 mmHg at 8.0 C and a normal boiling point of 78.4 C. estimate the vapor pressure at 45 C using (a) the Antoine equation. (b) the Clausius-Clapeyron equation and the two given data points; and (c) linear interpolation between the two given points. taking the 1st estimate to be correct, calculate the percentage error associated with the second and third estimates.

Answer 1

Vapor pressure of C_2H_5OH at 800 degree c = 20 mm Hg Normal boiling point of C_2H_5OH = 78.4 degree c v.p of C_2H_5OH at 45 degree c = ? For C_2H_5OH A = 8.20417, B = 1642.89 C = 230.3 Antoine equation log p = A - B/(C + T) = > 8.20417 - 1642.89/(230.3 + 45) lop p = > 2.24 p = 173.78 mmHg According clausius-clapey equation. log (p_1/p_2) = delta H_vap/2.303 k (1/T_1 - 1/T_2) p_1 = 760 mmHg T_1 = 78.4 + 273 = > 351.4 k p_2 = 20 mmHg T_2 = 8 + 273 = > 281 k log (760/20) = delta H_vap/2.303 times 8.314 (1/351.4 - 1/281) delta H_vap = 4.24 times 10^4 J At 45 degree c = 45 + 273 = > 318 k log (760/p_2) = 4.24 times 10^4/2.303 times 8.314 (1/351.4 - 1/3 8) p_2 = m 169.64 mmHg linear interpolation formula process p = p_0 + (T - T_0) [(p_1 - p_0)/(T_1 - T_0)] = 20 + (318 - 281) [(760 - 20)/(351.4 - 281)] = 408.87 mmHg