Calculating Enthelpy of Vaporization using Clapeyron Equation

[cjc0117]

Hi everyone. I am having a problem that hopefully someone here can help me with. For the purposes of flash calculations, I’m trying to find the enthalpy of vaporization of a compound using the Antoine equation and Clapeyron equation. I am using heptane at 15.5597 psia as an example. For the Antoine equation in the form log₁₀(P^sat) = A-B/(T^sat+C), where P^sat is in units of mmHg and T^sat is in units of °C, I have Antoine coefficients for heptane of A = 6.89385, B = 1264.37, and C = 216.636. At P^sat = 15.5597 psia = 804.592 mmHg, this gives me a saturation temperature of T^sat = 100.386 °C. The Clapeyron equation for a vapor-liquid phase change is dP^sat/dT^sat=Δh_vap/(T^satΔν_vap). Rearranging yields Δh_vap = (dP^sat/dT^sat)(T^sat•Δν_vap). Using the Rackett equation and the Peng-Robinson equation of state, I have found within reasonable accuracy that Δν_vap = 4.385 ft³/lb. Taking the derivative of the Antoine equation with respect to temperature yields dP^sat/dT^sat = BP^satln(10)/(C+T^sat)². Thus, Δh_vap = BP^satT^satΔν_vapln(10)/(C+T^sat)². Plugging everything in results in a value of Δh_vap = 198.348 ft³•psi/lb, which is equivalent to 36.703 BTU/lb. The actual value of Δh_vap for heptane at 15.5597 psia should be somewhere around 135 BTU/lb. I’ve looked over my method and calculations multiple times but I can’t find an error. Perhaps the Antoine equation cannot be differentiated because it uses empirical parameters? Thanks. Any help would be much appreciated.

 

[Chestermiller]

In the Clapyron equation, you did remember that T^sat is absolute temperature, correct?

 

[cjc0117]

Perfect, that's exactly what I did wrong. I left the T^sat in the denominator in °C because the Antoine coefficients are for temperatures in °C, but I converted the other T^sat to Kelvin and now I'm getting 136.6 BTU/lb. Thanks a lot. It didn't make sense to me at first that I should convert to Kelvin because then the temperature units wouldn't seem to cancel out (K/ °C). But then I remembered that "per degree celsius" is the same as "per degree Kelvin" because a degree Kelvin is equal to a degree Celsius. Thanks again.