A differential equation for vapor pressure as a function of temperature

A new approach is proposed to develop a vapor pressure equation. The slope term of the Clapeyron equation and the logarithm of the reduced pressure multiplied by a coefficient are added together to set up a differential equation. The coefficient is determined such that a homogeneous solution is a term in the Wagner vapor pressure equation. The behavior of a source function is observed using data from the NIST (National Institute of Standards and Technology) WebBook; the source function is essentially linear in the reduced temperature. The linearity gives a new vapor pressure equation. Data from the WebBook for 75 substances are fitted to the new equation and yield an average relative deviation of 0.12%. The results compare favorably with the existing three-parameter equations such as Riedel (0.47%), Xiang–Tan (0.25%), and Mejbri–Bellagi (0.25%). It is also shown that the new equation successfully fits experimental data for CF3I and R161. Drawbacks of using the three-parameter equations are discussed for N2, ethane, and SF6 with extremely accurate data.