Enthalpy Calculator

The enthalpy calculator lets you find the enthalpy of any endothermic or exothermic reaction.

Enthalpy H = U + pV502.24152 kJinternal energy plus the pV work — enthalpy is the energy accounting that INCLUDES making room for the system against its surroundings, which is why constant-pressure heat transfers equal ΔH

Van der Waals pressure2,241.51616 kPa22.41516 bar for carbon dioxide

Ideal gas pressure2,494.33879 kPa11.279% HIGHER than the real value

Compressibility factor Z0.898641below 1: attraction between molecules dominates, pulling them together and REDUCING the pressure below ideal

Attraction term an²/V²364 kPasubtracted from the pressure — molecules pulling on each other hit the walls a little less hard

Excluded volume nb0.04267 litres4.267% of the container. This is subtracted from the volume, because the molecules cannot move through each other

Critical temperature303.998 K30.848 °C — above this no pressure whatever will liquefy carbon dioxide. That the critical point falls out of two fitted constants is the equation's real triumph

Critical pressure74.0444 bar

Critical molar volume0.12801 litres/mol

Critical compressibility0.375van der Waals predicts exactly 3/8 = 0.375 for EVERY gas. Real gases cluster around 0.27, so the equation is qualitatively right and quantitatively off — which is a fair summary of it overall

Reduced temperature T/T_c0.98685below critical, so this gas CAN be liquefied by pressure alone

The pV term alone2.24152 kJ0.448% of the internal energy

The formula

(p + an²/V²)(V − nb) = nRT; H = U + pV

Two corrections, in opposite directions

The van der Waals equation adjusts the ideal gas law twice. Molecules attract one another, so they strike the walls a little less hard — the an²/V² term is added to the measured pressure. And molecules occupy space, so less volume is available than the container suggests — the nb term is subtracted from the volume.

The two pull opposite ways. At moderate pressures attraction wins and the compressibility factor Z falls below 1; at high pressures the excluded volume dominates and Z rises above 1. Every real gas shows this crossover, and it is why Z-charts have the shape they do.

The critical point falls out for free

The equation's real triumph is that setting the first and second derivatives of pressure with respect to volume to zero gives a critical temperature, pressure and volume in terms of a and b alone. Two constants fitted at ordinary conditions predict the point above which a gas cannot be liquefied at all.

It gets the number only roughly right: van der Waals predicts a critical compressibility of exactly 3/8 for every substance, while real gases cluster near 0.27. Qualitatively illuminating, quantitatively approximate — a fair summary of the equation as a whole.