# Enthalpy in the van't Hoff equation

In the van't Hoff equation, why do we say that the change in enthalpy at standard pressure is constant? My book derives the equation for a mixture of ideal gases reacting with each other. The proof itself is good, until the authors declare that the equation says that the graph of $$\ln K$$ with $$\frac{1}{T}$$, where $$K$$ is the equilibrium constant and $$T$$ is the temperature of the mixture, will be a straight line. This would only be true if the change in enthalpy is constant (since the slope of the curve is proportional to this change). But isn't the enthalpy of an ideal gas proportional to temperature? So why is the change in enthalpy constant in $$T$$, then?

I've attached an example of this effect, as presented by the book. See the image below.

• It is a simplifying assumption. Could you provide more details about the gases involved, the pressure, and the temperature window? May 6, 2021 at 11:53
• @BuckThorn I don't have any particular gases or temperature windows in mind (simply because that wasn't mentioned in the book), but they do provide an example of this effect. Do you think it's a good idea to include that in my question? May 6, 2021 at 11:55

• The $\Delta C_p\Delta T$ is quite small compared the $\Delta H$ even though the temperature range is large. Typically $C_p$ is in tens of J/mol/K where as $\Delta H$ is in hundreds of kilo J/mol. May 6, 2021 at 17:10