# Van ‘t Hoff isotherm

The Gibbs free energy can change with the change of the temperature and pressure of the thermodynamic system. The**Van ‘t Hoff isotherm** can be used to determine the Gibbs free energy for non-standard state reactions at a constant temperature:

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where is the Gibbs free energy for the reaction, and is the reaction quotient. When a reaction is at equilibrium, . The Van ‘t Hoff isotherm can help estimate the equilibrium reaction shift. When , the reaction moves in the forward direction. When , the reaction moves in the backwards directions. See Chemical equilibrium.

## Van ‘t Hoff plot

For a reversible reaction, the equilibrium constant can be measured at a variety of temperatures. This data can be plotted on a graph with on the Y-axis and on the X-axis. The data should have a linear relationship, the equation for which can be found by fitting the data using the linear form of the Van ‘t Hoff equation

This graph is called the **Van ‘t Hoff plot** and is widely used to estimate the enthalpy and entropy of a chemical reaction. From this plot, is the slope and is the intercept of the linear fit.

By measuring the equilibrium constant, *K _{eq}*, at different temperatures, the Van ‘t Hoff plot can be used to assess a reaction when temperature changes. Knowing the slope and intercept from the Van ‘t Hoff plot, the enthalpy and entropy of a reaction can be easily obtained using

The Van ‘t Hoff plot can be used to quickly determine the enthalpy of a chemical reaction both qualitatively and quantitatively. Change in enthalpy can be positive or negative, leading to two major forms of the Van ‘t Hoff plot.

### Endothermic reactions

For an endothermic reaction, heat is absorbed, making the net enthalpy change positive. Thus, according to the definition of the slope:

for an endothermic reaction,

and R is the gas constant

So

Thus, for an endothermic reaction, the Van ‘t Hoff plot should always have a negative slope.

### Exothermic reactions

For an exothermic reaction, heat is released, making the net enthalpy change negative. Thus, according to the definition of the slope:

from an exothermic reaction,

and R is the gas constant

So

Thus, for an exothermic reaction, the Van ‘t Hoff plot should always have a positive slope.