What is the Van't Hoff equation?

The Van't Hoff equation is a formula that relates the change in the equilibrium constant of a chemical reaction to the change in temperature.

The Van't Hoff equation is a fundamental principle in physical chemistry, named after the Dutch chemist Jacobus Henricus Van't Hoff. It is a mathematical representation of the relationship between the equilibrium constant (K) of a chemical reaction and the temperature at which the reaction occurs. The equation is derived from the principles of thermodynamics, specifically the concept of Gibbs free energy.

The equation is expressed as: dlnK/dT = ΔH°/RT². Here, dlnK/dT is the rate of change of the natural logarithm of the equilibrium constant with respect to temperature, ΔH° is the standard enthalpy change of the reaction, R is the universal gas constant, and T is the absolute temperature.

The Van't Hoff equation is particularly useful in predicting the effect of temperature changes on the position of equilibrium in a chemical reaction. If the reaction is exothermic (ΔH° < 0), an increase in temperature will shift the equilibrium to the left, favouring the reactants. Conversely, if the reaction is endothermic (ΔH° > 0), an increase in temperature will shift the equilibrium to the right, favouring the products. Understanding this behaviour is crucial in contexts such as dynamic equilibrium.

The equation also allows us to calculate the enthalpy change of a reaction if the equilibrium constant is known at different temperatures. This calculation often uses concepts explained in the section on energy profiles, which helps in understanding the energy changes during a reaction.

In summary, the Van't Hoff equation is a powerful tool in physical chemistry, providing a quantitative link between thermodynamics and the equilibrium properties of chemical reactions. It is a key concept for understanding how temperature affects chemical equilibria and reaction rates.