The Van't Hoff equation determines the relation to the change of the equilibrium constant K_{eq} of a chemical reaction given the standard rate of enthalpy change ∆H^{⊖} in temperature T.
This formula has been widely implemented in exploring the alterations of state functions in a given thermodynamic system. Derived from this equation is the Van't Hoff plot, that effectively estimates the change in total energy and number of microstates that are accessible in a chemical reaction.
Under standard temperature and pressure conditions, the Van't Hoff equation is denoted as:
d
dT

ln K_{eq} = 
∆H^{⊖}
RT^{2}

d
dT

ln K_{eq} = 
∆H^{⊖}
RT^{2}

Where:
At any single temperature, the above equation is exact and in practice if often integrateed between two temperatures in the case that the reaction enthalpy ΔH is constant. This integrated equation is only an approximation given that both enthalpy and entropy vary by temperature for the majority of processes.
Gibbs free energy changes with the pressure and temperature of the thermodynamic system. The Van't Hoff isotherm is utilized to determine the Gibbs free energy at a constant temperature for nonstandard rate reactions using the following:
( 
dG
dξ

)_{T, p} = ∆_{r}G + (RT)ln(Q_{r}) 
( 
dG
dξ

)_{T, p} = ∆_{r}G + (RT)ln(Q_{r}) 
Where:
This isotherm can assist in estimating the reaction shift of equillibrium. When ∆_{r}G < 0, the reaction moves in a forward direction. Conversely, when ∆_{r}G > 0, the reaction moves in a backward direction.
For reversible reactions, the equillibrium constant allows measurement at a variety of temperatures. The data can be plotted utilizing ln K_{eq} on the yaxis and 1 / T on the xaxis. The data requires a linear relationship and implement the following equation which can be found through the following linear form of the Van't Hoff equation:
ln K_{eq} = ( 
∆H^{⊖}
RT

) + ( 
∆S^{⊖}
R

) 
ln K_{eq} = ( 
∆H^{⊖}
RT

) + ( 
∆S^{⊖}
R

) 
Where:
is the slope.
is the intercept of linear fit.
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