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`Delta H^o = -R(ln(K_2/K_1))/(1/(T_2)-1/T_1)`

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The **Van't Hoff** equation, ln(K_{2}/K_{1}) = ΔH^{0}/R (1/T_{1} - 1/T_{2}), provides information about the temperature dependence of the equilibrium constant. T

**INSTRUCTIONS:** Choose units and enter the following:

- (
**K**) Equilibrium constant at absolute temperature T_{1}_{1}. - (
**K**) Equilibrium constant at absolute temperature T_{2}_{2}. - (
**T**) Absolute temperature one._{1} - (
**T**) Absolute temperature two._{2}

**ΔH ^{0}:** The calculator returns the reaction enthalpy (the standard heat of the reaction). This calculator uses the Ideal Gas Constant (R):8.3144626181532 J/(mol·K).

All temperatures are automatically converted to Kelvin.

The Van't Hoff equation was proposed in 1884 by Jacobus Henricus van't Hoff. Van't Hoff made great contributions to physical chemistry, specifically in chemical kinetics, stereochemistry, and chemical equilibrium.

The formula in this equation is as follows:

`ΔH^0 = R * ( -ln(K_2/K_1))/ (1/T_1 - 1/T_2)`

It is a form of : ln(K_{2}/K_{1}) = ΔH^{0}/R (1/T_{1} - 1/T_{2}) solved for ΔH^{0}.

If equilibrium constants are known for two different temperatures, then ΔH^{0} can be found for a substance. Likewise, if an equilibrium constant (K_{1}) for T_{1} and ΔH^{0} are known, then the equilibrium constant (K_{2}) can be calculated for a second temperature. The Van't Hoff equation does, however, assume that ΔH^{0} does not change with temperature. This is not necessarily true; ΔH^{0} does change with temperature, but the change is small enough that it is considered negligible when estimating K_{2}.

When the equilibrium constant and temperature are plotted against each other, both an exothermic and endothermic reaction will have a characteristic shape to its graph. Exothermic graphs tend to be linear with a positive slope, while endothermic reactions are linear with a negative slope, as shown below.

**R - Gas Constant:**8.3144626181532 J/(K⋅mol)**Boyle's Law Calculator**: P_{1}• V_{1}= P_{2}• V_{2}**Charles Law Calculator**: V_{1}• T_{2}= V_{2}• T_{1}**Combined Gas Law Calculator**: P•V / T= k**Gay-Lussac Law:**T_{1}•P_{2}=T_{2}•P_{1}**Ideal Gas Law**: P•V = n•R•T**Bragg's Law:**n·λ = 2d·sinθ**Hess' Law:**ΔH^{0}_{rxn}=ΔH^{0}_{a}+ΔH^{0}_{b}+ΔH^{0}_{c}+ΔH^{0}_{d}**Internal Energy**: ΔU = q + ω**Activation Energy**: E_{a}= (R*T_{1}⋅T_{2})/(T_{1}- T_{2}) ⋅ ln(k_{1}/k_{2})**Arrhenius Equation**: k = Ae^{E_a/(RT)}**Clausius-Clapeyron Equation**: ln(P_{2}/P_{1}) = (ΔH_{vap})/R * (1/T_{1}- 1/T_{2})**Compressibility Factor**: Z = (p*V_{m})/(R*T)**Peng-Robinson Equation of State**: p = (R*T)/(V_{m}- b) - (a*α)/(V_{m}^{2}+ 2*b*V_{m}- b^{2})**Reduced Specific Volume**: v_{r}= v/(R* T_{cr }/ P_{c})**Van't Hoff Equation**: ΔH^{0}= R * ( -ln(K_{2}/K_{1}))/ (1/T_{1}- 1/T_{2})

Whitten, et al. "Chemistry" 10th Edition. Pp. 699