Van Thoff Equation Calculator
Our chemical thermodynamics calculator computes van thoff equation accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
ln(K2/K1) = (-deltaH / R)(1/T2 - 1/T1)
The Van't Hoff equation relates the change in equilibrium constant to temperature through the standard enthalpy change. K1 and K2 are equilibrium constants at absolute temperatures T1 and T2, deltaH is the enthalpy of reaction (J/mol), and R is the gas constant (8.314 J/mol K).
Worked Examples
Example 1: Endothermic Reaction Equilibrium
Problem:A reaction has K = 1.5 at 300 K with deltaH = 50 kJ/mol. Find K at 350 K.
Solution:ln(K2/K1) = (-deltaH/R)(1/T2 - 1/T1)\nln(K2/1.5) = (-50000/8.314)(1/350 - 1/300)\nln(K2/1.5) = (-6014.9)(-0.000476) = 2.863\nK2 = 1.5 x e^2.863 = 26.27
Result:K2 = 26.27 at 350 K
Example 2: Finding Enthalpy Change
Problem:A reaction has K = 0.010 at 200 K and K = 0.050 at 400 K. Calculate deltaH.
Solution:ln(K2/K1) = (-deltaH/R)(1/T2 - 1/T1)\nln(0.050/0.010) = (-deltaH/8.314)(1/400 - 1/200)\nln(5) = (-deltaH/8.314)(-0.0025)\n1.6094 = deltaH x 0.000300\ndeltaH = 5357 J/mol = 5.36 kJ/mol
Result:deltaH = 5.36 kJ/mol (endothermic)
Frequently Asked Questions
What is the Van't Hoff equation?
The Van't Hoff equation describes how the equilibrium constant of a chemical reaction changes with temperature. It is expressed as ln(K2/K1) = (-deltaH/R)(1/T2 - 1/T1), where K1 and K2 are the equilibrium constants at temperatures T1 and T2 respectively, deltaH is the standard enthalpy change of the reaction, and R is the universal gas constant (8.314 J/mol K). This equation is derived from thermodynamic principles and assumes that deltaH remains approximately constant over the temperature range considered. It is widely used in chemistry to predict equilibrium shifts with temperature changes.
What assumptions does the Van't Hoff equation make?
The standard Van't Hoff equation assumes that the enthalpy change (deltaH) of the reaction is constant over the temperature range being considered. This is a reasonable approximation for small temperature intervals but becomes less accurate over large temperature ranges because heat capacities of reactants and products cause deltaH to vary with temperature. The equation also assumes ideal behavior of the species involved and uses thermodynamic equilibrium constants. For more accurate calculations over wide temperature ranges, a modified form that incorporates the temperature dependence of deltaH through heat capacity differences (deltaCp) can be used.
What is the difference between the Van't Hoff equation and the Arrhenius equation?
While both equations describe temperature dependence using similar mathematical forms, they apply to different quantities. The Van't Hoff equation relates the equilibrium constant (K) to temperature and uses the enthalpy change (deltaH), describing thermodynamic equilibrium. The Arrhenius equation relates the rate constant (k) to temperature and uses the activation energy (Ea), describing reaction kinetics. The Van't Hoff equation tells you where equilibrium lies at a given temperature, while the Arrhenius equation tells you how fast the reaction approaches equilibrium. Both have the form ln(ratio) = -(energy/R)(1/T2 - 1/T1).
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy