Equilibrium Constant Shift Calculator Formula

Understand the math behind the equilibrium constant shift calculator. Each variable explained with a worked example.

Use the Equilibrium Constant Shift Calculator

Formulas Used

K at Temperature T2

k2 = k1 * exp(dh_j / 8.314 * (1/t1 - 1/t2))

K2 / K1 Ratio

ratio = exp(dh_j / 8.314 * (1/t1 - 1/t2))

Variables

VariableDescriptionDefault
k1K at Temperature T1100
t1Temperature T1(K)298
t2Temperature T2(K)350
delta_hEnthalpy of Reaction (delta H)(kJ/mol)-50
dh_jDerived value= delta_h * 1000calculated

How It Works

Van't Hoff Equation

The van't Hoff equation predicts how the equilibrium constant changes with temperature.

Formula

ln(K2/K1) = (delta_H/R) × (1/T1 - 1/T2)

where R = 8.314 J/(mol·K) is the gas constant and delta_H is the reaction enthalpy.

  • Exothermic reactions (delta_H < 0): K decreases as T increases
  • Endothermic reactions (delta_H > 0): K increases as T increases

    • This is the thermodynamic basis for Le Chatelier's principle regarding temperature.

    Worked Example

    An exothermic reaction with K=100 at 298 K, delta_H = -50 kJ/mol. Find K at 350 K.

    k1 = 100t1 = 298t2 = 350delta_h = -50
    1. 01ln(K2/K1) = (-50000/8.314) × (1/298 - 1/350)
    2. 021/298 - 1/350 = 0.003356 - 0.002857 = 0.000499
    3. 03ln(K2/K1) = -6013.4 × 0.000499 = -3.001
    4. 04K2/K1 = exp(-3.001) = 0.0498
    5. 05K2 = 100 × 0.0498 = 4.98

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