Van’t Hoff Equation – Chemical Equilibrium – Derivation, Formula

Van’t Hoff Equation – Chemical Equilibrium – Derivation, Formula

This equation gives the quantitative temperature dependence of equilibrium constant (K). The relation between standard free energy change (ΔG°) and equilibrium constant is

ΔG° = – RTln K ……………. (1)
We know that
ΔG° = ΔH° – TΔS° ………………. (2)
Substituting (1) in equation (2)
– RTln K = ΔH° – TΔS°

Rearranging

Van’t Hoff Equation img 1

Differentiating equation (3) with respect to temperature,

Van’t Hoff Equation img 2

Equation 4 is known as differential form of van’t Hoff equation.

Van’t Hoff Equation

On integrating the equation 4, between T1 and T2 with their respective equilibrium constants K1 and K2.

Van’t Hoff Equation img 3

Equation 5 is known as integrated form of van’t Hoff equation.

Problem:

For an equilibrium reaction Kp = 0.0260 at 25° C ΔH = 32.4 kJmol-1, calculate Kp at
37° C

Solution:

T1 = 25 + 273 = 298 K
T2 = 37 + 273 = 310 K
ΔH = 32.4 KJmol-1 = 32400 Jmol-1
R = 8.314 JK-1 mol-1
Kp1 = 0. 0260
Kp2 = ?

Van’t Hoff Equation img 4

Van’t Hoff Charle’s law at the constant concentration the osmotic pressure of a dilute solution is directly proportional to the absolute temperature(T) i.e. παT. παCT. v=CRT. The equation is called van’t Hoff general solution equation.

The Van’t Hoff equation gives the relationship between the standard gibbs free energy change and the equilibrium constant. It is represented by the equation -ΔG°=RTlogeKp.

The Van ‘t Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the Van ‘t Hoff factor is essentially 1.

Van’t Hoff Equation

The van’t Hoff theory describes that substances in dilute solution obey the ideal gas laws, resulting to the osmotic pressure formula π = (n/V)RT = [Ci]RT where R is the gas constant, T the absolute temperature, and [Ci] the molar concentration of solute i in dilute solution (1).

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