Chemical reaction isotherm and the relationship between KΘ and =△rGmΘ

4.
2.
1 Chemical reaction isotherm

If react

The Gibbs free energy of the reaction at any time is △ _r G _m , and the reaction relative quotient is Q ^Θ , then

△ _r G _m =△ _r G _m ^Θ +RTInQ ^Θ

This is the chemical reaction isotherm
.

4.

When the system is in equilibrium

△ _r G _m =0 Q ^Θ =K ^Θ

Substituting into the chemical reaction isotherm formula, we get

0=△ _r G _m ^Θ +RTInK ^Θ

which is

△ _r G _m ^Θ =-RTInk ^Θ

The relationship establishes the relationship between the standard Gibbs free energy change △ _r G _m ^Θ and the standard equilibrium constant, and the standard equilibrium constant KΘ of chemical reactions can be calculated from the thermodynamic data △ _r G _m ^Θ
.

Substituting the formula △ _r G _m ^Θ =-RTInK ^Θ into the chemical reaction isothermal formula △ _r G _m =△ _r G _m ^Θ +RTInQ ^Θ , we have

△ _r G _m =-RTInK ^Θ +RTInQ ^Θ

Organized

This formula relates the Gibbs free energy change △ _r G _m when the reaction is in a non-standard state and the ratio of the reaction relative quotient Q ^Θ to the standard equilibrium constant K ^Θ .

When Q ^Θ <K ^Θ , △ _r G _m <0, the reaction proceeds forward

When Q ^Θ = K ^Θ , △ _r G _m =0, the reaction reaches equilibrium

When Q ^Θ >K ^Θ , △ _r G _m >0, the reaction proceeds in reverse

[Example 4-4] After mixing 1 mol SO ₂ , 2 mol O ₂ and 7 mol Ne, the gas reacts under normal pressure

The reaction reaches equilibrium at 912K, and 70% of SO _{2 is} converted to SO _{3 to} obtain the reaction △ _r G _m ^Θ
.

The solution is based on the reaction equation, the amount of substance in each gas after the reaction equilibrium is

The total amount of substances in the gas after the reaction is

n=nso ₂ +nO ₂ +nso ₃ +n _Ne =9.

The mole fraction of each gas after the reaction is

According to the gas partial pressure law, the partial pressure of a gas is equal to the product of its mole fraction and the total pressure, then the partial pressure of each gas after the reaction

The standard equilibrium constant of the reaction is

and so