The equilibrium conversion of a reversible reaction

A reversible reaction has reached the equilibrium when r_A = 0, i.e. dU_A/dt = 0

When you write the kinetic differential equation for the reaction and substitute the concentration by the conversion U_A, you get the maximum conversion for dU/dt = r = 0 :

U_A,max = k₁/(k₁+k₂)

You can rearrange this equation to give k₂ and substitute k₂ in the basic kinetic equation :

dU_A/dt = k₁( 1- U_A/U_A,max)

You can solve this differential equation and get by integration in the boarders U_A = 0 to 0.9* U_A,max the time that the reaction takes to reach 90% of the equilibrium conversion.

On the other hand you can carry out the (simulation) and take the control values for comparison.

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