How Is the Equilibrium Formula Derived?

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The equilibrium constant formula, Keq = ([C]c[D]d)/([A]a[B]b), is derived from the law of mass action, which states that at equilibrium, the rate of the forward reaction equals the rate of the backward reaction. The equilibrium constant (Keq) can be expressed as the ratio of the rate constants for the forward (kf) and backward (kb) reactions, leading to the relationship Keq = kf/kb. This foundational concept is crucial in understanding chemical equilibria and is often discussed in general chemistry courses.
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In my general chemistry class, my professor proved the equilibrium formula:

Keq = ([C]c[D]d)/([A]ab)

However, I lost my notes :frown:; hopefully someone can help derive it for me. Thanks.
 
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it's not proved in my book
 
Write Law of mass action for forward and backward rxn

At equilibrium rate of forward rxn= rate of backward rxn
And K_{eq} = \frac{k_f}{k_b}

Where kf & kb represent the rate constant for fwd & bkw rxn
 
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