How are the forward and reverse rate constants for a one-step reaction related to the equilibrium constant for the reaction?
A)Kc = kf x kr
B) Kc = kf - kr
C) Kc = kf + kr
D) Kc = kf/kr
The answer to this question is D) Kc = kf/kr.
To understand why, let's first understand the concepts of forward and reverse rate constants and the equilibrium constant.
In a one-step chemical reaction, the forward rate constant (kf) represents the speed or rate at which reactants are converted into products. On the other hand, the reverse rate constant (kr) represents the speed or rate at which products are converted back into reactants.
The equilibrium constant (Kc) for a reaction is a measure of the concentration of products and reactants at equilibrium. It is calculated by dividing the concentration of products (raised to their stoichiometric coefficients) by the concentration of reactants (also raised to their stoichiometric coefficients).
Now, when a reaction reaches equilibrium, the forward and reverse rates become equal. This means that the rate at which products are formed (kf) is equal to the rate at which reactants are formed (kr).
So, at equilibrium, we have:
kf = kr
Now, let's express the equilibrium constant (Kc) in terms of kf and kr. The equilibrium constant is defined as the ratio of the concentration of products to the concentration of reactants at equilibrium. This can be represented as:
Kc = [Products]/[Reactants]
Now, we can substitute the concentrations of products and reactants in terms of their respective rate constants:
Kc = (kf/kr)
So, the equilibrium constant (Kc) is equal to the ratio of the forward rate constant (kf) to the reverse rate constant (kr). Therefore, the correct answer is D) Kc = kf/kr.