Thank you for your response! If it helps to work backward, the correct answer according to USNCO is B: Rate = kr*[C]/[.B].
After some more research, I came across an equation (in Raymond Chang's AP Chemistry) that says the kf/kr = KC. Using this yields the correct answer. Is this equation applicable to any reversible equation, and does anyone know why it holds true? Also, how can we determine this without knowing the reaction mechanism?
I am not happy with this answer. In fact, I am not happy with any attempt to give a kinetic explanation of thermodynamic phenomena. The laws of thermodynamics dictate that [C]/[A][B ] = constant, without any reference to the mechanism, which we may not know, and which may not be simple. Of course, the forward and reverse rates must be the same at equilibrium, and I suppose (without going into it in detail) the principle of microscopic reversibility must mean that the forward and reverse mechanisms are so related that equal rates result in the thermodynamic equilibrium condition. But I think it's quite dodgy to try to draw conclusions in the way the question asks you to.
The question says that "under certain conditions" the forward rate is kf
[A]. It doesn't specify what the conditions are, but it would seem most likely that they involve using a large excess of B, so that [B ] is effectively constant throughout the reaction. In this case, [B ] is effectively hidden in kf
- if the true rate law is kf
'[A][B ], then kf
'[B ]. If you did another set of experiments with a different excess concentration of B, you would get the same rate law kf
[A], but a different value of kf
. In this scenario, the reverse rate law would not
In short, it is dangerous to apply Keq
without a clear understanding of the circumstances to which your data apply. (For example, in the above scenario with excess B, we could write K' = [C]/[A], where K' is constant for a given value of [B ], but varies with [B ]. Now what is kf
equal to - K or K'?)
In other words, it's a badly posed question to which the only reasonable answer is "there isn't enough information".