Define “reactivity”

Does reactivity of a compound depend on kinetic factors, thermodynamic factors, or both? i.e. how is reactivity defined? For example, out of a) 2-bromopropane and b) 4-bromobutan-2-one, which is more reactive to alcoholic KOH? Does the answer account for kinetic factors, or the fact that b) forms a conjugated ketone, and is hence more reactive?

Does reactivity of a compound depend on kinetic factors, thermodynamic factors, or both?

The reactivity of a compound depends on kinetic factors, but... The "but" arises because thermodynamic factors can be a part of the kinetic factors. Let me explain.

The following figure shows the conversion of a "Reactant" to a "Product". The product is more stable so the reaction is exothermic, heat is released. The rate of the reaction is determined by the height of the barrier (the activation energy, $E_{a}$) that a reactant molecule must pass over in order to become the product. The higher the barrier, the slower the reaction. Since the barrier height is contained in the kinetic equation describing the speed of a reaction (for example, the Arrhenius equation) we say that reactivity is determined by kinetics.

But now look at the reverse reaction. Suppose you had a bottle of "Product" and heated it to convert it to "Reactant". This reaction is endothermic, heat must be supplied. The free energy difference between product and reactant ($\Delta G^o)$ is a thermodynamic factor telling us whether the product or reactant is more stable. In the reverse reaction, the barrier that we must surmount is higher than it was for the forward reaction. The barrier for the back reaction is given as $E_{a} + \Delta G^o$.

So while the rate or reactivity depends on the barrier height which is a kinetic phenomenon, we can see how the free energy difference ($\Delta G^o$), a thermodynamic quantity, can be viewed as a factor influencing the barrier height.

out of a) 2-bromopropane and b) 4-bromobutan-2-one, which is more reactive to alcoholic KOH? Does the answer account for kinetic factors, or the fact that b) forms a conjugated ketone, and is hence more reactive?

1-bromobutane might make for a better comparison, in this case the bromine is attached to a terminal carbon as in 4-bromobutan-2-one, and both molecules contain 4 carbons - the only difference is that one is a ketone. In any case, the answer is based on kinetic factors. I don't know which one will react faster, but here's my thinking. They should have similar activation energies, but since the ketone reacts to produce a more stabilized conjugated $\alpha,\beta$-unsaturated ketone, the reaction of the bromo-ketone will be thermodynamically more exothermic than the bromo-alkane. This thermodynamic difference will reduce the height of the kinetic barrier for the bromo-ketone and make this reaction faster.

• Small nitpick to an otherwise very good answer: The depicted graph shows an exergonic reaction as it is based on $\Delta G$ It does not make any assumptions if the reaction occurring is also exotherm.|| Another note, the bigger $\Delta G^o$ is, the more energy is provided to following reactions, therefore fueling itself and speeding up the process. This is often the case for explosions. – Martin - マーチン Nov 25 '14 at 3:22