Since the reactants have to be in the same place at the same time, we could double the density of one of them and make that twice as likely to happen. We could double both of them and make it four times as likely to happen. In other words, the rate with which reactants meet successfully to become products in molecular collisions can be directly proportional to the concentrations (number density) of the reactants.
But we can do even better than that.
It is often the case that unless there is a minimum level of violence to the encounter, reactants can't jostle one another enough to change partners, for example. This molecular violence often comes from the energies with which reactants are thrown together by the vagaries of thermal collisions.
The Boltzmann Distribution of molecular translational energies to which we alluded in class falls off rather sharply at the higher collisional energies; so few collisions are likely, by chance, to have the requisite punch to react. But as we also showed, doubling the temperature doubles the average collisional energy by broadening the Boltzman Distribution out. While that makes factors of two-like differences at energies near the mean, those energies requisite for reaction characteristically lie far above the mean...and there the difference in probabilities becomes staggeringly high!
In fact (trust me on this), the likelihood of any given collision exceeding some energy E, where E is very much larger than RT, the mean energy (yes, it's the same R), is e-E/RT.
Suppose, for example, that at room temperature, E/RT is 20 (a representative figure, actually). That means that only 1 collision in exp(20)=485,000,000 would be effective (if properly oriented, of course). But if we double the temperature, now E/RT is only 10, which means that one collision in exp(10)=22,026 is effective, an increase in the reaction rate not by 2 but rather by a factor of 22,026! There's a huge (indeed exponential) advantage to warming things up, and chemical reaction rates are quite sensitive to temperature.
Putting both concentration and energy dependence together, the expectation is that the relative success of some reaction
kf
A + B 
C + D (name your poisons)
will vary with the concentration of reactants, [A] and [B], askf[A][B]
where kf depends on e-E/RT and represents a (temperature scaled) constant of proportionality for the concentration effects on the reaction rate.
Now we used a subscript "f" for forward to discriminate this chemistry from its antichemistry, i.e., the reverse reaction which undoes this one, namely
kr
C + D A + B (reverse your poison's name)
which you'd expect to depend upon the concentrations [C] and [D] for getting these guys together to unreact, as it were. Indeed, that reverse reaction rate would bekr [C] [D] where kr depends on e-E'/RT
and E' is how hard you have to shove the products together to get back the reactants.
What's all this do for us? At any given temperature, those k's are fixed. At the start of the reaction, there aren't any products! So there can't be an reverse reaction. BUT as A and B do their thing and begin to disappear and C and D become more plentiful, the chances of unreacting must eventually become as good as the chances of reacting! When that happens, to a macroscopic (large scale) observer like us, it appears that the reaction is over, but a microscopic observer would see both reactions are still going on...forever but at equal rates so the gross concentrations of all molecules no longer varies.
We can say the reaction is over, but it has just arrived at a "dynamic equilibrium". How much of what is still around then depends on the relative magnitudes of those k constants.
Since at (dynamic) equilibrium, kf[A] [B] = kr[C] [D], if kf >> kr, there must be lots more [C] [D] than [A] [B] to compensate.In other words, in that event, the reaction is virtually complete, or as chemists would say, "quantitative."
This notion of "dynamic equilibrium" will turn out to be a critical one; it will tell us, for example, how fiddling with products can help or hurt. Suppose, for example, we could selectively remove D as it's being formed. Then the reverse reaction (still dependent upon C finding D) would no longer take place! And that dynamic equilibrium would lie even further on the products side of the ledger. This would be the case for an aqueous phase (in water) reaction which produced a gaseous or solid product. The gas would bubble out or the solid would "precipitate" down; in either case, it would be GONE from the aqueous phase and impel the reaction forward!
One of the kinds of reactions we'll study is the precipitation reaction. The foregoing suggests why they are so effective.
There are broad categories of chemical reactions which describe what is happening with them. So synthesis reaction build larger molecules from their smaller constituent parts while decomposition reactions to the reverse.
But the more useful categorizations are the ones which help us understand why the chemistry is taking place. Precipitation is such a category; it's effective because it removes products from the reacting mixture. Oxidation/Reduction (called redox) reactions succeed because some molecules are more eager for electrons than others and impel a transfer of those electrons. The same is true of Acid Base reactions, except here it will be a hunger for protons rather than electrons which impels the chemistry.