[yotsuba]

Hey guys, hope you can help me out a bit... this is pretty much kind of a basic question  , I guess I just need some direction about what to read up about before I understand this.
Here goes....

In general, bonds between atoms form when orbitals overlap right? Or is that not right?

For example, in this kind of reaction:
A+B -> C
when you add energy to this reaction (by heating it up for example), the reaction may go faster because the atoms move more and collide more. More collisions means that the probability of orbitals overlapping increase so then the probability of bond formation increases too... right?

But then, what about this...
Let's say I have 100 atoms in a box. These atoms can form bonds (sigma bonds, e.g.) with each other.
In the beginning, I put my box in the fridge, so all the atoms are cold and move kind of slowly, so they don't collide that much with each other.
Then one day I take the box out and put it on my stove and heat it up.
Now the box heats up and the atoms heat up and they have more energy and collide more.
I think if I put the stove at Gas mark 4 (the highest), then the probability that bonds are going to form will increase because the atoms will collide more than if I put the stove at Gas mark 2.

But now I don't know how to quantify this. How do I tell someone else that the probability of (e.g.) 1 bond forming between 2 atoms from 100 atoms in the box is X% at Gas mark 4 and (X-Y)% at Gas mark 2?
Cos obviously when I'm calculating the probability of a bond forming, I will need to take into account the velocity of the moving atoms in the box. I will also need to take into account that even when 2 atoms collide that won't necessarily form a bond because the orbitals might not overlap (e.g. if the atoms have some sp orbitals... I guess if they have isotropic orbitals that might be easier...).

Hope you can point me in some direction. I feel kind of lost now (and also stupid =_= cos I guess I should have already learnt this in high school....)


Thanks! 

[Yggdrasil]

Your example is overly simplified because in most chemical reactions, we are not dealing with isolated atoms as these chemical species are very unstable.  In general, there are two steps in the formation of new chemical bonds: old bonds must be broken and new bonds must be formed.  For example, in the reaction H₂ + Cl₂ --> 2HCl, the H-H and Cl-Cl bonds must be broken for the H-Cl bonds to be formed.  Often times, bond breakage is coupled to bond formation (i.e. they occur simultaneously).

The requirement for bond breakage means that all reactions will have some activation energy.  That is, you need to put energy into the reaction to break the bonds even if forming the new bonds releases energy.  Because this activation energy is generally provided by thermal energy, temperature plays a large part in the rate of chemical reactions.

We can model the effect of activation energy on reaction rate using the Arrehnius equation:

$$ k = Ae^{\frac{-E_a}{k_BT}} /$$

That is to say, the rate constant (k) for a chemical reaction depends on the rate of collision (A), and the value of the activation energy (E_a) relative to the amount of thermal energy available (k_BT).  As the rate of collision increases, the rate of reaction will increase.  Also, if the activation energy is much larger than the thermal energy available, the reaction will proceed very slowly.  On the other hand, as the amount of thermal energy available increases (as temperature increases), the rate of reaction will increase (this will also affect the rate of collision, but the effect is much more pronounced on the exponential term). 

For gas phase reactions, we can apply collision theory to derive the rate of collision A (also known as the Arrehnius pre-exponential factor) from first principles (equation in the wikipedia article).

Note that you shouldn't feel bad for not knowing these equations very well.  The Arrhenius equation isn't usually covered until the second semester of freshman chemistry (and then it's covered only briefly).  You don't get into collision theory until advanced physical chemistry courses (e.g. statistical mechanics).